## Exchange of Heat

The heat exchanger is a combination of two words ''Heat'' and ''Exchanger''. It is a mechanical device that is used to exchange heat energy between two fluids.

## Applications of Heat Exchanger

Exchangers are used for exchanging thermal energy of the fluids. The applications of the exchangers are found in the following engineering processes:

- To transfer heat energy from hotter to colder fluid.
- To evaporate the fluid flowing in the tubes of the heat exchanger.
- To condense the vapor flowing in the tubes of the heat exchanger.
- Cooling of the engine of an automobile.
- For heating and cooling purposes.
- In chillers’ towers for the cooling of water.

## Heat Exchangers are classified into the following types

1) On the Basis of construction:

- Double pipe type
- Shell and tube type
- Coiled type
- Plate and frame type

2) On the basis of the transfer process:

- Direct contact.
- Indirect contact.

3) On the basis of flow arrangement

- Parallel Flow
- Counter-flow
- Cross-flow

4) On the basis of the number of passes:

- Single-pass
- Multiple passes

5) On the basis of the phase

- Gas to gas
- Liquid to liquid

## Parallel Flow Heat Exchanger

In the parallel-flow heat exchanger, both the hotter and the colder fluid flow in the same direction. The flow configuration of a parallel flow exchanger is shown in the diagram.

## Counter- Flow Heat Exchanger

In the counter-flow heat exchanger, the hotter fluid and the colder fluid flow in the opposite direction. The flow configuration of a counter-flow exchanger is shown in the diagram.

The counter flow heat exchanger is most widely used for the heating and cooling process.

## Terms used in the Analysis of a Heat Exchanger

**1) Heat Transfer**: The rate at which heat energy is transferred from the fluid at higher temperature to that at lower temperature is called the rate of heat transfer. It is denoted by ‘Q’.

If a fluid of mass (m) at a temperature (T) is flowing through the tubes of an exchanger, the amount of heat that can be transferred by the fluid is expressed by the following equation:

**Q=mcΔ T**

Where

- Q is the heat transferred
- m is the mass of fluid
- c is the specific heat capacity of the fluid
- Δ T is the change in temperature

**2) Heat Pipe:** Heat pipes are the superconductors used to obtain high rates of heat flow. Different materials used for the manufacturing of heat pipes are silver, aluminium, etc.

**3) Thermal heat Capacity:** It is the product of mass and specific heat capacity of a certain fluid.

## Analysis of Heat Exchanger

The rate of heat transfer in the heat exchanger is related to the following parameters:

- Overall heat transfer coefficient
- Surface area
- Inlet and outlet temperature of the fluids.
- Specific heat of the fluid

Let **h** denote the hot and **c** denote the cold fluid.

The heat lost by the hotter fluid is:

**Q=m _{h }C_{h }Δ T**

m_{h }C_{h }is the heating capacity or the thermal capacity

The heat absorbed by the colder fluid

**Q=m _{c }C_{c }Δ T**

m_{c }C_{c} is the cooling capacity

The total heat transferred in the exchanger is:

**Q=U A T _{m}**

- U is the overall heat transfer coefficient
- T
_{m}is the logarithmic temperature difference. - A is the surface area

## Logarithmic Temperature Difference

To calculate the LMTD of heat exchangers, the following assumptions are made:

- The steady-state flow of fluid
- Constant overall heat transfer coefficient
- Specific heat of the fluids is constant
- Kinetic and potential energy change is zero.

The logarithmic temperature difference is the mean of the two temperatures (the temperatures of the hot and cold fluid). It is also denoted by the symbol θm. If subscript 1 denote the inlet of the heat exchanger and subscript 2 denote the outlet of the heat exchanger.

### For parallel flow heat exchanger

${\theta}_{m}=\frac{\left({\theta}_{1}-{\theta}_{2}\right)}{\mathrm{ln}({\theta}_{1}-{\theta}_{2})}$

$\begin{array}{l}{\theta}_{1}={T}_{h1}-{T}_{\begin{array}{l}c2\\ \end{array}}\\ {\theta}_{2}={T}_{h2}-{T}_{c1}\end{array}$

Hence the rate of heat transfer for the counter-flow exchanger is greater than the parallel flow exchanger.

For the evaporator and condenser, the LMTD is equal for both counter flow and the parallel flow exchanger.

## Fouling

When the fluid is flowing through tubes of the heat exchanger, the tube surface gets covered with ash, dirt, and scale, etc. The process of deposition of ash and scale on the surface is called the Fouling process.

The fouling process reduces the rate of heat transfer. The following parameters affect the fouling process:

- The velocity of the fluid
- The temperature of the fluid
- Properties of tube material.

if **hs** is the heat transfer coefficient of scaling, then the reciprocal of **hs** is called the fouling factor.

The overall heat transfer coefficient is dependent on the following parameters:

1)The flow rate or the discharge rate of the fluid

2) Fouling factor

3) Thickness of the tube

4) Thermal properties of the fluid.

### How to calculate the surface area of the tube

If d is the diameter of the tube in which fluid is flowing, the surface area is expressed as:

**A=ΠdL**

- d is the diameter of the tube
- L is the length of the tube

### Volumetric flow rate

The volumetric flow rate of the fluid is equal to the product of the cross-section area of the tube and the velocity of the fluid.

If V is the velocity and A is the cross-section area of the liquid flowing in a pipe, the volumetric flow rate of liquid is expressed as AV.

## Effectiveness

The effectiveness of an exchanger is expressed as the ratio of the actual heat transfer to the maximum possible heat transfer.

Mathematically it is expressed as:

$\epsilon =\frac{Q}{{Q}_{\mathrm{max}}}$Actual heat transfer:

Q=**C _{h }Δ T=C_{c }Δ T**

Maximum heat transfer:

${Q}_{\mathrm{max}}={C}_{\mathrm{min}}({t}_{h1}-{t}_{c1})$C_{min} is the minimum fluid capacity rate

## NTU (Number of Transfer Units)

NTU is an analytical approach to determine the heat transfer rate. NTU is a dimensionless number that defines the effectiveness of a heat exchanger.

If NTU increases, the effectiveness increases.

If the outlet temperature of the fluid is not given, the NTU technique is used to determine the rate of heat transfer.

**Capacity ratio**

It is a dimensionless number denoted by the letter (R) and it is the ratio of the minimum heat capacity to the maximum heat capacity of the fluid.

For evaporator and condenser, the value of R=0

For a gas turbine, the value of R=1

## Context and Application

This topic is significant for both graduate and undergraduate courses, especially for:

- Bachelors in Technology in Mechanical Engineering
- Masters in Technology in Mechanical Engineering
- Bachelors in Science - Physics
- Masters in Science - Physics

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