HEAT EXCHANGERS AND LMTD

HEAT EXCHANGERS

In day to day life the use of heat exchangers is unavoidable. Not only in domestic but also commercially it has high viability. In air conditioning, refrigeration, chemical and production plants etc it is used since decades.

When two fluid are at different temperature then the appliance known as heat exchangers are used to facilitate heat transfer in between these two fluid. In heat exchanger there is a wall which separates the two fluids. Both conduction and convection of heat transfer phenomenon occur in the appliance. Conduction occurs through the wall separating the two fluids and convection occurs in fluid layer.
The construction of heat exchanger is very simple. A very simple heat exchanger consists of two concentric tubes in which hot fluid is allowed to flow through inner tube and cold fluid flows in outer concentric tube.

TYPES OF HEAT EXCHANGERS ON BASIS OF FLOW OF FLUID:-

• Parallel flow heat exchanger
• Counter flow heat exchanger
• Cross flow heat exchanger

Depending on the mode of flow of fluid or we can say depending on the direction of hot and cold fluid type of heat exchangers are characterized. In parallel flow heat exchangers the hot and cold fluid in the concentric tube move in same direction. In counter flow heat exchangers the case is reverse, here the fluid enters from opposite ends and the flow is is in opposite direction. Both the hot and cold fluid moves in opposite direction. Such heat exchangers provides greater heat transfer per unit volume.

Other type of its classification is cross flow heat exchanger in which fluid flow is perpendicular to each other. A best heat exchanger is one which provides maximum surface area for heat transfer and minimum resistance in the flow of fluid, otherwise the rate of heat transfer may reduce.

fig:-heat exchanger

Area density of heat exchanger is nothing but the ratio of heat transferring area of heat exchanger to the volume. Area density decides the compactness of heat exchangers. When the area density is greater than 750 m^2/m^3.

LOGARITHMIC MEAN TEMPERATURE DIFFERENCE (LMTD)

Transfer of heat from one fluid to another is given by Q = UA (LMTD). Where "U" is overall heat transfer coefficient. "A" is the area cross section and the mean temperature difference is indicated by LMTD.

Consider a parallel flow heat exchanger of length  "L" . The temperature distribution of cold and hot flow along the length is given by logarithmic mean temperature difference (LMTD).

                      LMTD = (ΔT1-ΔT2)/ln(T1/T2)

Where  ΔT1 and ΔT2 are temperature difference of fluid at entry and exit. The average temperature difference is ( ΔT1 + ΔT2)/2.

The overall heat transfer  "U" depends on the flow velocity and not on the direction of flow. The overall heat transfer coefficient across the flow in a heat exchanger is given by

where "hi" is convective heat transfer coefficient at inside the surface of wall, "ho" is heat transfer coefficient outside of wall surface of pipe and thickness be delta. "k" is coefficient of thermal conductivity of material.

NTU method of effectiveness of heat exchanger:-
Heat exchanger effectiveness is defined as ratio of actual heat transfer to maximum possible heat that can be transferred. 

E = actual heat transfer/maximum heat that can be transferred

Larger is the value of NTU, depicts greater the size of heat exchanger.

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BOILING AND CONDENSATION

 Boiling and condensation

At constant pressure if the temperature of the liquid is raised to saturation temperature then the liquid boils.  Similarly condensation occurs when the temperature of vapour is lowered to saturation temperature at constant pressure condition, the vapour changes to liquid. Such heat transfer occurring during boiling and condensation is categorized under convection mode of heat transfer. As purely heat is transferred by fluid motion.

Condensation and boiling depends mainly of the three factors. These are surface tension, latent heat of vaporization and liquid-gas interface. Large amount of latent heat is absorbed and released during boiling and condensation. At equilibrium condition the temperature remains constant. The rate of heat transfer during condensation and boiling is very high as compared to other modes of convection heat transfer.

BOILING

Many of us gets confused when we hear the two words i.e. boiling and evaporation. Most of us think that both these words have same meaning. To some extent it is correct because in both boiling and evaporation phase change takes place from liquid to vapour. But friends, at grass root level there is large difference between these two words.

At certain temperature when the vapour pressure is less than the saturation pressure evaporation occurs. The best example for it is evaporation of sweat from our body.

Boiling can be understood as when the vapour pressure crosses the saturation pressure at certain temperature. The example can be heating of water. Saturation pressure is nothing but the pressure exerted by the atmosphere or the weight of atmosphere. At any instant when the vapour pressure of liquid exceeds the atmospheric pressure, the liquid starts boiling.

This can be explained at microscopic level.When we heat the liquid, it molecules absorbs energy and gains kinetic energy. At certain temperature the kinetic energy crosses threshold limit and overcomes the saturation pressure or atmospheric pressure and it starts boiling. The process is started by formation of bubble at the interface of liquid and vapour and slowly it starts rising. The bubbles are formed at super critical temperature. The bubbles are formed due to surface tension at the interface region and as the temperature increases the surface tension decreases, as a results bubbles are lost and vapour rises.

Boiling is of two types depending on the motion of bulk fluid:-

1) Pool boiling

2) Flow boiling

When there is no bulk fluid motion is is referred as pool boiling. The fluid is stationary and any motion is by natural convection current. On the other hand flow boiling is associated with bulk motion of fluid. Flow is provided by applying external devices like pump.

BOILING REGIMES

1) Natural convection boiling

2) Nucleate boiling

3) Transition boiling

4) Film boiling

When the liquid is heated two- three degrees above the saturation temperature then the fluid motion is by natural convection current.

Nucleate boiling can be sub divided into two parts. In the first part very few bubbles are formed at the interface and they are dissipated as soon as they leave the surface. In the second part the bubble formation increases. Colum of vapour is generated. The column of vapour rises up to the interface and then rises up in atmosphere. The bubbles at the bottom forms the cluster and it decreases then heat transfer rate.

In transition boiling as large number of bubbles covers the heater surface heat transfer rate decreases. This will act as insulator. This region lies in between nucleate boiling and film boiling.

Film boiling is important as because if the temperature of the heater surface is further increased radiation mode of heat transfer becomes predominant. Under film boiling the heat flux is minimum. This is because the heater surface is completely covered by vapour and bubble. There is no possibility of transfer of heat. But if the temperature of heater is further increased heat transfer is increased and radiation heat transfer is observed.

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HEAT TRANSFER BY CONDUCTION,CONVECTION AND RADIATION

As we all know energy exists in various forms. Heat is also a form of energy. In this section our prime importance is to study about the transfer of heat energy. Temperature is function of heat, which gives us idea of degree of coldness or hotness of a body. Heat can flow from one point to another as a result of temperature difference. Always remember that heat flows from higher temperature to lower temperature.

So we can say that heat transfer is branch of science and engineering that deals with rate of heat transfer between bodies.

MODES OF HEAT TRANSFER:-

In this context we will know the modes of heat transfer. There are three known modes of heat transfer. These are conduction, convection and radiation. All these three forms require temperature difference. When two bodies are at same temperature no heat transfer takes place.

CONDUCTION:-

It is mode of heat transfer from one point to another in the same body or from one body to another body when they are in direct contact with each other. It is transfer of energy from more energetic particle to subsequently less energetic particle due to direct interaction.

Solids has compact structure and the atoms and molecules are tightly bound. When these atoms gain energy they start vibrating about their mean position and subsequently other atoms in contact with it also starts vibrating at their mean position. In this way heat is propagated in solids. Hence conduction is mode of heat transfer without appreciable movement of molecules rather only molecular interaction is needed.

The various factors that affect the rate of heat transfer by conduction is:-

• Temperature difference across the medium
• Medium material
• Geometry of medium
• Thickness of material

Heat flow through single homogeneous solid is directly proportional to area of section at right angle to heat flow and change in temperature with respect to length of path of flow of heat.

         Q  =  -kA(THOT-TCOLD)

                -------------------------------------------------
                     L 

K=Coefficient of thermal conductivity.

A=Area of section.
L=Length

Unit of rate of heat flow=Watt

Unit of K=watt/meter*Kelvin

Some important points:-

1. Conduction of heat occurs fastest in metal and slowest in insulator. Conductivity of non-metal lies between metal and insulator.

2. Thermal conductivity (K) is measure of material ability to conduct heat. Iron's thermal conductivity is 120 times more than water.

3. With increase in density of gas its conductivity decreases.

4. Gases having higher molecular weight has low thermal conductivity (K).

CONVECTION HEAT TRANSFER

Convection is another mode of heat transfer which takes place between solid and adjacent liquid or gas which is in motion. The rate of heat transfer depends on the speed of fluid flow. In other words it can be said that greater is the speed of fluid greater is the convection heat transfer. If the fluid motion is not high then the heat transfer between the solid body and the fluid as result of temperature difference will be by pure conduction.

     
Convection heat transfer is given by

                               Q = hA ΔT

Where h is convection heat transfer coefficient
A is area
ΔT is change in temperature

Convection is broadly classified as under

1.     Free natural convection

2.     Forced convection

Free natural convection:-

When there is temperature difference between the fluid layers, the density will also differ depending on the temperature of layers. As a result fluid motion is caused by buoyancy.

The denser portion will experience greater force of gravity hence it will tend to move down as compared to less denser layer which will experience less force.

Forced convection:-

Forced convection is situation in which the fluid is forced to flow over the surface by external means like blowers, pumps and fans. Also when the fluid phase change occurs it is characterized under convection. This is due to the fact that vapour bubbles rise during boiling and during condensation it falls under gravity.

RADIATION HEAT TRANSFER

Apart from conduction and convection, radiation is another mode of heat transfer which does not require any intervening medium for transfer of heat. All bodies whose temperature is above absolute zero temperature emit thermal radiations. It is surface phenomenon in which electromagnetic waves are emitted from the body which is caused by change in electronic configuration of atoms and molecules of the body. Radiation heat transfer is fastest heat transfer among all the three modes. 

Numerical problems.

1) Heat transfer occurs from?

1) Cold body to hot body
2) Hot body to cold body
3) Bigger body to small body
4) In any direction.

2) In conduction, greater the coefficient of thermal conductivity depicts __________ conduction.

1) Lesser
2) Greater
3) Constant

4) Radiation mode of heat transfer requires

1) Some intervening medium for transfer of heat.
2) No medium for heat transfer.
3) Both, depending on situation.

5) How many mode of heat transfer is possible?

1) Two
2) Three
3) Four
4) One

  

Be first to answer the question via comment.
Thankyou.

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DIFFUSION, OSMOSIS AND DIFFUSION IN SOLIDS

                      

Many people gets confused between the two terms diffusion and osmosis. In this section we will focus on these two related terms and study briefly diffusion in solids.

Diffusion occurs when atoms and molecules gain kinetic energy and crosses the threshold limit as a result of which it randomly moves to other location and occupies other new place. This movement of atoms and molecules resulting due to gain of kinetic energy is called diffusion. This can be understood by example shown below. Due to kinetic energy gain the atoms and molecules move to other interstitial sites or location.  Diffusion occurs in solid, liquids as well as gases. Various solid diffusion is explained in this context.

It is very important to know about diffusion in solids when we are learning material science. The diffusion effect various parameters like surface hardening, edge hardening etc which are very important in industrial application.

Osmosis is phenomenon which depends on the concentration of two fluid. The fluids are separated by a semi permeable membrane in such a manner that solvent can pass through the permeable membrane being smaller in size as compared to solute. The solvent concentration is very less as compared to solute. Osmosis occurs from lower concentration to higher concentration. 

Consider case when on the both side of semi permeable membrane there is same fluid ( say water). In such case there is no osmosis phenomenon occurrence. I t occurs when there is pressure differential. Osmosis is of great biological importance. Pictorial representation of osmosis can be observed below. 

Diffusion in solids

Diffusion in solid occurs to rise in thermal energy of atoms or molecules which allows them to move at different location in a solid crystal. We all know well that atoms and molecules are closely packed in a solid crystal. Hence it is practical to say that diffusion will be zero in case of perfect solid crystal. But in actual case such perfect crystal does not imperfections in it which becomes predominant at high temperature as diffusion rate increases at high temperature.

Effects of diffusion:-

• Phase change in alloy.
• Molecular bonding.
• Surface hardening/characteristics.
• Grain propagation.
• Edge hardening.

Type of diffusion:-

• Surface diffusion 
• Volume diffusion
• Inter diffusion
• Self diffusion

Surface diffusion:-

When the migration or movement of atoms takes place at the surface of the crystal, then it is called surface diffusion. The atoms or molecule moves from one interstitial site to another. The figure depicts the surface  atomic movement. It is the vapor-solid interface. 

Volume diffusion:-

It is movement of atom in a matter in bulk amount throughout the material. One atom can move anywhere inside the crystal and occupy interstitial position. This type of diffusion plays an important role in change of property of entire crystal. The distribution of diffused atom may be uniform or may not be uniform.

Self diffusion:-

In this case atoms does not remain in equilibrium at on interstitial site and hence move here and there abruptly. The above figure depicts self diffusion of a crystal.

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