Heat transfer is a basic science that deals with the rate of transfer of thermal energy. 
The science of thermodynamics deals with the amount of heat transfer as a system undergoes a process from one equilibrium state to another, and makes no reference to how long the process will take. 

There are three basic mechanisms of heat transfer, which are conduction, convection, and radiation.
Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent, less energetic ones as a result of interactions between the particles. Convection is the mode of heat transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion.Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules. 

The energy transfer is always from the higher temperature medium to the lower temperature one, and the energy transfer stops when the two mediums reach the same temperature. 
Heat is the form of energy that can be transferred from one system to another as a result of temperature difference.

Thermodynamics deals with equilibrium states and changes from one equilibrium state to another. Heat transfer, on the other hand, deals with systems that lack thermal equilibrium, and thus it is a nonequilibrium phenomenon. 

The basic requirement for heat transfer is the presence of a temperature difference. There can be no net heat transfer between two mediums that are at the same temperature. The temperature difference is the driving force for heat transfer.

The rate of heat transfer in a certain direction depends on the magnitude of the temperature gradient (the temperature difference per unit length or the rate of change of temperature) in that direction. The larger the temperature gradient, the higher the rate of heat transfer. 

The portion of the internal energy of a system associated with the kinetic energy of the molecules is called sensible energy or sensible heat. 

The internal energy is also associated with the intermolecular forces be- tween the molecules of a system. These are the forces that bind the molecules to each other, and, as one would expect, they are strongest in solids and weakest in gases. If sufficient energy is added to the molecules of a solid or liquid, they will overcome these molecular forces and simply break away, turning the system to a gas. This is a phase change process and because of this added energy, a system in the gas phase is at a higher internal energy level than it is in the solid or the liquid phase. The internal energy associated with the phase of a system is called latent energy or latent heat.

Energy Transfer
Energy can be transferred to or from a given mass by two mechanisms: heat Q and work W. An energy interaction is heat transfer if its driving force is a temperature difference. Otherwise, it is work. A rising piston, a rotating shaft, and an electrical wire crossing the system boundaries are all associated with work interactions. 
The rate of heat transfer per unit area normal to the direction of heat transfer is called heat flux, and the average heat flux is expressed as 

Heat Transfer Mechanism
The science that deals with the determination of the rates of such energy transfers is the heat transfer. The transfer of energy as heat is always from the higher-temperature medium to the lower-temperature one, and heat transfer stops when the two mediums reach the same temperature. 
Heat can be transferred in three different modes: conduction, convection, and radiation. All modes of heat transfer require the existence of a temperature difference, and all modes are from the high-temperature medium to a lower-temperature one. 

Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions be- tween the particles. Conduction can take place in solids, liquids, or gases. In gases and liquids, conduction is due to the collisionsand diffusion of the molecules during their random motion. In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons. 

The rate of heat conduction through a medium depends on the geometry of the medium, its thickness,and the material of the medium, as well as the temperature difference across the medium. 

Thermal conductivity 
It is a measure of the ability of a material to conduct heat. The thermal conductivity of a material can be defined as the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity of a material is a measure of the ability of the material to conduct heat. A high value for thermal conductivity indicates that the material is a good heat conductor, and a low value indicates that the material is a poor heat conductor or insulator. 

The kinetic theory of gases predicts and the experiments confirm that the thermal conductivity of gases is proportional to the square root of the absolute temperature T, and inversely proportional to the square root of the molar mass M. Therefore, the thermal conductivity of a gas increases with increasing temperature and decreasing molar mass. The thermal conductivity of gases is independent of pressure. The mechanism of heat conduction in a liquid is complicated by the fact that the molecules are more closely spaced, and they exert a stronger intermolecular force field. The thermal conductivity of a substance is normally highest in the solid phase and lowest in the gas phase. 

Unlike gases, the thermal conductivities of most liquids decrease with increasing temperature, with water being a notable exception. Like gases, the conductivity of liquids decreases with increasing molar mass. Liquid metals such as mercury and sodium have high thermal conductivities and are very suitable for use in applications where a high heat transfer rate to a liquid is desired, as in nuclear power plants. 
In solids, heat conduction is due to two effects: the lattice vibrational waves induced by the vibrational motions of the molecules positioned at relatively fixed positions in a periodic manner called a lattice, and the energy trans- ported via the free flow of electrons in the solid.

The relatively high thermal conductivities of pure metals are primarily due to the electronic component. The lattice component of thermal conductivity strongly depends on the way the molecules are arranged. For example, diamond, which is a highly ordered crystalline solid, has the highest known thermal conductivity at room temperature. 

The thermal conductivity of an alloy of two metals is usually much lower than that of either metal. 
Temperatureis a measure of the kinetic energies of the particles such as the molecules or atoms of a substance. In a liquid or gas, the kinetic energy of the molecules is due to their random translational motion as well as their vibrational and rotational motions. The higher the temperature, the faster the molecules move and the higher the number of such collisions, and the better the heat transfer. 

Fourier’s law of heat conduction 
The relation above indicates that the rate of heat conduction in a direction is proportional to the temperature gradient in that direction. Heat is conducted in the direction of decreasing temperature, and the temperature gradient becomes negative when temperature decreases with increasing x. The negative sign ensures that heat transfer in the positive direction is a positive quantity. The heat transfer area is always normal to the direction of heat transfer. 

Thermal Diffusivity 
The thermal diffusivityrepresents how fast heat diffuses through a material and is defined as 
Therefore, the thermal diffusivity of a material can be viewed as the ratio of the heat conducted through the material to the heat stored per unit volume. 
A material that has a high thermal conductivity or a low heat capacity will obviously have a large thermal diffusivity. The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat will be conducted further. 

Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion. The faster the fluid motion, the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid is by pure conduction. The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid, but it also complicates the determination of heat transfer rates. 

Convection is called forced convection if the fluid is forced to flow over the surface by external means such as a fan, pump, or the wind. In contrast, convection is called natural(or freeconvection if the fluid motion is caused by buoyancy forces that are induced by density differences due to the variation of temperature in the fluid.

Despite the complexity of convection, the rate of convection heat transfer is observed to be proportional to the temperature difference, and is conveniently expressed by Newton’s law of cooling as                                               

where h is the convection heat transfer coefficient,Ais the surface area through which convection heat transfer takes place, Tis the surface temperature, and  is the temperature of the fluid sufficiently far from the surface. 
The convection heat transfer coefficient is not a property of the fluid. It is an experimentally determined parameter whose value depends on all the variables influencing convection such as the surface geometry, the nature of fluid motion, the properties of the fluid, and the bulk fluid velocity. 

Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules. Unlike conduction and convection, the transfer of energy by radiation does not require the presence of an intervening medium. 
In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. 
Radiation is a volumetric phenomenon, and all solids, liquids, and gases emit, absorb, or transmit radiation to varying degrees. However, radiation is usually considered to be a surface phenomenon for solids that are opaque to thermal radiation such as metals, wood, and rocks since the radiation emitted by the interior regions of such material can never reach the surface, and the radiation incident on such bodies is usually absorbed within a few microns from the surface. 

Stefan–Boltzmann law 

The idealized surface that emits radiation at this maximum rate is called a blackbody, and the radiation emitted by a black- body is called blackbody radiation 
The property emissivity, whose value is in the range , is a measure of how closely a surface approximates a blackbody for which 

Another important radiation property of a surface is its absorptivity , which is the fraction of the radiation energy incident on a surface that is absorbed by the surface. Like emissivity, its value is in the range 
A blackbody absorbs the entire radiation incident on it. That is, a blackbody is a perfect absorber () as it is a perfect emitter. 

In general, both  and  of a surface depend on the temperature and the wavelength of the radiation. Kirchhoff’s law of radiation states that the emissivity and the absorptivity of a surface at a given temperature and wavelength are equal. 

The net rate of radiation heat transfer between these two surfaces is given by 

During transient heat transfer, the temperature normally varies with time as well as position. In the special case of variation with time but not with position, the temperature of the medium changes uniformly with time. Such heat transfer systems are called lumped systems.

Heat Generation
A medium through which heat is conducted may involve the conversion of electrical, nuclear, or chemical energy into heat (or thermal) energy. In heat conduction analysis, such conversion processes are characterized as heat generation.
Note that heat generation is a volumetric phenomenon. That is, it occurs throughout the body of a medium. Therefore, the rate of heat generation in a medium is usually specifiedper unit volume and is denoted by g·.

Heat Conduction Equation in a Large Plane Wall 
Variable conductivity: 

Constant conductivity: 

Heat Conduction Equation in a Long Cylinder 
Variable conductivity: 
Constant conductivity: 

Heat Conduction Equation in a Sphere 
Variable conductivity: 
Constant conductivity: 

Combined One-Dimensional Heat Conduction Equation 
where 0 for a plane wall, 1 for a cylinder, and 2 for a sphere. In the case of a plane wall, it is customary to replace the variable by x. 

Boundary Conditions

Many practical heat transfer applications involve the conversion of some form of energy into thermal energy in the medium. Such mediums are said to involve internal heat generation, which manifests itself as a rise in temperature throughout the medium.
Flat slab
Note that the rise in surface temperature Tis due to heat generation in the solid.
Again the heat generated within this inner cylinder must be equal to the heat conducted through the outer surface of this inner cylinder. That is, from Fourier’s law of heat conduction, 
When the variation of thermal conductivity with temperature k(T) is known, the average value of the thermal conductivity in the temperature range be- tween Tand Tcan be determined from 
This relation is based on the requirement that the rate of heat transfer through 
a medium with constant average thermal conductivity kave equals the rate of heat transfer through the same medium with variable conductivity k(T). 
The variation in thermal conductivity of a material with temperature in the temperature range of interest can often be approximated as a linear function and expressed as 
where Beta is called the temperature coefficient of thermal conductivity. The average value of thermal conductivity in the temperature range Tto Tin this case can be determined from 

Note that the average thermal conductivity in this case is equal to the thermal conductivity value at theaverage temperature. 

The Thermal Resistance Concept 
Flat plate


Note that when the convection heat transfer coefficient is very large (), the convection resistance becomes zero and T=T. That is, the surface offers no resistance to convection, and thus it does not slow down the heat transfer process. This situation is approached in practice at surfaces where boiling and condensation occur.

When the wall is surrounded by a gas, the radiation effects, which we have ignored so far, can be significant and may need to be considered. The rate of radiation heat transfer between a surface of emissivity 􏰌and area Aat temperature Tand the surrounding surfaces at some average temperature Tsurr can be expressed as 
is the thermal resistance of a surface against radiation, or the radiation resistance, and  
is the radiation heat transfer coefficient. 
A surface exposed to the surrounding air involves convection and radiation simultaneously, and the total heat transfer at the surface is determined by adding (or subtracting, if in the opposite direction) the radiation and convection components. 
where hcombined is the combined heat transfer coefficient. This way all the complications associated with radiation are avoided. 

Thermal Resistance Network 

Multilayer Plane Walls 

Multilayered Cylinders and Spheres 

Adding insulation to a cylindrical pipe or a spherical shell, however, is a different matter. The additional insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface because of the increase in the outer surface area for convection. The heat transfer from the pipe may increase or decrease, depending on which effect dominates. 
For Cylinder
For Sphere

We start with the analysis of lumped systems in which the temperature of a solid varies with time but remains uniform throughout the solid at any time. Then we consider the variation of temperature with time as well as position for one-dimensional heat conduction problems such as those associated with a large plane wall, a long cylinder, a sphere, and a semi-infinite medium using transient temperature charts and analytical solutions. 



Criteria for Lumped Systems

1.Heat transfer coefficient of surrounding fluid should be small
2.Material which have high value of thermal conductivity
Where,             ,         
For Flat plate,                
For cylinder,                  
For sphere,                    

When a solid body is being heated by the hotter fluid surrounding it (such as a potato being baked in an oven), heat is first convected to the body and subsequently conducted within the body. The Biot number is the ratio of the internal resistance of a body to heat conduction to its external resistance to heat convection. Therefore, a small Biot number represents small resistance to heat conduction, and thus small temperature gradients within the body. 

Lumped system analysis assumes a uniformtemperature distribution throughout the body, which will be the case only when the thermal resistance of the body to heat conduction (the conduction resistance) is zero. 

Conduction and convection are similar in that both mechanisms require the presence of a material medium. But they are different in that convection requires the presence of fluid motion. 
Heat transfer through a solid is always by conduction, since the molecules of a solid remain at relatively fixed positions. Heat transfer through a liquid or gas, however, can be by conduction or convection, depending on the presence of any bulk fluid motion. 
The fluid motion enhances heat transfer, since it brings hotter and cooler chunks of fluid into contact, initiating higher rates of conduction at a greater number of sites in a fluid. Therefore, the rate of heat transfer through a fluid is much higher by convection than it is by conduction. In fact, the higher the fluid velocity, the higher the rate of heat transfer. 
Experience shows that convection heat transfer strongly depends on the fluid properties dynamic viscosity neuthermal conductivity k, density rho, and specific heat Cp, as well as the fluid velocity v. It also depends on the geome try and the roughnessof the solid surface, in addition to the type of fluid flow (such as being streamlined or turbulent). 

The no-slip condition is responsible for the development of the velocity pro- file for flow. Because of the friction between the fluid layers, the layer that sticks to the wall slows the adjacent fluid layer, which slows the next layer, and so on. A consequence of the no-slip condition is that all velocity profiles must have zero values at the points of contact between a fluid and a solid. The only exception to the no-slip condition occurs in extremely rarified gases. 

A similar phenomenon occurs for the temperature. When two bodies at different temperatures are brought into contact, heat transfer occurs until both bodies assume the same temperature at the point of contact. Therefore, a fluid and a solid surface will have the same temperature at the point of contact. This is known as no-temperature-jump condition. 

An implication of the no-slip and the no-temperature jump conditions is that heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction, since the fluid layer is motionless, and can be expressed as 
Note that convection heat transfer from a solid surface to a fluid is merely the conduction heat transfer from the solid surface to the fluid layer adjacent to the surface. Therefore, 
The convection heat transfer coefficient, in general, varies along the flow (or x-) direction. The averageor mean convection heat transfer coefficient for a surface in such cases is determined by properly averaging the local convection heat transfer coefficients over the entire surface. 

Nusselt Number 
It is also common practice to nondimensionalize the heat transfer coefficient with the Nusselt number, defined as 
where is the thermal conductivity of the fluid and Lis the characteristic length. 
which is the Nusselt number. Therefore, the Nusselt number represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. The larger the Nusselt number, the more effective the convection. A Nusselt number of Nu =1 for a fluid layer represents heat transfer across the layer by pure conduction. 

Convection heat transfer is closely tied with fluid mechanics, which is the science that deals with the behaviour of fluids at rest or in motion, and the inter- action of fluids with solids or other fluids at the boundaries. 

Viscous versus Inviscid Flow 
When two fluid layers move relative to each other, a friction force develops between them and the slower layer tries to slow down the faster layer. This internal resistance to flow is called the viscosity,which is a measure of internal stickiness of the fluid. Viscosity is caused by cohesive forces between the molecules in liquids, and by the molecular collisions in gases. There is no fluid with zero viscosity, and thus all fluid flows involve viscous effects to some degree. Flows in which the effects of viscosity are significant are called viscous flows. The effects of viscosity are very small in some flows, and neglecting those effects greatly simplifies the analysis without much loss in ac- curacy. Such idealized flows of zero-viscosity fluids are called frictionless or inviscid flows. 

Compressible versus Incompressible Flow 
The condition of flow is to be compressible or incompressible depends upon fact that whether the change in density/volume is appreciable due to change in pressure brought by the flow.
Change in volume is less than or equal to 5% is incompressible flow. Change in volume is more than 5% due to pressure brought by flow is compressible flow.
Generally, in all engineering application, for the flow of liquid change in volume/density is quite small because change in pressure brought by the flow, hence the flow of liquid can be considered as incompressible flow.
But for gases, it is not sure. Change in volume/density may be significant or insignificant depending upon magnitude of pressure change brought by flow.

For incompressible flow,

Where Ma is mac number and it is defined as ratio of velocity of fluid to velocity of sound in same fluid.

Laminar versus Turbulent Flow 
Some flows are smooth and orderly while others are rather chaotic. The highly ordered fluid motion characterized by smooth streamlines is called laminar. The flow of high-viscosity fluids such as oils at low velocities is typically laminar. The highly disordered fluid motion that typically occurs at high velocities characterized by velocity fluctuations is called turbulent. The flow of low-viscosity fluids such as air at high velocities is typically turbulent. The flow regime greatly influences the heat transfer rates and the required power for pumping. 

Natural (or Unforced) versus Forced Flow 
A fluid flow is said to be natural or forced, depending on how the fluid motion is initiated. In forced flow, a fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan. In natural flows, any fluid motion is due to a natural means such as the buoyancy effect, which manifests itself as the rise of the warmer (and thus lighter) fluid and the fall of cooler (and thus denser) fluid.

Steady versus Unsteady (Transient) Flow 
The term steady implies no change with time. The opposite of steady is unsteady, or transient.The term uniform, however, implies no change with location over a specified region. 
Many devices such as turbines, compressors, boilers, condensers, and heat exchangers operate for long periods of time under the same conditions, and they are classified as steady-flow devices. During steady flow, the fluid properties can change from point to point within a device, but at any fixed point they remain constant. 

The region of the flow above the plate bounded by  in which the effects of the viscous shearing forces caused by fluid viscosity are felt is called the velocity boundary layer. The boundary layer thickness, , is typically de- fined as the distance from the surface at which u=0.99u
The hypothetical line of 0.99u divides the flow over a plate into two regions: the boundary layer region, in which the viscous effects and the velocity changes are significant, and the inviscid flow region, in which the frictional effects are negligible and the velocity remains essentially constant. 
The region of the flow in which the effects of the viscous shearing forces caused by fluid viscosity are felt is called boundary region and that thickness is called boundary layer.
          for Laminar Flow,  
        for Turbulent flow, 

Viscous Stress:The net force acting between the two layer of the fluid particle per unit area.

Boundary Layer Separation
It has been observed that how is reversed at the vicinity of the wall under certain conditions, the phenomenon is taken as BLS. Separation takes place due to excessive momentum lose.
·        , decelerating flow

Hydrodynamic entrance length
The region from the inlet of the pipe to the point at which boundary layer merges at the centerline is called hydrodynamic entrance region and length of this region is called hydrodynamic entrance length.
For Laminar,         where, D is pipe diameter
For Turbulent,             Re is Reynolds number

Thickness over which the temperature of the fluid reaches 99% of upstream temperature.
In the immediate layer of the surface the heat is transferred by the basic mechanism of heat transfer called conduction. Transport of the heat in other layer is by conduction with advection and combined form is called convection.
Since in upper layer, the fluid has some velocity, hence the energy will advected by the motion of the fluid and to makeup this energy, the more and more energy has to be supplied from the wall to fluid and hence the rate of heat transfer get increases.


  for Laminar Flow,  
 for Turbulent flow, 

If          Pr = 1 ⇒ δ =δt

If          Pr < 1 ⇒ δ <δt
If          Pr > 1 ⇒ δ >δt

Prandtl Number 
The relative thickness of the velocity and the thermal boundary layers is best described by the dimensionless parameterPrandtl number, defined as 
Liquid metals such as mercury have high thermal conductivities, and are commonly used in applications that require high heat transfer rates. However, they have very small Prandtl numbers, and thus the thermal boundary layer develops much faster than the velocity boundary layer. 

The flow regime in the first case is said to be laminar, characterized by smooth streamlines and highly-ordered motion, and turbulent in the second case, where it is characterized by velocity fluctuations and highly-disordered motion. The transitionfrom laminar to turbulent flow does not occur suddenly; rather, it occurs over some region in which the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent. 

The very thin layer next to the wall where the viscous effects are dominant is the laminar sublayer. The velocity profile in this layer is nearly linear, and the flow is streamlined. Next to the laminar sublayer is the buffer layer, in which the turbulent effects are significant but not dominant of the diffusion effects, and next to it is the turbulent layer, in which the turbulent effects dominate. 

The intense mixing of the fluid in turbulent flow as a result of rapid fluctuations enhances heat and momentum transfer between fluid particles, which increases the friction force on the surface and the convection heat transfer rate. It also causes the boundary layer to enlarge. Both the friction and heat transfer coefficients reach maximum values when the flow becomes fully turbulent. 

Reynolds Number 
Reynolds discovered that the flow regime depends mainly on the ratio of the inertia forces to viscous forces in the fluid. This ratio is called the Reynolds number, which is a dimensionless quantity, and is expressed for external flow as 
At large Reynolds numbers, the inertia forces, which are proportional to the density and the velocity of the fluid, are large relative to the viscous forces, and thus the viscous forces cannot prevent the random and rapid fluctuations of the fluid. At small Reynolds numbers, however, the viscous forces are large enough to overcome the inertia forces and to keep the fluid “in line.” Thus the flow is turbulent in the first case and laminar in the second. 

The Reynolds number at which the flow becomes turbulent is called the critical Reynolds number. The value of the critical Reynolds number is different for different geometries. 

Reynolds Analogy
In the development of the boundary layer theory, one may notice the strong relationship between the dynamic boundary layer and the thermal boundary layer. Reynold’s noted the strong correlation and found that fluid friction and convection coefficient could be related. This is known as the Reynolds Analogy. 

Conclusion from Reynold’s analogy 
Knowing the frictional drag, we know the Nusselt Number. If the drag coefficient is increased, say through increased wall roughness, then the convective coefficient will also increase. 
It is applicable if

Chilton Colburn analogy

The drag force is the net force exerted by a fluid on a body in the direction of flow due to the combined effects of wall shear and pressure forces. The part of drag that is due directly to wall shear stress 􏰭is called the skin friction drag (or just friction drag) since it is caused by frictional effects, and the part that is due directly to pressure is called the pressure drag (also called the form drag because of its strong dependence on the form or shape of the body). When the friction and pressure drag coefficients are available, the total drag coefficient is determined by simply adding them, 
CCD, friction CD, pressure 

The friction drag is the component of the wall shear force in the direction of flow, and thus it depends on the orientation of the body as well as the magnitude of the wall shear stress . The friction drag is zero for a surface normal to flow, and maximum for a surface parallel to flow since the friction drag in this case equals the total shear force on the surface. 
Flat plate:                                  C=CD, friction Cf

At low Reynolds numbers, most drag is due to friction drag. This is especially the case for highly streamlined bodies such as airfoils. The friction drag is also proportional to the surface area. Therefore, bodies with a larger surface area will experience a larger friction drag. 

The pressure drag is proportional to the difference between the pressures acting on the front and back of the immersed body, and the frontal area. Therefore, the pressure drag is usually dominant for blunt bodies, negligible for streamlined bodies such as airfoils, and zero for thin flat plates parallel to the flow. 

Forced Convection
The experimental data for heat transfer is often represented conveniently with reasonable accuracy by a simple power-law relation of the form 
Nu=Re LPr 
where and are constant exponents, and the value of the constant depends on geometry and flow. 

The transition from laminar to turbulent flow depends on the surface geometry, surface roughness, upstream velocity, surface temperature, and the type of fluid, among other things, and is best characterized by the Reynolds number. 

For Laminar
For turbulent

For Laminar Flow,
For Turbulent Flow,
Average heat transfer coefficient for Laminar flow
Average heat transfer coefficient for Turbulent flow

Effect of Surface Roughness 
We mentioned earlier that surface roughness, in general, increases the drag coefficient in turbulent flow. This is especially the case for streamlined bodies. For blunt bodies such as a circular cylinder or sphere, however, an increase in the surface roughness may actually decrease the drag coefficient. This is done by tripping the flow into turbulence at a lower Reynolds number, and thus causing the fluid to close in behind the body, narrowing the wake and reducing pressure drag considerably. This results in a much smaller drag coefficient and thus drag force for a rough- surfaced cylinder or sphere in a certain range of Reynolds number compared to a smooth one of identical size at the same velocity. 

The value of the mean velocity Vin a tube is determined from the requirement that the conservation of mass principle 
Therefore, when we know the mass flow rate or the velocity profile, the mean velocity can be determined easily. 
The value of the mean temperature Tis determined from the requirement that the conservation of energy principle be satisfied. 
Note that the mean temperature Tof a fluid changes during heating or cooling. Also, the fluid properties in internal flow are usually evaluated at the bulk mean fluid temperature, which is the arithmetic average of the mean temperatures at the inlet and the exit. That is, T(Tm, i +Tm, e)/2.

Laminar and Turbulent Flow In Tubes 
For fully developed turbulent flow through a circular smooth pipe

The length from the entrance up to which both boundary layer merges is called hydrodynamic entry length.
The region of hydrodynamic entrance length is called hydrodynamic developing region and any region beyond the hydrodynamic entrance length is called hydrodynamic fully developed region.

The region of flow over which the thermal boundary layer develops and reaches the tube centre is called the thermal entrance region, and the length of this region is called the thermal entry length LtFlow in the thermal entrance region is called thermally developing flow since this is the region where the temperature profile develops. The region beyond the thermal entrance region in which the dimensionless temperature profile expressed as (T-T)/ (T-Tm) remains unchanged is called the thermally fully developed region. The region in which the flow is both hydrodynamically and thermally developed and thus both the velocity and dimensionless temperature profiles remain unchanged is called fully developed flow. 


In the hydrodynamic developed region
In the hydrodynamic developing region

Entry Lengths 
The hydrodynamic entry length is usually taken to be the distance from the tube entrance where the friction coefficient reaches within about 2 percent of the fully developed value. 
Lh, laminar 0.05 Re D
t, laminar 0.05 Re Pr Pr Lh, laminar 
Lh, turbulent Lt, turbulent 10
·     The Nusselt numbers and thus the convection heat transfer coefficients are much higher in the entrance region. 
·     The Nusselt number reaches a constant value at a distance of less than 10 diameters, and thus the flow can be assumed to be fully developed for 10D. 
·     The Nusselt numbers for the uniform surface temperature and uniform surface heat flux conditions are identical in the fully developed regions, and nearly identical in the entrance regions. Therefore, Nusselt number is insensitive to the type of thermal boundary condition, and the turbulent flow correlations can be used for either type of boundary condition. 

The thermal conditions at the surface can usually be approximated with reasonable accuracy to be constant surface temperature (Tconstant) or constant surface heat flux (q·=constant). 
  1. Constant wall/surface temperature
  2. Constant wall heat flux
The constant surface temperature can be maintained by condensation or vaporization over surface of tube/pipe.
The constant wall heat flux can be maintained by wrapping the wire resistance heater.

Constant wall heat flux
(since flow is fully developed)

Constant surface/wall temperature
In case of turbulent flow, the method of heating does not play important role but in the case of laminar flow, the method plays important role. That’s why all above analysis we have done only for fully developed laminar flow.

For fully developed laminar flow in a pipe for constant heat flux, the Nusselt number is constant and equal to 4.36 but for constant wall temperature Nusselt number is 3.66.
In case of developing region of laminar flow, the Nusselt number is not constant.

We mentioned earlier that flow in tubes is laminar for Re<2300, and that the flow is fully developed if the tube is sufficiently long (relative to the entry length) so that the entrance effects are negligible.
The velocity profile v(r) is obtained by applying the boundary conditions dV/d=0 at 0 (because of symmetry about the centreline) and V=0 at r=R (the no-slip condition at the tube surface). We get 

This is a convenient form for the velocity profile since Vcan be determined easily from the flow rate information. 
Vmax 2V
Therefore, the mean velocity is one-half of the maximum velocity. 

Pressure Drop 
A quantity of interest in the analysis of tube flow is the pressure drop 􏰇since it is directly related to the power requirements of the fan or pump to maintain flow. We note that dP/dx=constant, and integrate it from x=0 where the pressure is Pto where the pressure is P2. We get 
This equation shows that in laminar flow, the friction factor is a function of the Reynolds number only and is independent of the roughness of the tube surface. Once the pressure drop is available, the required pumping power is determined from 

Temperature Profile and the Nusselt Number 
which states that the rate of net energy transfer to the control volume by mass flow is equal to the net rate of heat conduction in the radial direction. 

The Nusselt number in turbulent flow is related to the friction factor through the Chilton–Colburn analogy expressed as
Nu 0.125 RePr1/3 
Once the friction factor is available, this equation can be used conveniently to evaluate the Nusselt number for both smooth and rough tubes. 
For fully developed turbulent flow in smooth tubes, a simple relation for the Nusselt number can be obtained by substituting the simple power law relation 0.184 Re-0.2 for the friction factor into above equation
which is known as the Colburn equation. The accuracy of this equation can be improved by modifying it as 

The Nusselt number relations above are fairly simple, but they may give errors as large as 25 percent. This error can be reduced considerably to less than 10 percent by using more complex but accurate relations such as the second Petukhov equation.

The relations given so far do not apply to liquid metals because of their very low Prandtl numbers. For liquid metals (0.004 <Pr <0.01), the following relations are recommended by Sleicher and Rouse for 10<Re 106
Liquid metals, T constant: Nu 4.8 0.0156 Re0.85 Pr0.93 
Liquid metals, q· constant: Nu 6.3 0.0167 Re0.85 Pr0.93 

Rough Surfaces 
Any irregularity or roughness on the surface disturbs the laminar sublayer, and affects the flow. Therefore, unlike laminar flow, the friction factor and the convection coefficient in turbulent flow are strong functions of surface roughness. 
Colebrook equation 

Heat Transfer Enhancement 
Tubes with rough surfaces have much higher heat transfer coefficients than tubes with smooth surfaces. Therefore, tube surfaces are often intention- ally roughened, corrugated, or finnedin order to enhance the convection heat transfer coefficient and thus the convection heat transfer rate.

Natural convection in gases is usually accompanied by radiation of comparable magnitude except for low-emissivity surfaces. 

We know that a hot boiled egg (or a hot baked potato) on a plate eventually cools to the surrounding air temperature. The egg is cooled by transferring heat by convection to the air and by radiation to the surrounding surfaces. 

As soon as the hot egg is exposed to cooler air, the temperature of the outer surface of the egg shell will drop somewhat, and the temperature of the air adjacent to the shell will rise as a result of heat conduction from the shell to the air. Consequently, the egg will soon be surrounded by a thin layer of warmer air, and heat will then be transferred from this warmer layer to the outer layers of air. The cooling process in this case would be rather slow since the egg would always be blanketed by warm air, and it would have no direct contact with the cooler air farther away. 

The temperature of the air adjacent to the egg is higher, and thus its density is lower, since at constant pressure the density of a gas is inversely proportional to its temperature. Thus, we have a situation in which some low-density or “light” gas is surrounded by a high-density or “heavy” gas, and the natural laws dictate that the light gas rise. The space vacated by the warmer air in the vicinity of the egg is replaced by the cooler air nearby, and the presence of cooler air in the vicinity of the egg speeds up the cooling process. The rise of warmer air and the flow of cooler air into its place continues until the egg is cooled to the temperature of the surrounding air. The motion that results from the continual replacement of the heated air in the vicinity of the egg by the cooler air nearby is called a natural convection current, and the heat transfer that is enhanced as a result of this natural convection current is called natural convection heat transfer. 
In a gravitational field, there is a net force that pushes upward a light fluid placed in a heavier fluid. The upward force exerted by a fluid on a body completely or partially immersed in it is called the buoyancy force. The magnitude of the buoyancy force is equal to the weight of the fluid displaced by the body. That is, 
Fbuoyancy = rhofluid gVbody 
In heat transfer studies, the primary variable is temperature, and it is desirable to express the net buoyancy force in terms of temperature differences. But this requires expressing the density difference in terms of a temperature difference, which requires a knowledge of a property that represents the variation of the density of a fluid with temperature at constant pressure. 
The property that provides that information is the volume expansion coefficient , defined as 
The magnitude of the natural convection heat transfer between a surface and a fluid is directly related to the flow rate of the fluid. The higher the flow rate, the higher the heat transfer rate. In fact, it is the very high flow rates that in- crease the heat transfer coefficient by orders of magnitude when forced convection is used. 

The flow regime in natural convection is governed by the dimensionless Grashof number, which represents the ratio of the buoyancy force to the viscous force acting on the fluid.
The role played by the Reynolds number in forced convection is played by the Grashof number in natural convection. As such, the Grashof number provides the main criterion in determining whether the fluid flow is laminar or turbulent in natural convection. For vertical plates, for example, the critical Grashof number is observed to be about 109. Therefore, the flow regime on a vertical plate becomes turbulent at Grashof numbers greater than 109

TheroleofGrashofnumberinthefreeconvectionissimilartothatofrole ofReynold number in the forcedconvection.
Grashof number is measure of relative importance of buoyancy force to viscous force.
If              it means the heat transfer by natural convection is dominating than                                forced convection.
              it means the heat transfer by forced convection is dominating than                               natural convection.
          it means the heat transfer by natural convection and forced
                          convection both dominating.

For Laminar Flow,

For Turbulent flow.

Rayleigh number, which is the product of the Grashof and Prandtl numbers: 

The presence of a temperature gradient in a fluid in a gravity field always gives rise to natural convection currents, and thus heat transfer by natural convection. Therefore, forced convection is always accompanied by natural convection. 
Natural convection can enhance orinhibit heat transfer, depending on the relative directions of buoyancy-induced motion and the forced convection motion. 
·       In assisting flow, the buoyant motion is in the same direction as the forced motion. Therefore, natural convection assists forced convection and enhances heat transfer. An example is upward forced flow over a hot surface. 
·       In opposing flow, the buoyant motion is in the opposite direction to the forced motion. Therefore, natural convection resists forced convection and decreases heat transfer. An example is upward forced flow over a cold surface. 
·       In transverse flow, the buoyant motion is perpendicular to the forced motion. Transverse flow enhances fluid mixing and thus enhances heat transfer. An example is horizontal forced flow over a hot or cold cylinder or sphere. 
where Nuforced and Nunatural are determined from the correlations for pure forced and pure natural convection, respectively. 

In a household refrigerator, for example, the refrigerant absorbs heat from the refrigerated space by boiling in the evaporator section and rejects heat to the kitchen air by condensing in the condenser section (the long coils behind the refrigerator). 

Boiling is a liquid-to-vapor phase change process just like evaporation, but there are significant differences between the two. Evaporation occurs at the liquid–vapor interface when the vapor pressure is less than the saturation pressure of the liquid at a given temperature. Water in a lake at 20°C, for example, will evaporate to air at 20°C and 60 percent relative humidity since the saturation pressure of water at 20°C is 2.3 kPa and the vapor pressure of air at 20°C and 60 percent relative humidity is 1.4 kPa.

Boiling, on the other hand, occurs at the solid–liquid interface when a liquid is brought into contact with a surface maintained at a temperature Tsufficiently above the saturation temperature Tsat of the liquid.
The boiling process is characterized by the rapid formation of vapor bubbles at the solid–liquid interface that detach from the surface when they reach a certain size and attempt to rise to the free surface of the liquid. 

Bubbles owe their existence to the surface-tension at the liquid–vapor interface due to the attraction force on molecules at the interface toward the liquid phase. The surface tension decreases with increasing temperature and becomes zero at the critical temperature. This explains why no bubbles are formed during boiling at supercritical pressures and temperatures. 

the temperature and pressure of the vapor in a bubble are usually different than those of the liquid. The pressure difference between the liquid and the vapor is balanced by the surface tension at the interface. The temperature difference between the vapor in a bubble and the surrounding liquid is the driving force for heat transfer between the two phases. When the liquid is at a lower temperature than the bubble, heat will be transferred from the bubble into the liquid, causing some of the vapor inside the bubble to con- dense and the bubble to collapse eventually. When the liquid is at a higher temperature than the bubble, heat will be transferred from the liquid to the bubble, causing the bubble to grow and rise to the top under the influence of buoyancy. 

Boiling is classified as pool boiling or flow boiling, depending on the presence of bulk fluid motion. Boiling is called pool boiling in the absence of bulk fluid flow and flow boiling (or forced convection boiling) in the presence of it.

In pool boiling, the fluid is stationary, and any motion of the fluid is due to natural convection currents and the motion of the bubbles under the influence of buoyancy. The boiling of water in a pan on top of a stove is an example of pool boiling. Pool boiling of a fluid can also be achieved by placing a heating coil in the fluid. In flow boiling, the fluid is forced to move in a heated pipe or over a surface by external means such as a pump. Therefore, flow boiling is always accompanied by other convection effects. 

Pool and flow boiling are further classified as subcooled boiling or saturated boiling, depending on the bulk liquid temperature. Boiling is said to be subcooled (or local) when the temperature of the main body of the liquid is below the saturation temperature Tsat (i.e., the bulk of the liquid is subcooled) and saturated (or bulk) when the temperature of the liquid is equal to Tsat (i.e., the bulk of the liquid is saturated). At the early stages of boiling, the bubbles are confined to a narrow region near the hot surface. This is because the liquid adjacent to the hot surface vaporizes as a result of being heated above its saturation temperature. But these bubbles disappear soon after they move away from the hot surface as a result of heat transfer from the bubbles to the cooler liquid surrounding them. This happens when the bulk of the liquid is at a lower temperature than the saturation temperature. The bubbles serve as “energy movers” from the hot surface into the liquid body by absorbing heat from the hot surface and releasing it into the liquid as they condense and collapse. Boiling in this case is confined to a region in the locality of the hot surface and is appropriately called local or subcooled boiling. 

When the entire liquid body reaches the saturation temperature, the bubbles start rising to the top. We can see bubbles throughout the bulk of the liquid, and boiling in this case is called the bulk or saturated boiling. 

Boiling Regimes and the Boiling Curve 
Four different boiling regimes are observed: natural convection boiling, nucleate boiling, transition boiling, andfilm boiling. 

Natural Convection Boiling (to Point on the Boiling Curve) 
A pure substance at a specified pressure starts boiling when it reaches the saturation temperature at that pressure. The liquid is slightly superheated in this case (a metastablecondition) and evaporates when it rises to the free surface. The fluid motion in this mode of boiling is governed by natural convection currents, and heat transfer from the heating surface to the fluid is by natural convection. 

Nucleate Boiling (between Points and)
The first bubbles start forming at point of the boiling curve at various preferential sites on the heating surface. The bubbles form at an increasing rate at an increasing number of nucleation sites as we move along the boiling curve toward point C. 

The nucleate boiling regime can be separated into two distinct regions. In region ABisolated bubbles are formed at various preferential nucleation sites on the heated surface. But these bubbles are dissipated in the liquid shortly after they separate from the surface. The space vacated by the rising bubbles is filled by the liquid in the vicinity of the heater surface, and the process is repeated. The stirring and agitation caused by the entrainment of the liquid to the heater surface is primarily responsible for the increased heat transfer coefficient and heat flux in this region of nucleate boiling. 

In region BC, the heater temperature is further increased, and bubbles form at such great rates at such a large number of nucleation sites that they form numerous continuous columns of vapor in the liquid. These bubbles move all the way up to the free surface, where they break up and release their vapor content. The large heat fluxes obtainable in this region are caused by the combined effect of liquid entrainment and evaporation. 

At large values of Texcess, the rate of evaporation at the heater surface reaches such high values that a large fraction of the heater surface is covered by bubbles, making it difficult for the liquid to reach the heater surface and wet it. Consequently, the heat flux increases at a lower rate with increasing Texcess, and reaches a maximum at point C. The heat flux at this point is called the critical (or maximumheat flux, q·max

Transition Boiling (between Points andon the Boiling Curve)
As the heater temperature and thus the  Texcess is increased past point C, the heat flux decreases. This is because a large fraction of the heater surface is covered by a vapor film, which acts as an insulation due to the low thermal conductivity of the vapor relative to that of the liquid. In the transition boiling regime, both nucleate and film boiling partially occur. Nucleate boiling at point is completely replaced by film boiling at point D.

Film Boiling (beyond Point )
In this region the heater surface is completely covered by a continuous stable vapor film. Point D, where the heat flux reaches a minimum, is called the Leidenfrost point.

The presence of a vapor film between the heater surface and the liquid is responsible for the low heat transfer rates in the film boiling region. The heat transfer rate increases with increasing excess temperature as a result of heat transfer from the heated surface to the liquid through the vapor film by radiation, which becomes significant at high temperatures. 

Enhancement of Heat Transfer in Pool Boiling
the rate of heat transfer in the nucleate boiling regime strongly depends on the number of active nucleation sites on the sur- face, and the rate of bubble formation at each site. Therefore, any modification that will enhance nucleation on the heating surface will also enhance heat transfer in nucleate boiling. It is observed that irregularitieson the heating surface, including roughness and dirt, serve as additional nucleation sites during boiling.

Enhancement in nucleation and thus heat transfer in such special surfaces is achieved either by coatingthe surface with a thin layer (much less than 1 mm) of very porous material or by forming cavities on the surface mechanically to facilitate continuous vapor formation. Boiling heat transfer can also be enhanced by other techniques such as mechanical agitation and surface vibration. 

In flow boiling, the fluid is forced to move by an external source such as a pump as it undergoes a phase-change process. The boiling in this case exhibits the combined effects of convection and pool boiling. The flow boiling is also classified as either externaland internal flow boiling depending on whether the fluid is forced to flow over a heated surface or inside a heated tube. 

Condensation occurs when the temperature of a vapor is reduced below its saturation temperature Tsat. This is usually done by bringing the vapor into contact with a solid surface whose temperature Tisbelow the saturation temperature Tsat of the vapor. But condensation can also occur on the free surface of a liquid or even in a gas when the temperature of the liquid or the gas to which the vapor is exposed is below Tsat

Condensation: Itis the process of a substance in a gaseous state transforming into a liquid state.
Two distinct forms of condensation are observed: film condensation and dropwise condensation. 

Film wise Condensation:
In film condensation, the condensate wets the sur- face and forms a liquid film on the surface that slides down under the influence of gravity. The thickness of the liquid film increases in the flow direction as more vapor condenses on the film. 

Heat Transfer Correlations for Film Condensation 
1 Vertical Plates 
The analytical relation for the heat transfer coefficient in film condensation on a vertical plate described above was first developed by Nusselt in 1916 under the following simplifying assumptions: 
·      Both the plate and the vapor are maintained at constant temperatures of Ts and Tsat, respectively, and the temperature across the liquid film varies linearly. 
·      Heat transfer across the liquid film is by pure conduction (no convection currents in the liquid film). 
·      The velocity of the vapor is low (or zero) so that it exerts no drag on the condensate (no viscous shear on the liquid–vapor interface). 
·      The flow of the condensate is laminar and the properties of the liquid are constant. 
·      The acceleration of the condensate layer is negligible. 
Average heat transfer coefficient

2 Inclined Plates 
hinclined =hvert (cos1/4 (laminar)
3 Horizontal Tubes and Spheres 
Nusselt’s analysis of film condensation on vertical plates can also be extended to horizontal tubes and spheres. The average heat transfer coefficient for film condensation on the outer surfaces of a horizontal tube is determined to be 
A comparison of heat transfer relation for vertical tube of height L and horizontal tube of diameter D.
Both the heat transfer coefficient become same if
Setting hvertical =hhorizontal gives, which implies that for a tube whose length is 2.77 times its diameter, the average heat transfer coefficient for laminar film condensation will be the same whether the tube is positioned horizontally or vertically. For L=2.77D, the heat transfer coefficient will be higher in the horizontal position. 

4 Horizontal Tube Banks 
Horizontal tubes stacked on top of each other are commonly used in condenser design. The average thickness of the liquid film at the lower tubes is much larger as a result of condensate falling on top of them from the tubes directly above. Therefore, the average heat transfer coefficient at the lower tubes in such arrangements is smaller. 

Effect of vapor velocity
When the vapor velocity is high, the vapor will cool the liquid at the interfacealong.Sincethevaporvelocityatinterfacemostdroptovalue of the liquidvelocity.
If the vapor flow downward in the same direction of liquid. This additional velocity will increase the averagevelocity of liquid. Hence decreasethefilmthicknessandconsequentlyitreducesthefilmresistance and thus increase the heattransfer.
Upward vapor flow has an opposite effect because vapor exert a forceon the liquid in the opposite direction to the flow and thickness of the liquid film increase and thus decrease the heat transfer.

Effect of non-condensable gases in condensate
Even a small amount of non-condensable gases in vapor causes a significant drop in heat transfer coefficient during condensation.
Any non-condensable gases remain in the vicinity of the surface and it messes difficult for the vapor to come to the surface and it reduces the heat transfer coefficient.

If surface does not get wet by liquid then vapor after condensation forms droplets. Which does not coalesce on the surface and they will get out in the form of droplets.
In dropwise condensation, the small droplets that form at the nucleation sites on the surface grow as a result of continued condensation, coalesce into large droplets, and slide down when they reach a certain size, clearing the sur- face and exposing it to vapor. There is no liquid film in this case to resist heat transfer. As a result, with dropwise condensation, heat transfer coefficients can be achieved that are more than 10 times larger than those associated with film condensation. 

Total emissive power: It is defined as total radiant energy emitted from a surface per unit area per unit time.
Total emissive power of a black body
Where, is absolute temperature
EmissivityIt is defined as ratio of radiation emitted by real surface to black body at same temperature.
Gray Body:The gray body is the body for which the monochromatic emissivity does not depends upon the wavelength.
Planck's Law:Planck Law shows the relation for (spectral or monochromatic) emissive power for black body with temperature and wavelength.

Absorptivity, Reflectivity, and Transmissivity 
Radiation flux incident on a surfaceis called irradiation and is denoted by G. 
When radiation strikes a surface, part of it is absorbed, part of it is reflected, and the remaining part, if any, is transmitted. The fraction of irradiation absorbed by the surface is called the absorptivity the fraction reflected by the surface is called thereflectivity , and the fraction transmitted is called the transmissivity. That is, 
The average absorptivity, reflectivity, and transmissivity of a surface can also be defined in terms of their spectral counterparts as 

Kirchoff's Law: When the body is in thermal equilibrium with surrounding then absorbity’’will be equal to emissivity.

View Factor/Surface factor ()
indicates the fraction of radiant energy emitted from surface i and falls on surface j.
Net radiation energy transfer of any two-surface having area and 

Radiation shield

Heat exchangers are devices used to transfer heat energy from one fluid to another.

The simplest type of heat exchanger consists of two concentric pipes of different diameters called the double-pipeheat exchanger. One fluid in a double-pipe heat exchanger flows through the smaller pipe while the other fluid flows through the annular space between the two pipes. Two types of flow arrangement are possible in a double-pipe heat exchanger: in parallel flow, both the hot and cold fluids enter the heat exchanger at the same end and move in the same direction. In counter flow, on the other hand, the hot and cold fluids enter the heat exchanger at opposite ends and flow in opposite directions. 
Perhaps the most common type of heat exchanger in industrial applications is the shell-and-tube heat exchanger. Shell-and-tube heat exchangers contain a large number of tubes (sometimes several hundred) packed in a shell with their axes parallel to that of the shell. Heat transfer takes place as one fluid flows inside the tubes while the other fluid flows outside the tubes through the shell. Baffles are commonly placed in the shell to force the shell-side fluid to flow across the shell to enhance heat transfer and to maintain uniform spacing between the tubes. 
Shell-and-tube heat exchangers are further classified according to the number of shell and tube passes involved. Heat exchangers in which all the tubes make one U-turn in the shell, for example, are called one-shell-pass and two- tube-passes heat exchangers. Likewise, a heat exchanger that involves two passes in the shell and four passes in the tubes is called a two-shell-passes and four-tube-passes heat exchanger. 

A heat exchanger typically involves two flowing fluids separated by a solid wall. Heat is first transferred from the hot fluid to the wall by convection, through the wall by conduction, and from the wall to the cold fluid again by convection. 
In the analysis of heat exchangers, it is convenient to combine all the thermal resistances in the path of heat flow from the hot fluid to the cold one into a single resistance R, and to express the rate of heat transfer between the two fluids as 
When the wall thickness of the tube is small and the thermal conductivity of the tube material is high, as is usually the case, the thermal resistance of the tube is negligible 
When the tube is finned on one side to enhance heat transfer, the total heat transfer surface area on the finned side becomes 
AAtotal Afin Aunfinned 
Heat transfer enhancement
Increasing the friction factor increases heat transfer coefficient. Roughness of the surface increase the friction factor. Cooled tubes can serveasaheattransferenhancementdevicebecausethesecondaryflow producedbythecurvaturecausesanincreaseinheattransfercoefficient.

Material deposits on the surfaces of the heat exchanger tubes may add more thermal resistances to heat transfer. Such deposits, which are detrimental to the heat exchange process, are known as fouling.
For an unfinned shell-and-tube heat exchanger, it can be expressed as 
where A=Dand Ao=Dare the areas of inner and outer surfaces, and Rfand Rfare the fouling factors at those surfaces. 

Fin type heat exchanger
      Fin type heat exchanger used forair cooled heatexchanger.
      For fluid having low heat transfercoefficient.
       Finareusedtoincreasetherateofheattransferbyincreasingthe surfacearea.
      Fins are extendedsurface.

There are two methods used in the analysis of heat exchangers. Of these, the log mean temperature difference (or LMTD) method is best suited for the first task and the effectiveness–NTU method for the second task as just stated. 

Assumptions involved in the derivation of LMTD
             Overall heat transfer coefficient is constant throughout the heat exchanger.
             In case anyfluid undergoes phase change, the phase change offers throughout the heatexchanger.
             Thespecificheatandmassflowrateofeachfluidisconstant.I.e. heat capacity rate isconstant.
             No heat loss tosurrounding.

             There is no conduction in the direction of flow neither in a fluid nor in the tube or shellwall.
             Each of the fluid may be characterized by single temperature at any crosssection.

The heat transfer rate in a heat exchanger is equal to the heat capacity rate of either fluid multiplied by the temperature change of that fluid. Note that the only time the temperature rise of a cold fluid is equal to the temperature drop of the hot fluid is when the heat capacity rates of the two fluids are equal to each other 
Two special types of heat exchangers commonly used in practice are condensers and boilers. One of the fluids in a condenser or a boiler undergoes a phase-change process, and the rate of heat transfer is expressed as 
where m· is the rate of evaporation or condensation of the fluid and hfg is the enthalpy of vaporization of the fluid at the specified temperature or pressure. 
The rate of heat transfer in a heat exchanger can also be expressed in an analogous manner to Newton’s law of cooling as 
where is the overall heat transfer coefficient, Ais the heat transfer area, and Tis an appropriate average temperature difference between the two fluids. Here the surface area Acan be determined precisely using the dimensions of the heat exchanger. However, the overall heat transfer coefficient and the temperature difference between the hot and cold fluids, in general, are not constant and vary along the heat exchanger. 

In phase change operation, there is no any meaning of parallel and counter current flow.
log mean temperature differenceis the suitable form of the average temperature difference for use in the analysis of heat exchangers. Here Tand Trepresent the temperature difference between the two fluids at the two ends (inlet and outlet) of the heat exchanger. 

 Counter-Flow Heat Exchangers 
Note that the hot and cold fluids enter the heat exchanger from opposite ends, and the outlet temperature of the cold fluid in this case may exceed the outlet temperature of the hot fluid. In the limiting case, the cold fluid will be heated to the inlet temperature of the hot fluid. However, the outlet temperature of the cold fluid can never exceed the inlet temperature of the hot fluid, since this would be a violation of the second law of thermodynamics. 
When heat capacity rate is same for both hot and cold fluids, then

Multipass and Cross-Flow Heat Exchangers: Use of a Correction Factor 
The log mean temperature difference Tlm relation developed earlier is limited to parallel-flow and counter-flow heat exchangers only. Similar relations are also developed for cross-flow and multipass shell-and-tube heat exchangers, but the resulting expressions are too complicated because of the complex flow conditions. 
The correction factor is less than unity for a cross-flow and multipass shell- and-tube heat exchanger. That is, F<1. The limiting value of =1 corresponds to the counter-flow heat exchanger. Thus, the correction factor for a heat exchanger is a measure of deviation of the Tlm from the corresponding values for the counter-flow case. 

Parallel/Co-current flow

If is not equal to then we don’t use LMTD.

The log mean temperature difference (LMTD) method is easy to use in heat exchanger analysis when the inlet and the outlet temperatures of the hot and cold fluids are known or can be determined from an energy balance. Once Tlm, the mass flow rates, and the overall heat transfer coefficient are available, the heat transfer surface area of the heat exchanger can be determined from 
Q· =U A  l m 
Therefore, the LMTD method is very suitable for determining the size of a heat exchanger to realize prescribed outlet temperatures when the mass flow rates and the inlet and outlet temperatures of the hot and cold fluids are specified. 
With the LMTD method, the task is to select a heat exchanger that will meet the prescribed heat transfer requirements. The procedure to be followed by the selection process is: 
·       Select the type of heat exchanger suitable for the application. 
·       Determine any unknown inlet or outlet temperature and the heat transfer rate using an energy balance. 
·       Calculate the log mean temperature difference Tlm and the correction factor F, if necessary. 
·       Obtain (select or calculate) the value of the overall heat transfer coefficient U. 
·       Calculate the heat transfer surface area As . 
The task is completed by selecting a heat exchanger that has a heat transfer surface area equal to or larger than A

If the inlet and the outlet temperatures of the hot and cold fluids are unknown or can’t be determined from an energy balance. The LMTD method could still be used for this alternative problem, but the procedure would require tedious iterations, and thus it is not practical. In an attempt to eliminate the iterations from the solution of such problems, and the Effectiveness-NTU Method can be used.

Effectiveness of the heat exchanger
It is defined as the ratio of actual heat transfer to maximum possible heat transfer.
But the maximum temperature difference can be achieved first by the fluid having lowest heat capacity rate.
Number of transfer units (NTU)
                                  where, A is surface area,
                                                U is overall heat transfer coeff
                                                C is heat capacity rate
NTU is a measure of effectiveness of heat exchanger.
Heat capacity rate ratio(R)
   for phase change operation

Relationship between effectiveness and NTU for different cases
Parallel flow
Counter current



Parallel flow

Counter current

Design of Shell and tube heat exchanger
Calculation of inside (tube side) heat transfer coefficient
                  ,             ,            

Calculation of outside (Annular) heat transfer coefficient
                  ,          ,         
Wetted perimeter
Heat transfer
Pressure drop

Purpose of using baffles
      It is used to direct the shell sidefluid.
      It also provides supportto thetubes.
       Italsoincreasestheshellsideheattransfercoefficientbyreducing the distance between two adjacentbaffles.
Baffle Spacing Centre to center distance between two adjacent baffles is called baffle spacing.
Tie RodIt is used to tie tube bundles.

Calculation of tube side heat transfer coefficient
Where,is total number of tubes
            is total number of passes
            is cross sectional area of one tube

Calculation of shell side heat transfer coefficient
Where, is tube pitch
            is outer diameter of tube
            is Shell side diameter 
            is baffle spacing

Tube pitch and tube arrangement
Triangular pitch arrangement

Square pitch arrangement
Application of different tube arrangements
             The number of tubes in triangular pitch arrangement is more than in square pitcharrangement.
             The triangular and rotated square pitch arrangementprovide high heat transfercoefficient.
             The square and rotated square pitch arrangement is used for highly fouling or viscousfluid.
             Triangular and rotated pitch arrangement providehighly heat transfer coefficient on shell side fluid at a cost of high pressure drop.
Fluid allocation
             The corrosiveand fouling fluids are allocated in the tube. It is easy to replace the tube. If we place the corrosive fluid on shell side, it will corrode/effect the tube & shellboth.
             Highly viscous fluid should be placedin the shellside.
             Hightemperatureandhigh-pressure fluidshouldbeplacedintube side because they have high tendency to corrode thematerials.
             Fluid with lowest allowed pressure drop should be placed in the tubeside.
             Fluid with slowest flow rate should be placed in shellside.

Number of baffles

Pressure drop calculation
Tube Side

Shell side

·      Heat Transfer Rate 
·      Cost 
·      Pumping Power 
·      Size and Weight 
·      Type 
·      Materials 
Fluid mechanics is defined as the science that deals with the behaviour of fluid at rest or in motion and the interaction of fluid with solid or other fluid at boundaries.

Fluid is a substance which has ability to flow. Fluid deform continuously under the influence of shear stress no matter how small.

Types of fluid:
●     Newtonian Fluid
●     Non-Newtonian Fluid

Studies of behaviour of non-newtonian fluid is called Rheology.

Newtonian Fluid: 
The fluid which obeys the newton’s law of viscosity is called Newtonian fluid. A fluid where the shearing stress is linearly related to the rate of shearing strain - is designated as a Newtonian Fluid.

Non-Newtonian fluid classified into two parts:
●     Time dependent
●     Time independent

Time dependent Non-Newtonian Fluid Classified into two Parts:
●     Thixotropic
●     Rheopectic

Thixotropic Fluids:
The viscosity of a thixotropic fluid decreases with increasing time at a constant shear rate.

The viscosity of a Rheopectic fluid increases with increasing time at a constant shear rate.

Time independent Non-Newtonian Fluid classified into three parts:
●     Bingham Plastic
●     Pseudo Plastic
●     Dilatant

Shear-thinning or Pseudoplastic Fluids:
A Shear-thinning or pseudo-plastic fluid is a fluid where viscosity decreases with increasing shear rate.

Dilatant Fluids:
A Shear Thickening Fluid - or Dilatant Fluid - increases the viscosity with agitation or shear rate.

Bingham Plastic Fluids:
A Bingham Plastic Fluid has a yield value which must be exceeded before it will start to flow like a fluid. 

Viscosity and Temperature:
●     For liquids viscosity decreases with temperature
●     For gases viscosity increases with temperature

Ideal Fluid:
Fluid which viscosity is zero. 

What is the Driving force for fluid flow:
Driving force for fluid flow is Energy per unit mass or total head
available at the point of location.

Viscosity is measure of transport capacity of momentum disturbance within the fluid and it is acting as a messenger of momentum transport within the fluid.

Viscosity is caused by cohesive force between the molecules in liquids and by molecular collision in gas.

Density is measure of restoration capacity of momentum disturbance within the fluid.

Momentum diffusivity:
It is defined as relative importance of momentum transport within the fluid to the momentum stored by the fluid.

Viscous Flow:
Flow in which the frictional effects are significant are called viscous flow.

Laminar Flow:
The highly ordered fluid motion characterised by smooth layers of fluid. laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion.

Turbulent Flow:
The highly disordered fluid motion that typically occurs at high velocity and is characterised by velocity fluctuations is called turbulent. turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.

Creeping Flow:
These are flow in which the reynolds number is very small.

Surface tension:
Liquid droplets behaves like small spherical balloons filled with the liquid and the surface of the liquid act like a stretched elastic membrane under tension. The pulling force that cause this tension acts parallel to the surface and is due to the attractive force between the molecules of the liquid. The magnitude of this force per unit length is called surface tension.

Capillary effects:
Capillary effect is the rise or fall of a liquid in a small diameter tube inserted into the liquid.

A streamline is a curve that is everywhere tangent to the instantaneous local velocity vectors.

It is actual path traveled by an individual fluid particle over some time period.

Bernoulli’s equation:
The sum of K.E, P.E,and flow energy of a fluid particle is constant along a streamline during steady flow.
●     Steady state flow
●     Incompressible flow
●     Inviscid

Boundary Layer:
The region of the flow in which the effects of the viscous shearing forces caused by fluid viscosity are felt is called boundary region and that thickness is called boundary layer.

Hydrodynamic entrance length:
The region from the inlet of the pipe to the point at which boundary layer merges at the centreline is called hydrodynamic entrance region and length of this region is called hydrodynamic entrance length.

Turbulent Flow in Pipes:
Turbulent flow along a wall can be considered to consist of four regions, Characterised by the distance from the wall. The very thin layer next to the wall where viscous effect are dominated is the viscous sublayer. The velocity profile in this layer vary linearly and the flow is streamlined. Next to the viscous sublayer is the buffer layer in which turbulent effects are becoming significant but the flow is still dominating by viscous effects. Above the buffer layer is transition layer, also called the inertial sublayer in which the turbulent effect are much more significant but still not dominating. Above that is the outer layer in the remaining part of the flow in which turbulent effect dominate over molecular diffusion effects.

The Moody charts:
This is used to find friction factor
The friction factor in laminar flow is inversely proportional to Reynolds number and in fully developed turbulent pipe flow depends on the reynolds number and the relative roughness.

Types of control Valve:
Check Valve:
Check Valves are used when unidirectional flow is desired.They are automatic in operation and prevent flow in one direction but allow in the other.

Globe Valve:
The essential features of these valves is a globular body with a horizontal internal partition having a circular passageway. The glove valve is ordinarily used in smaller size. It is generally considered a poor practice to use a globe valve in a size larger than 2 inch. Globe valve are widely used for controlling flow. The fluid passes through a restricted opening and changes direction several times. As a result the pressure drop in this of valve is large.

Gate Valve:
Gate valves are universally used in larger size. Gate valve are not recommended for controlling flow and are usually left fully open or fully closed.

Types of Flowmeters:
A)  Variable Area Flowmeter
A variable area meter is a meter that measures fluid flow by allowing the
cross sectional area of the device to vary in response to the flow,
causing some measurable effect that indicates the rate.

Some important features of Rotameters
●     Pressure drop is constant
●     These rotameters can be used for liquids and gases.
Rotameter consists of a gradually tapered tube, it is arranged in vertical position. The tube contains a float, which is used to indicate the flow of the fluid. This float will be suspended in the fluid while fluid flows from bottom of the tube to top portion. The entire fluid will flow through the annular space between the tube and float. The float is the measuring element. The tube is marked with the divisions and the reading of the meter is obtained from the scale reading at the reading edge of the float. Here to convert the reading to the flow rate a calibration sheet is needed.

●     Pressure drop is constant
●     No special fuel or external energy is required to pump
●     Very easy to construct and we can use a wide variety of materials to construct.

●     Due to its use of gravity, a rotameter must always be vertically oriented and right way up, with the fluid flowing upward.
●     Rotameters normally require the use of glass (or other transparent material), otherwise the user cannot see the float. This limits their use in many industries to benign fluids, such as water.

B) Constant Area flowmeters
1) Venturi meter
When a fluid, whose flow rate is to be determined, is passed through a Venturi meter, there is a drop in the pressure between the Inlet section and Cylindrical Throat of Venturi meter. The drop in pressure can be measured using a differential pressure measuring instrument. Since this differential pressure is in direct proportion to the flow rate as per the Bernoulli's Equation hence the differential pressure instrument can be configured to display flow rate instead of showing differential pressure.
Correction in Flowrate:Recalling the fact that the measured value of the piezometric pressure drop for a real fluid is always more due to friction than that assumed in case of an inviscid flow, a coefficient of discharge CD(always less than 1) has to be introduced to determine the actual flow rate.
Advantage of venturi meter:●      The Venturi tubes can be used to handle fluids that contain slurries / sludges (for example: Sugar Cane Mill) , because these Venturi tubes contain no sharp corners and do not project into the fluid stream.
●      Negligible possibility of clogging with deposits or sludge.
●      A higher Coefficient of discharge obtainable.
●      Operational response can be designed with perfection.
●      Installation direction possibilities: Vertical / Horizontal / Inclined.
Limitations of venturi meter:●      Venturi meters are expensive
●      Cannot be used in space constrained application because of their significant size.
●      Flow straighteners are required at the inlet and the outlet to attain streamline flow thereby increasing the cost and space for installation further.
●      Minimum line size for Installation of Venturi meter is limited to 1/2" (0.5 inch).

2) Orifice meter
Construction: An orifice meter provides a simpler and cheaper arrangement for the measurement of flow through a pipe. An orifice meter is essentially a thin circular plate with a sharp edged concentric circular hole in it.

When a liquid / gas, whose flow-rate is to be determined, is passed through an Orifice Meter, there is a drop in the pressure between the Inlet section and Outlet Section of Orifice Meter. This drop in pressure can be measured using a differential pressure measuring instrument. Since this differential pressure is in direct proportion to the flow-rate as per the Bernoulli's Equation hence the differential pressure instrument can be configured to display flow-rate instead of showing differential pressure.
Correction in Flow Rate:
Recalling the fact that the measured value of the piezometric pressure drop for a real fluid is always more due to friction than that assumed in case of an inviscid flow, a coefficient of velocity Cv(always less than 1) has to be introduced to determine the actual Flow Rate.
If a coefficient of contraction Cis defined as, Cc= A/A0, where A0is the area of the orifice,Ais the area of vena-contracta.
Vena contracta is the point in a fluid stream where the diameter of the stream is the least, and fluid velocity is at its maximum
Advantage of Orifice meter:
●     The Orifice meter is very cheap as compared to other types of flow meters.
●     Less space is required to Install and hence ideal for space constrained applications
●     Operational response can be designed with perfection.
●     Installation direction possibilities: Vertical / Horizontal / Inclined.

Limitations of Orifice meter:
●      Easily gets clogged due to impurities in gas or in unclear liquids
●      The minimum pressure that can be achieved for reading the flow is sometimes difficult to achieve due to limitations in the vena-contracta length for an Orifice Plate.
●      Unlike Venturi meter, downstream pressure cannot be recovered in Orifice Meters. Overall head loss is around 40% to 90% of the differential pressure .
●      Flow straighteners are required at the inlet and the outlet to attain streamline flow thereby increasing the cost and space for installation.
●      Orifice Plate can get easily corroded with time thereby entails an error.
●      Discharge Coefficient obtained is low.

Pitot Tube:
Pitot tube is used to measure point velocity or local velocity in a open channel or closed channel.

 Velocity Profiles:
●     Pseudoplastic shows flater profile compare to profile to newtonian
●     For extreme Pseudoplastic fluid the plug flow profile is obtained across the entire pipe
●     For dilatant fluid the profile is more pointed and narrower
●     For extreme dilatant fluid the velocity profile is linear function of radius.
●     For Bingham plastic fluid is parabolic near the surface and it is flat near the center

Differences between pipe and tube:
Pipes and tubes are specified in terms of their diameter and wall thickness.
 Heavy walled
 Relatively large in diameter
 comes in moderate lengths (20 to 40 ft)
 Threading is possible
 Pipe walls are rough
 Lengths of pipes are joined by screwed, flanged and welded

 Thin walled
 Less diameter
 available in the form of coils also, several hundred meters
 Cannot be threaded
 Tube walls are smooth
 These are joined by compression fittings, flare fittings, or soldered

Types of pumps:
A pump is a device that moves fluids by mechanical action. Pumps can be classified into three major groups according to the method they use to move the fluid: dynamics and displacement.

Positive displacement pumps:
A positive displacement pump makes a fluid move by trapping a fixed amount and forcing (displacing) that trapped volume into the discharge pipe.

1)  Rotary positive displacement pumps
These pumps move fluid using a rotating mechanism that creates a vacuum that captures and draw in the liquid.

Rotary positive displacement pumps fall into three main types:
Gear pumps:
A simple type of rotary pump where the liquid is pushed between two gears

Screw pumps:
The shape of the internals of this pump is usually two screws turning against
each other to pump the liquid

Rotary vane pumps:
Similar to scroll compressors, these have a cylindrical rotor encased in
a similarly shaped housing. As the rotor orbits, the vanes trap fluid between the rotor and the casing, drawing the fluid through the pump.

2) Reciprocating pumps
Reciprocating pumps move the fluid using one or more oscillating pistons, plungers, or membranes (diaphragms), while valves restrict fluid motion to the desired direction.

Reciprocating pumps fall into three main types:

Plunger pumps:
A reciprocating plunger pushes the fluid through one or two open valves, closed by suction on the way back.

Diaphragm pumps:
Similar to plunger pumps, where the plunger pressurizes hydraulic oil which is used to flex a diaphragm in the pumping cylinder. Diaphragm valves are used to pump hazardous and toxic fluids.

Piston pumps displacement pumps:
Usually simple devices for pumping small amounts of liquid or gel manually. The common hand soap dispenser is such a pump.
Centrifugal Pumps:
A centrifugal pump is a pump consisting of an impeller fixed on a rotating shaft and enclosed in a casing.

Major components of centrifugal pumps
●      Volute casing
●      diffuser/guide vanes
●      rotors/impeller

It is the gap between the casing and the impeller. In this volute kinetic energy is converted into pressure energy. As the cross section area increases, the volute reduces the velocity of the liquid and increases the pressure of the liquid.

Operating Principle:
As the fluid enters at the eye of the impeller it thrown radially outward via centrifugal force. As the fluid passes through impeller, the area of the flow increases which reduces the velocity of the fluid and consequently increase the pressure energy of the fluid. The fluid at the exit of the impeller enter into diffuser vanes which provide increasing area for the fluid to flow hence it convert more K. E. into pressure energy.

Net positive suction head is defined as minimum amount of head that must be available at the suction to avoid the cavitation.

There are two types of NPSH
●      NPSH available
●      NPSH required

All pump have different value of NPSH required and it can be obtained from the manufacturer.

(NPSH)R is defined as the minimum suction pressure required at the pump inlet for the pmp to avoid the cavitation.

To avoid the cavitation, the (NPSH)A should be greater than (NPSH)R.

Cavitation takes place when the liquid get converted into vapour because of lower available head at suction of the pump in compare to the saturation or vapour pressure head of liquid at constant temperature.
As vapour forms enters in the impeller where the pressure is high, due to high pressure the vapour get implode/explode and high velocity jet is going to form which strike on the wall of the impeller, hence the impeller will get crode and unique sound is going to generate due to striking of the gas to the impeller.

To avoid the cavitation the total head available at the suction of the pump should larger than the saturation pressure head of that liquid at given temperature.

Methods to avoid cavitation:
●     By changing the location of the pump
●     By lowering the temperature of process fluid
●     By Pressurizing the vessel
●     By proper installation of the system or by reducing the number of fittings and joints
●     By reducing the speed of the impeller

Does excessive amount of air at the pump suction cause cavitation:
No. Air has nothing to do with it. Cavitation is caused by the collapsing (imploding) vapor (not air) bubbles. These bubbles are simply a vaporized liquid in the region where static pressure dropped below vapor pressure.

When the pump is at stop condition or not in operation, then suction pipe, discharge pipe, casing should be filled with process fluid. If it is not so then those section is going to filled with air. Hence enough pressure will not able to create to suck the liquid from reservoir to impeller. To avoid this problem, these section should be filled with process fluid when the pump are not in use and that is called priming.

Pump Characteristics Curve:
It is the curve of head, Power and efficiency versus discharge at the constant speed of the Impeller.

Break horse power(BHP):It is power supplied to the pump.

Water horse power(WHP):it is power supplied to the fluid by the pump.

An impeller is a part of a pump or compressor that rotates at a high speed and acts as a proper to increase a fluid pressure and flow rate.

Types of impeller:
  1. Forward curved
  2. Backward curved
  3. Radial curved
Most widely used is backward curved impeller.

Which type of pump used For highly viscous fluid ?
 Reciprocating pumps used for viscous fluid. Centrifugal pumps cannot be used for highly viscous fluid as increased viscosity will lead to the consumption of more power. The head and pump performance will decrease.

What is centrifugal pump?
A centrifugal pump is a pump consisting of an impeller fixed on a rotating shaft and enclosed in a casing.

What is positive displacement pump?
A positive displacement pump is a pump which makes a fluid move by trapping a fixed amount of fluid and forcing that fluid to discharge pipe.

Those operation in which transfer of mass or mole take place from one point to another point in a phase or one phase to another phase due to chemical deriving force and results some changes occurs.
Chemical driving force can be concentration difference, Partial pressure difference or mol fraction difference.
Mass transfer occurs if resistance and driving force both exists.
Example:Drying of clothes under the sun, Lumps of sugar added into a cup of tea.

Industrial examples:
●     Separation of C02 from flue gas by absorption
●     Separation of ethanol from ethanol water mixture by distillation
●     Separation of toluene from toluene water mixture by extraction operation using benzene as solvent

Unit operation in which solute/pollutant of gas is removed from gas with the help of suitable liquid solvent on the basis of solubility.

Unit operation in which solute/pollutant of liquid is removed from liquid with the help of suitable gas on the basis of solubility.

It is defined as transfer of liquid vapour into gas.

Humidity is defined as amount of water vapour in dry air.

The removal of vapour from a gas is called Dehumidification.

Distillation is the Process of separation of two or more component on the basis of relative volatility with the help of reboiler followed by condensation.

Drying is removal of moisture from substance by supplying heat and making use of driving force for the mass transfer.

Adsorption is surface phenomena in which solute transferred from fluid to surface of solid.

It is the transferring component or solute which has to be adsorbed on surface of solid.

The solid material on which the solute is going to transfer is called adsorbent.

The equipment in which the adsorption is going to take place is called adsorber.

In leaching solute is transferred from solid phase to liquid phase.

Process of removal of solute from a liquid solution by heating or cooling.

Molecular Diffusion:
The Molecular mass transfer is due to molecular diffusion by virtue of thermal energy of the molecules.

How to increase rate of molecular diffusion:
●     By increasing the temperature. K.E of the molecules get increases, that will increase the net movement, that increase the rate of molecular diffusion.
●     By lowering the pressure. The mean free path get decreases, that implies that number of collision get decreases which increase the net movement.

Convective mass transfer:
It is due to random and macroscopic or bulk movement of the molecules and it predominant in the turbulent flow.

Driving force for Mass Transfer:
In a single phase, the driving force for mass transfer is concentration difference while for more than one phase the driving force is chemical potential.

Chemical Potential:
The chemical potential of the i-component of a thermodynamic system in a given phase is a thermodynamic state function. It defines changes of the Gibbs energy and other thermodynamic potentials when the number of particles of a corresponding component is changed. Chemical potential of the ith-component of the system is the derivative of any thermodynamic potential divided by the quantity (or number of molecules) of this component when the values of the other thermodynamic variables, given a thermodynamic potential, are constant, e.g., μi= (G/ni)T,p,nj, where G is the Gibbs energy of the phase; ni, the number of moles of the i-component of the phase; T, the absolute temperature; p, pressure, and nj, the number of moles of all other components (j = i).

Fick’s First Law of diffusion:
The flux of any species i w.r.t. Molar average velocity is Proportional to concentration gradient in that direction.

Fick’s First Law of diffusion:
The rate of change of concentration at a point in a space is proportional to second derivative of concentration with space.

Interphase Mass transfer:
●     Transfer of solute from bulk of the gas to interphase
●     At the interphase the solute comes to the equilibrium with solute in the liquid phase and this assumed that at the interphase mas is going to transfer from gas phase to liquid phase those of suddenly reached to the equilibrium.
●     There is transfer of solute from interphase to bulk of liquid.

Film Theory:
●     Whitman in 1923
●     Steady state molecular diffusion
●     Concentration gradient lies in hypothetical film

Penetration Theory:
●     Given by Higbie in 1935.
●     Unsteady state mass transfer occurs at gas-liquid interphase and this is given by Fick’s 2nd Law.
●     Equilibrium is immediately attained at the interface.
●     Each liquid element is in contact with the gas at interface for same length of time.

Surface Renewable Theory:
●     Given by Bankward.
●     The liquid element at the gas-liquid interface are being randomly replaced by fresh liquid element.
●     Unsteady state mass transfer occurs at liquid-gas interface.
●     At any moment, each of the liquid element at gas-liquid interface has same probability of being replaced by fresh element.

Distillation is the Process of separation of two or more component on the basis of relative volatility with the help of reboiler followed by condensation.

We know that mixture is the combination of more than one substance which may or may not be in same phase. There are several techniques which can be used to separate the components of a mixture. The mixtures which have all components in same phase are called as homogenous mixture like water in ethanol. On the contrary, if components of a mixture are present in different phase, it is called as heterogeneous mixture. Distillation, chromatography, separating funnel are some common methods of separation of components of mixture. Out of all these methods, distillation is one of the most common methods of separation of components of a mixture. This method is mainly used for liquid mixtures which contains components with different boiling points. 

In the distillation of mixture of liquids, the liquid can be heated to convert them to gaseous state. Since they have different boiling points, they condense back at different rate and can easily separate. Similarly reverse process can be used to separate gases in which different gases liquefy at different rate by changing temperature or pressure. Distillation has several applications in different fields like it is widely used in the production of gasoline, distilled water, xylene, alcohol, paraffin and kerosene. Distillation can be different types such as fractional distillation, destructive distillation, vacuum distillation etc. 

Applications of distillation:
The application of distillation can roughly be divided in four groups: laboratory scale, industrial distillation, distillation of herbs for perfumery and medicinals (herbal distillate), and food processing.

Batch distillation:
Simple distillation is mainly used for the separation of liquid from a mixture. In this method, liquid is evaporated and condensed back to separate from its mixture. 
For example, if we want to separate to separate pure water from a salt solution, take a beaker of the salt solution and heat it to the boiling point. At boiling point, liquid will convert into vapour state and vapour will pass through condenser that is connected to another beaker or collector. By continuing this process, liquid or pure water will collect at another side of apparatus and salt will remain in beaker.

Example of Distillation:
Distillation is mainly used for the separation of
●      different fractions from petroleum products,
●      mixture of methanol and ethanol,
●      acetone and water,
●      impurities from alcohol,
●      Water from salt.

Fractional distillation:
Principle of Fractional Distillation:
The miscible liquids boil at different temperature and evaporate at different temperature. When the mixture is heated, the liquid with lower boiling point boils and turns into vapours. So the mixture is heated to a temperature at which one or two components of the mixture will vaporise. Fractional distillation involves repeated distillations and condensations.

Fractional Distillation Uses:
There are number of uses of fractional distillation.
●      One of the important use of using fractional distillation is to separate the crude oil into its various components such as gasoline, kerosene oil, diesel oil, paraffin wax, liberating oil.
●      Fractional distillation is also used for the purification of water. Water contains many dissolved impurities; these can be removed by this process.
●      It is also used for separating acetone and water.
●      Industrial use of fractional distillation is in petroleum refineries, chemical plants, natural gas processing and separation of pure gases from mixture of gases.
●      It has other industrial uses as it is used for purification and separation of many organic compounds.

Fractional Distillation of Crude Oil:
Fractional distillation is used to separate the various components of crude oil. Various components of crude oil such as gasoline, paraffin wax, lubricating oil, diesel oil, fuel oil, naphtha, kerosene are separated. Crude oil is heated and the mixture stars boiling. Hydrocarbon gases are introduced into the column. 
The temperature decreases in going up the fractionating column.  The hot vapours rise up in the fractionating column. Therefore vapours with higher boiling point condense in the lower part and the vapours of components with low boiling point condense at the top. The condensed vapours are removed from the sides of the column.

Tx-y Diagram:
●     Mixture of vapour and liquid remain at its saturation curve, it doesn’t leave saturation curve until complete vaporization or condensation occurs.
●     Liquid and vapour coexists.

Px-y Diagram:
In order to avoid getting confused about what you're looking at, think: what causes a liquid to vaporize? Two things should come to mind:
●      Increasing the temperature
●      Decreasing the pressure
Therefore, the region with the higher pressure is the liquid region, and that of lower pressure is vapor, as labeled.
The distillation operation can not carried out at high pressure. If pressure reach to the critical pressure of anyone component then the mixture will behave as non ideal because it is very difficult to differentiate between the liquid and vapour at critical pressure or above critical pressure and no further separation take place.

Some Important points:
●     When we provide heat to water, temperature increase from 50°C to 100°C, internal energy of water molecules increase. The water molecule at surface of water has tendency to leave but molecule within the bulk which is surrounded by 360° can’t leave bulk. At 100°C each and every molecules of water has tendency to leave the bulk. When we continue give heat, temperature will remain 100°C and phase change will occurs. Temperature will be still 100°C till complete vaporization happen. Now if we give more heat then it will increase the temperature of vapour.
●     For the mixture boiling point doesn’t exist, boiling range exists.
●     For mixture dew point doesn’t exists, dew point range exists.
●     Initial phase of vaporization is governed by more volatile component.
●     At a particular temperature, the component exerting more vapour pressure is more volatile      component.
●     During boiling more volatile component governed the process.
●     Less volatile component is easily condensable.
●     More volatile component are easily vaporizable.
●     During condensation less volatile component govern the process.

Flash or equilibrium Distillation:
●     Flash distillation is used often extensively in petroleum refinery in order to reduce the load on main fractionating column.
●     In Flash distillation, the petroleum fraction are heated in pipe still and heated fluid is flashed into vapour via pressure reducing valve.
●     After flashing vapour and liquid are separated to each other and each containing many components.
Flash or equilibrium distillation is generally used for the component which has very large difference in boiling point or have large relative volatility.
The equilibrium composition only depends upon temperature and pressure and it remain as it no matter even if we change the feed composition.

Vacuum Distillation:
Vacuum distillation method is mainly used in refineries. It involves expanding oil to produce high surface area that facilitates the vaporous extraction of water and other contaminants.  The distillation includes heating, vaporization, condensation and cooling of vapors. It separates all the components of a liquid mixture with the help of partial vaporization. It results the separation of vapor and liquid residue. 
In this process, the more volatile components like water vaporized and less volatile components remain in the oil. The water vapors can be condensed and back to liquid state. Various properties of components of mixture and efficiency of the distillation process will determine the completeness of separation of components.

Steam Distillation:
distillation of a liquid in a current of steam, used especially to purify liquids that are not very volatile and are immiscible with water.

Azeotropic distillation:
Azeotropes are mixtures of two or more different liquids which can either have a higher boiling point than either of the components or they can have a lower boiling point. Unlike azeotropes, ideal solutions have uniform mixtures of components. Ideal solutions always follow Raoult’s law. 

Mixture of benzene and toluene is good example of ideal solution. Azeotropes do not follow Raoult’s law because during boiling, the ratio of component in solution and vapor is same. Azeotropic distillation can be defined as the technique of addition of another component to form a new low boiling point azeotropic solution such as benzene can be added to the solution of ethanol and water in azeotropic distillation. Let’s discuss the azeotropic distillation method.

Azeotropic Distillation Method:

The azeotropic distillation unit consists of a container to feed the azeotrope, decanter and steamer. For example; the mixture of acetic acid and water can be separate out with the addition of an ester like n-butyl acetate. Remember the boiling point of acetic acid is 118.1oC and water is 100oC. Addition of ester whose boiling point is 125oC forms a minimum-boiling azeotrope with water with boiling point 90.2oC. Hence azeotropic mixture will be distilled over as vapor and leave acetic acid at bottoms. The overhead vapor is condensed and collected in a decanter. 

Here it forms two insoluble layers in which the top layer contains pure butyl acetate with water, and a bottom layer contains pure water saturated with butyl acetate. The top layer is returned to the distillation column and bottom layer is sent to another column for the recovery of the ester by steam stripping. 

Extractive distillation:
A method of separating two components of very similar boiling point from a mixture. A third, miscible and high-boiling-point solvent is added to the mixture which causes a change in the volatilities of the components. These components are then vaporized by the application of heat and cooled by the action of cold water in a condenser.

Mccabe thiele method:
●     Specific heat capacity of both the component must be same.
●     Only latent heat transport, no sensible heat transport.
This method uses the equilibrium curvediagram to determine the number of theoretical stages (trays) required to achieve a desired degree of separation. It is a simplified method of analysis making use of several assumptions, but nonetheless a very useful tool for the understanding of distillation operation.
The VLE data must be available at the operating pressure of the column.
In its essence, the method involves the plotting on the equilibrium diagram 3 straight lines: the rectifying section operating line (ROL), the feed line(also known as the q-line) and the stripping section operating line (SOL).
Each of these lines passes through the points representing the mole fractions of the more volatile component in the distillate, bottoms and feed (xD, xBand xF) respectively. These lines represent the relationship between the concentrations in the vapour phase (y) and the liquid phase (x).
The number of theoretical stages required for a given separation is then the number of triangles that can be drawn between these operating lines and the equilibrium curve. The last triangle on the diagram represents the reboiler.
To obtain the number of theoretical trays using the McCabe-Thiele Method, we shall used the "Parts-Whole Relationship": analysis is first carried out by partitioning the column into 3 sections: rectifying, feed and stripping sections as shown in left Figurebelow. These sections are then represented on the equilibrium curve for the binary mixture in question and re-combined to make a complete design, as shown in the Figure.
In the simplest case, the McCabe-Thiele Method to determine the number of theoretical stages follows the steps below:
  1. Analysis of the Rectifying section, and determine the ROL using xD and R
  2. Analysis of the Feed section, and determine the feed condition (q) 
  3. Determination of the feed line (q-line)using xFand q
  4. Locate the intersection point between ROL and q-line
  5. Analysis of the Stripping Section, and determine the SOL using (4) and xB
On the completed design (equilibrium diagram): The number of points on equilibrium curve = Number of theoretical trays + 1 Reboiler (last triangle).
●    Most reboilers are partial reboilers, that is they only vaporize part of the liquid in the column base. Partial reboilers also provide an ideal separation stage.
●    Only phase change occurs in total condenser, but phase change as well as separation occurs in partial condenser.
●    No heat loss, no heat gain. No heat of mixing.
●    As heat given to boiler is equal to heat taken from condenser.
●    Stream on the same side of the tray lies on the operating line.
Relative Volatility:
It is defined as concentration ratio of i to j in vapour phase to same ratio in the liquid phase. Relative volatility is a measure of the difference between the vapor pressure of the more volatile components of a liquid mixture and the vapor pressure of the less volatile components of the mixture.
The quantity α is unitless. When the volatilities of both key components are equal, it follows that α= 1 and separation of the two by distillation would be impossible under the given conditions. As the value of αincreases above 1, separation by distillation becomes progressively easier.

Variation of Relative Volatility with Column Pressure
In the case of Distillation column, Relative volatility is the main driving force. Relative volatility is strong function of temperature and as temperature increase, Relative Volatility increase.
As the column Pressure increase, Bubble point curve and Dew point curve come closer which in turn decreases the width of the tie line and in turn, it increase difficulty of separation.
Conclusion is increase in the column pressure, increase the difficulty of separation. That’s why Distillation column are always preferred to operate at atmospheric pressure or even at vacuum to enhance the ease of separation.

Some Points:
●    If relative volatility is very high, we need special refrigerator/coolant. In this case we use partial condenser instead of total condenser.
●    If we need product in the form of vapour then use partial condenser.
●    In case of non condensable component, use partial condenser.
Reflux Ratio:
It is defined as the number of moles feed back to column to the number of moles withdrawn.
Total Reflux ratio:
●     Slope of rectifying line merge with diagonal line.
●     Slope of striping line is 1, thus stripping line merge with diagonal line.
●     Feed line doesn’t exists, only point exists.
●     In this case we need equilibrium relationship to solve problems.
●     At total reflux condition, duty of reboiler is maximum, size of reboiler and condenser are maximum. Column diameter is maximum and the number of equilibrium stages desired for separation is minimum.

Minimum Reflux ratio:
The point where rectifying line, stripping line , feed line and equilibrium curve touch is known as pitch point.
●     In minimum reflux condition, reboiler duty decreases, diameter of column decreases, size decreases but number of theoretical trays increases.
Some Points:
●     As reflux ratio increase slope of rectifying line section increase and the rectifying operating line shift away from the equilibrium line.
●     Increase in reflux ratio, increase duty of condenser and reboiler, increasing the size of condenser and reboiler which increase column diameter.
●     As reflux increases, the number of equilibrium stages for separation decreases.
●     If reflux is cold, it will increase the mass transport at 1st tray. Cold liquid will cooled vapour steam and condense vapour, it will increase more volatile component in vapour stream. Initially flow rate of distillate decrease then it increase.
●     Cold reflux will act as same as that of maximum reflux.
●     Coold reflux will increase the duty of condenser which also increase the duty of reboiler and size of condenser and reboiler increases. Also it increase size of the column which decrease the number of tray to get same mass transport.
●     When vapour increase, it will make cold liquid to saturated liquid, because duty of condenser is fixed. So disturbance will come for a short time only.
The vapour velocity is more. It carries the liquid droplets with it. Which is known as entrainment. If this phenomena continue, a stage will come when the tray belonging to stripping section gets empty and liquid will transfer to rectifying section. Every tray of rectifying section holds more liquid than its capacity because of which condition of flood occurs. This is known as flooding.
To avoid flooding, decrease the reboiler duty which turn decrease the flow/generation of vapour in turn decrease the potential at trays which maintain the smooth runnability.
If the vapour velocity is less than resistance offered by the vapour to the liquid to hold it on a tray is not enough and liquid gets come down through the holes which is known as wheeping.
Effect of pressure on distillation:
●     If pressure increase y decrease
●     If pressure increase, width of tie line decrease
●     As pressure decrease equilibrium curve shifted away from diagonal
●     As pressure decrease, number of equilibrium stages decreases
●     Pressure increases, relative volatility decreases and very high pressure relative volatility become unity.
Extraction is a process of separating a solute from a solution via solvent on the basis of relative solubility.
●     Extraction is always an equilibrium phenomena.
●     Leaving streams are in equilibrium.
●     Only liquid-liquid-liquid mixture can be separated.
●     Minimum component id distillation is binary while trinary in extraction.
Why we use condenser in Distillation column?
Condenser is used to remove heat from column and condense vapour to liquid.
Why Reboiler?
It act as the pressure filler to column.
Why Partial reboiler not total reboiler?
It take less heat, Separation occurs, Purge capability, At initial more volatile component vaporized, less heat required to vaporize more volatile component, steam economy.
Raoult's Law:
Equilibrium Partial pressure of any species i in vapour phase or gas phase is proportional to mole fraction of that species in liquid phase and proportionality constant is vapour pressure in pure form at that temperature.

Absorption Factor:
It is defined as ratio of slope of operating lime to slope of equilibrium line.
●      A>>1, Effective separation
●      A=1, Limiting Separation
●      A<<1, No separation
Driving force is minimum at top of the tower and maximum at bottom of the tower.
Absorption is exothermic process, we decrease temperature from top to bottom of the tower.
Dalton's law:
Dalton's law states that the total vapor pressure is the sum of the vapor pressures of each individual component in the mixture.
Physical Meaning of NTU:
NTU is defined as ratio of actual change in composition(Y1-Y2) to the average mean driving force.
For desire separation(fixed value of Y1-Y2), if NTU increase it means average driving force is only a small fraction of actual desire change. That means larzer height of tower is required.
Absorption followed by chemical reaction in the liquid phase is generally used to completely removal of solute from gas mixture.
Why distillation, Why not adsorption or leaching:
In distillation the new phase generated is different from the original by phase, or heat content only. This heat can be removed or added by easy operations. But in case of adsorption or leaching the a foreign substance is introduced to separate the phases. The new phase generated using these processes is a new solution which in turn may be
separated using other separation methods unless the new solution is directly useful. This makes the distillation process to more economical.
Difference between partial condenser and total condenser:
In a total condenser, all of the vapor leaving the top of the column is condensed. Consequently, the composition of the vapor leaving the top tray y1 is the same as that of the liquid distillate product and reflux, xD.
In a Partial condenser, all of the vapor leaving the top of the column is Partially condensed. Consequently, the composition of the vapor leaving the top tray y1 is different from that of the liquid distillate product and reflux, xD.
A partial condenser functions as an equilibrium separation stage, so columns with a partial condenser effectively have an extra ideal stage.
If column Delta P decreases what happens to the purity:
Distillate Purity will increase and separation becomes more easier as driving force is going to increase if Pressure decrease and consequently relative volatility increase. 

When reflux ratio to the column is minimum, what will happen ?
When reflux ratio is minimum, Reboiler duty decrease, diameter of column decreases but number of theoretical trays increases.
What is dew point Temperature?
It is the temperature at which vapour is about to condense.
What is bubble point  Temperature?
It is the temperature at which liquid is about to vaporise.
What is Driving force for Evaporation?
The driving force for evaporation is the gradient of the water vapour pressure near the skin surface.
Dry Bulb Temperature:
The Dry Bulb Temperature refers basically to the ambient air temperature. It is called "Dry Bulb" because the air temperatureis indicated by a thermometer not affected by the moisture of the air.
Wet Bulb Temperature:
The Wet Bulb temperature is the adiabatic saturation temperature. Wet Bulb temperature can be measured by using a thermometer with the bulb wrapped in wet muslin. The adiabatic evaporation of water from the thermometer bulb and the cooling effect is indicated by a "wet bulb temperature" lower than the "dry bulb temperature" in the air.
The rate of evaporation from the wet bandage on the bulb, and the temperature difference between the dry bulb and wet bulb, depends on the humidity of the air. The evaporation from the wet muslin is reduced when air contains more water vapor.
At 100% saturation :
Dry bulb temperature = wet bulb temperature = Dew point

Heat transfer:
Heat transfer is thermal energy in transit due to a spatial temperature difference.
Modes of heat transfer:
●    Conduction
●    Convection
●    radiation
Driving force for Heat Transfer:
Temperature gradient is the driving force for heat transfer.
Conduction Heat Transfer:
Conduction Heat transfer is the transfer of thermal energy between adjacent molecules in a substance due to temperature gradient. Conduction takes place in all forms of matter like solids,liquids, and gases.
In solids conduction heat transfer is due to combination of vibrations of molecules in the lattice and the energy transport by free electrons.
Fourier’s Law:
Heat flux is proportional to the temperature gradient.
q = − k T
Thermal Conductivity:
Thermal conductivity (k) is the intrinsic property of a material which relates its ability to conduct heat. K is measure of propagation of thermal energy.
Effect of temperature on thermal conductivity
●     For Metals, K decrease with increasing temperature
●     For Nonmetals, K increase with increasing temperature
●     For Gases, K increase with increasing temperature
●     For Liquids, K decrease with increasing temperature except water
●     For alloy, value of K is less than that of pure metals
Factors affecting the thermal conductivity:
●     Chemical compositions
●     Temperature & Pressure(till critical)
●     Phase involved
●     Void fraction/porosity in solids
Thermal diffusivity:
It is defined as relative importance of transport capacity of thermal energy to storage capacity of thermal energy.

Heat transfer by basic mode of conduction and advection. Advection refers transport due to bulk fluid motion.
The convection heat transfer mode is sustained both by random molecular motion and by the bulk motion of the fluid within the boundary layer. The contribution due to random molecular motion dominates near the surface where the fluid velocity is low.

Forced convection:
Forced convection when the flow is caused by external means such as by fan, a pump or atmospheric wind.
Free convection:
Free convection the flow is induced by buoyancy force, which are due to density difference caused by temperature variation in the fluid.
Nusselt number:
It is defined as dimensionless temperature gradient at wall.
Prandtl number:
It is defined as relative thickness of hydrodynamic boundary layer to thermal boundary layer or in other words, it is defined as relative importance of momentum diffusivity to thermal diffusivity.
Assumption involved in the derivation of LMTD:
●     Overall heat transfer coefficient is constant throughout the heat exchanger.
●     In case any fluid undergoes phase change, the phase change offers throughout the heat exchanger.
●     The specific heat and mass flow rate of each fluid is constant.
●     No heat loss to surrounding.
●     There is no conduction in the direction of flow neither in a fluid nor in the tube or shell wall.
Purpose of using buffle:
●     It is used to direct the shell side fluid.
●     It also provide support to the tubes.
●     It also increase the shell side heat transfer coefficient by reducing the distance between two adjacent baffles.
NTU is a measure of effectiveness of heat exchanger.

Fins are extended surface which is used to increase heat transfer rate due to increase in effective area.
Gray body:
The gray body is the body for which the monochromatic emissivity does not depends upon the wavelength.
Planck's Law:
It shows the relation between emissive power for black body with temperature and wavelength.
Reboilers are heat exchangerstypically used to provide heat to the bottom of industrial distillationcolumns. They boil the liquid from the bottom of a distillation column to generate vapors which are returned to the column to drive the distillation separation.
Types of Reboiler:
The most critical element of reboiler design is the selection of the proper type of reboiler for a specific service. Most reboilers are of the shell and tube heat exchangertype and normally steam is used as the heat source in such reboilers.
Commonly used heat exchanger type reboilers are:

Kettle Reboilers:
The layout of the kettle reboiler is illustrated schematically in Figure. Liquid flows from the column into a shell in which there is a horizontal tube bundle, boiling taking place from the outside this bundle. The vapor passes back to the column as shown. Kettle reboilers are widely used in the petroleum and chemical industries; their main problems are that of ensuring proper disentrainment of liquid from the outgoing vapor and the problem of the collection of scale and other solid materials in the tube bundle region over long periods of operation.
Vertical Thermosyphon Reboiler:
This type is illustrated in Figure. The liquid passes from the bottom of the tower into the reboiler, with the evaporation taking place inside the tubes. The two-phase mixture is discharged back into the tower, where the liquid settles back to the liquid pool and the vapor passes up the tower as shown. The heating fluid (typically condensing steam) is on the outside of the tubes. The vertical thermosyphon reboiler is less susceptible to fouling problems and in general has higher heat transfer coefficients than does the kettle reboiler. However, additional height is required in order to mount the reboiler.

Horizontal Thermosyphon Reboiler:
Here, the liquid from the column passes in cross flow over a tube bundle and the liquid-vapor mixture is returned to the column as shown. The heating fluid is inside the tubes. This design has the advantage of preserving the natural circulation concept while allowing a lower headroom than the vertical thermosyphon type.
Condenser, device for reducing a gasor vapour to a liquid. Condensers are employed in power plants to condense exhaust steam from turbines and in refrigerationplants to condense refrigerant vapours, such as ammonia and fluorinated hydrocarbons. The petroleum and chemical industries employ condensers for the condensationof hydrocarbons and other chemical vapours. In distilling operations, the device in which the vapour is transformed to a liquid state is called a condenser.
Air-Cooled Condenser:
Air-Cooled types are usually used in the residential and small offices applications. They are used in small capacity systems below 20 tons. The advantages of using this design include not having to do water piping, not necessary to have water disposal system, saving in water costs and not much scaling problems caused by the mineral content of the water. It is also easier to install and has lower initial cost.
Water-Cooled Condenser:
There are 3 types commonly being used. 
●     Shell and tube, 
●     Shell and coil,
●     Double tube. 
The most commonly used is the shell and tube type and are usually available from two tons up to couple of hundred tons. This design has lower power requirements per ton of refrigeration and the compressors can last longer compared to the air-cooled type. A water cooling tower is frequently used for higher capacity application.

Evaporative Condenser:
Evaporative type which is a combination of water and air-cooled.
Types of compressors:
Two principal methods are used to compress gases. The first method is to trap a volume of gas and displace it by the positive action of a piston or rotating member; we call these machines positive-displacement compressors. The second method uses dynamic compression; it is accomplished by the mechanical action of contoured blades, which impart velocity and hence pressure to the following gas.
Where does the head gets developed in a centrifugal compressors:
Head is developed in the compressors partially in the impeller itself and partially in the diffuser / volute.
Pressure ratio of a compressor:
Ration of discharge pressure to suction pressure is known as pressure ratio.
What sort of bearings are used for high speed compressors:
Hydrodynamic type bearing like sleeve or tilting pad bearings are generally used for compressors.

Heat exchanger:
Heat exchangers are devices used to transfer heat energy from one fluid to another.
Material deposits on the surfaces of the heat exchanger tubes may add more thermal resistances to heat transfer. Such deposits, which are detrimental to the heat exchange process, are known as fouling.

Evaporation is the removal of solvent as vapor from a solution, slurry or suspension of solid in a liquid. Solvent is mainly water.
Types of Evaporator:
Evaporator consists of a heat exchanger for boiling the solution with special provisions for separation of liquid and vapor phases. Most of the industrial evaporators have tubular heating surfaces. The tubes may be horizontal or vertical, long or short; the liquid may be inside or outside the tubes.
Why Don't we use odd number of tube passes in Shell and Tube Heat Exchanger:
Odd numbers of tube passes have more complicated mechanical stresses, etc. An exception: 1-1 exchangers are sometimes used for vaporizers and condensers.
Blowers develop little higher pressure in comparison to fans. They are used for pressure below 1.65 Psi. The centrifugal blower produces energy in the air stream by the centrifugal force and a velocity to the gas by the blades. The scroll shaped volute diffuses the air and creates an increase in the static pressure by reducing the gas velocity.


Thermodynamics is a fundamental subjects that describes law’s of the governing occurrences of physical process associated with transfer or transformation of energy.
Zeroth Law of thermodynamics:
When two systems are each in thermal equilibriumwith a third system, the first two systems are in thermal equilibriumwith each other.
First Law of thermodynamics:
The first law of thermodynamic is basically the law of conservation of energy and joule’s has derived expression for the conservation of energy.
The Algebraic sum of net heat and work interaction within system and surrounding in thermodynamic cycle is zero.
Second Law of thermodynamics:
Heat does not flow spontaneously from a colder region to a hotter region, or, equivalently, heat at a given temperature cannot be converted entirely into work. Consequently, the entropyof a closed system, or heat energy per unit temperature, increases over time toward some maximum value. Thus, all closed systems tend toward an equilibrium state in which entropyis at a maximum and no energy is available to do useful work.
Second Law also said that energy has not only quantity it has also quality.
Third Law of thermodynamics:
The entropy of a pure crystalline substance at absolute zero temperature is zero. Because there is no uncertainty about the state of the molecules at that instant.
Thermodynamic properties:
Identifiable and observable characteristics nature of the system by which a system can be specify is called thermodynamic property.

There are two types of thermodynamic properties:
●     Extensive properties
●     Intensive properties
Extensive property:
It Is defined as one which depends on quantity of matter specified in the system.
Intensive property:
It is defined as one which does not depends on the quantity of matter present in the system.
Thermodynamic State:
The system is said to be state when following two condition to be satisfied
●     Properties should be uniform throughout the system(All intensive properties should be uniform throughout the system).
●     They should be invariant with time at least temporarily for a moment when the state of the system is defined.
Thermodynamic System:
●     Control mass system
●     Control volume system
In control mass system the mass of the system is fixed as well as identity is fixed. It is also called close system and it involves energy interaction but no mass interaction.
In the control volume system, the volume of the system is fixed and it involved mas as well as energy interaction and the boundary control volume is called control surface. It is also called open system.
Thermodynamic equilibrium:
For the system to be in thermodynamic equilibrium, the system has to be in thermal, chemical as well as mechanically equilibrium.
If the system is in thermodynamic equilibrium it means there is no driving force for the process to be happen hence that system can be considered as a state. It means all states are in thermodynamic equilibrium always.
Quasi-static process:
Almost stop process or infinitely slow process is said to be quasi-static process.
Concept of degree of freedom:
To define the system at any state large number of variable are available but out of those variables only some of them are sufficient to define the system completely and it is defined as minimum number of independent intensive variable which should be fixed in order to define the system completely.
Different form of energy:
There are two form of energy
●     Energy in transit( it means energy that can be transfer), eg, Heat and work.
●     Energy in store(energy which are stored in the system)
Some points regarding Heat and Work
●     Heat and Work both are free phenomena, it mean it has to cross the boundary.
●     Both are inexact differential, it means heat and work both are path function.

Types of work
●     Displacement work
●     Paddle work
●     Flow work
●     Shaft work
Displacement work: The displacement work is only associated with control mass system because in control mass system, mass is fixed but volume can be change.
Paddle wheel work:If stirred is going to rotate in a container filled with fluid then the temperature of fluid get increase because of mechanical work is done by the stirred on the system and that types of work is called paddle wheel work. No change in volume but there is work.
Shaft work:In open system the shaft has to rotate against the resisting torque and that work is called as shaft work.
Shaft work is associated with open system.
Flow work:The flow work is work required to maintain the flow. It is only associated with open system.
Enthalpy is defined as summation of internal energy and pressure into volume. Enthalpy is used for open as well as for closed system. In open system, PV is called flow work. in closed system, PV is only pressure into volume.

Thermodynamic process:
●     Isothermal Process
●     Adiabatic process
●     Isochoric Process
●     Isobaric process
●     Polytropic Process
Slope of adiabatic curve is more than an isothermal curve.
Adiabatic curve is much more stripper/vertical than the isothermal.
Throttling Process:
In throttling process, When a gas is allowed to flow through a porous plug/capillary tube/Partially open valve, there is a reduction in the pressure because of the resistance to flow.
The enthalpy remain constant during throttling process hence throttling process is called iso enthalpy process.
Joule’s and thomson effect:
●     At inversion point dT/dP=0
●     For an ideal gas dT/dP=0
 Application of throttling process:
●     In the refrigeration and air conditioning system to cool the gas.
●     To find out the dryness fraction of steam.
Free expansion:
●     w=0, Q=0, PdV can’t be zero
●     Free expansion is highly irreversible
●     Uf=Ui which implies Tf=Ti but it is not isothermal
●     n1=n2, P1V1=P2V2
Specific heat:
The specific heat is defined as amount of the heat supplied to the system to raise the temperature of unit mass of substance by unit degree centigrade.
Heat engine:
All device are not able to convert heat energy into work energy but there is a device which operate in cyclic manner called heat engine which able to convert some parts of heat energy into work and it store remaining energy in the form of internal energy then it transfer to the surrounding.
Thermal reservoir:
●     It is hypothetical body which relatively large thermal capacity.
●     Supply or absorbs infinite amount of heat without change in temperature.
●     The reservoir that supply energy in form of heat is called source or high temperature reservoir.
●     The reservoir that absorbs energy in form of heat is called sink or low temperature reservoir.
Properties of heat engines:
●     It operate in a cyclic manner
●     It receive energy in the form of heat from the source
●     It converts some parts of received heat into work
●     It reject remaining heat to sink
Internal Energy:
The sum of all microscopic form of energy is called internal energy.
Ideal solutions:
●     The average intermolecular forces of attraction and repulsion in the solution are unchanged on mixing the solution
●     The volume of the solution varies linearly with composition.
●     the total vapor pressure of the solution varies linearly with composition expressed as mole fraction


Mechanical operation is that unit operation in which we study about the force acting on the solids.
Rittinger’s Law(1867):
It states that work required for crushing is directly proportional to the new surface area created.
Kick’s Law(1885):
It states that work require for crushing a particle will be same for same reduction ratio irrespective of their initial size.
Bond’s Law(1952):
It states that work required to crushing a particle is directly proportional to the square root of surface area to volume ratio of product from a very large feed size.
Work index:
It is defined as the gross energy required in kwh/ton to reduce a very large feed to such a size that 80% of the product may pass through a 100 micrometer screen.
Random movement of solid particle in a Solid-liquid mixture.
Vertically downward movement of solid particles in a Solid-liquid mixture.

Separation of fine size solids from S-L mixture by settling.
Drag force:
Force acting on a body opposite to the direction of flow is called drag force.
Terminal settling Velocity:
It is maximum attainable velocity by solid particles in a fluid at which force by solid particles become equal to resistive force.
It is defined as a unit operation of solid-liquid separation where we pass the slurry through a porous medium under the influence of pressure or vacuum where particulate undissolved suspended solid retain on the surface of the medium and liquid pass through it.
●     Deep bed filtration used for water purification.
●     Cross flow filtration used to concentrate the slurry.
●     Cake filtration used when solid concentration is high.
What is jigging and where it is used:
Jigging is a separation method in which the particle are separated by using the density difference between them. Usually it is used to separate metal slag form metals.

Crude Oil:Crude oil is a multicomponent mixture of hydrocarbons contain billions component and in distillation we get around 25 products.

Classification of crude oil:
●     Paraffinic crude oil 
●     Saturated(Olefinic) long chain hydrocarbons
●     Naphthene crude oil(Saturated ring compound )
●     Aromatic crude oil(unsaturated ring compound)

Products from Crude oil after distillation:
Refinery gas, Gasoline, naphtha, Aviation turbine fuel, Kerosene, Diesel, Gas oil, Lubricating Oil, Petroleum, Light fuel oil, Heavy fuel oil, Wax or Asphalt, Road making Bitumen, Residue
Flash Point/Fire point:
The minimum temperature at which an oil gives out sufficient vapours to form a flammable mixture with the air which catches fire.
If the flashes sustain for at least five seconds then it is known as fire point.
Cloud Point:
The temperature at which the oil become cloudy is known as cloud point of the oil.
Pour Point:
The temperature at which oil refuse to flow is called Pour point of the oil.
Octane Number:
Octane number is the characteristics properties of gasoline. It is defined as percentage by volume of isooctane in a mixture of iso-octane and n-heptane that have same knocking tendency as that of fuel. 

Cetane number:
Cetane number is the characteristics properties of diesel. It is defined as Percentage by volume of cetane in a mixture of cetane and methyl naphthalene which has same characteristics performance in the standard engine that of fuel.
Smoke Point:
Smoke point is characteristics properties of kerosene. It is the height of flame in mm without smoke formation when kerosene is burnt in a standard lamp under controlled condition.
Aniline Point:
It is the lowest temperature at which oil is completely miscible within equal volume of aniline. Aniline Point give qualitative analysis of the aromatic content.
Reid Vapor Pressure:
Reid vapor pressure (RVP)is a common measure of the volatility of gasoline. It is defined as the absolute vapor pressureexerted by a liquid at 37.8 °C (100 °F) as determined by the test method.
Anti-Knocking Agents:
Tetraethyllead, Alcohol,Toluene, Methylcyclopentadiene
Properties of Natural Gas:
Natural gas is a colourless, tasteless, odourless, and non-toxic gas. Because it is odourless, mercaptan is added to the natural gas, in very small amounts to give the gas a distinctive smell of rotten eggs. This strong smell can alert you of a potential gas leak.

Chemical Composition of Natural Gas:
Natural gas is primarily composed of methane, but also contains ethane, propane and heavier hydrocarbons. It also contains small amounts of nitrogen, carbon dioxide, hydrogen sulphide and trace amounts of water.
Chemical Composition of LPG:
LPG is composed mainly of propane and butane
Composition of water Gas:
It contain mainly CO and H2 in the ratio of 1:1
Composition of syngas:
It contain mainly CO and H2 in the ratio 1:2
Composition of producer gas:
It contain mainly CO and N2 in the ratio of 1:2
Cracking is defined as conversion of higher boiling petroleum to lower boiling petroleum fraction under the effect of temperature and pressure. It is an endothermic process.
It is two types.1)Thermal cracking 2) Catalytic cracking