# Heat Transfer/Heat Exchangers

Heat Exchangers
Heat exchangers are devices designed to transfer heat from one fluid to another, without the fluids coming into contact. There are a wide variety of applications for heat exchangers, for example: radiators, air conditioning and power plants.

### Types of Heat Exchangers

Heat exchangers are mainly classified by their flow arrangements. There are two basic types of heat exchangers: in line flow and cross flow. In addition so-called regenerative heat exchangers are used in some industries.

#### In line

In in line exchangers, the hot and cold fluids move parallel to each other. Heat exchangers where the fluids move in the same direction are referred to as parallel flow or co-current, exchangers where fluids move in the opposite direction are referred to as counter flow or counter-current.
In Parallel flow heat exchangers, the outlet temperature of the "cold" fluid can never exceed the outlet temperature of the "hot" fluid. The exchanger is performing at its best when the outlet temperatures are equal.
Counter flow heat exchangers are inherently more efficient than parallel flow heat exchangers because they create a more uniform temperature difference between the fluids, over the entire length of the fluid path. Counter flow heat exchangers can allow the "cold" fluid to exit with a higher temperature than the exiting "hot" fluid. However many industrial heat exchangers are more complex. To save space, fluids may go to the end of a unit then go back again, perhaps several times. Each time a fluid moves through the length is known as a pass. For example, one fluid may make 2 passes, the other 4 passes. Thus parts of the heat exchanger may be co-current, others counter-current, and calculations must take this into account.

#### Cross flow

In cross flow exchangers, the hot and cold fluids move perpendicular to each other. This is often a convenient way to physically locate the inlet and outlet ports in a small package, and moreover this is more efficient than counter flow design. Thermodynamically the effectiveness of cross flow heat exchanger is better than counter flow and parallel flow heat exchangers. Logarithmic mean temperature difference (LMTD) will always be greater for cross flow compared to parallel flow heat exchanger. For a given flow rate and at given inlet, outlet temperatures, a parallel flow heat exchanger requires maximum flow area whereas a cross flow heat exchanger requires minimum flow area and a counter flow heat exchanger area lies between two extreme limit. For this reason parallel flow heat exchanger not used in practice and cross flow arrangement is preferred. Therefore cross flow arrangement is most commonly used because it is easier to provide inlet and outlet header connections with cross flow rather than counter flow. Cross flow heat exchanger provide compact design of heat exchanger. Multi-pass cross flow heat exchanger can be easily manufactured compared to parallel and counter flow heat exchangers.
Some actual heat exchangers are a mixture of cross flow and counter flow due to design features that force the flow paths to wind back and forth.

#### Regenerative

Regenerative heat exchangers store heat and release it later. They contain a large mass of material which does not leave the exchanger but heats up (or in some cases, melts, absorbing latent heat) as hot fluid is passed through. Thus heat from one batch operation can be used to warm up the next one. Alternatively, they can be used in pairs (or more) with one absorbing heat from a hot stream while the other is discharging it to a cold stream. In some designs the bed of heat absorbing material moves to carry heat from one stream to another.
The term regenerative heat exchanger is also used for counter-flow exchangers in which one side is fluid entering the process and the other side fluid leaving the process.

### Analysis of Heat Exchangers

Imagine a simple heat exchanger in which a pipe containing one fluid (A) is surrounded by a jacket filled with another fluid (B) as shown in the diagram. Each fluid has a steady inlet temperature, and it is desired to know what area is necessary to achieve a given set of outlet temperatures.
In order to analyze a heat exchanger like this, one must resort to differential analysis because the temperature drop between fluids A and B is not constant.
To begin, there are three ways to express the total amount of heat that is exchanged between fluids A and B:
${\dot {Q}}={\dot {m}}_{B}*(C_{p})_{B}*(T_{B2}-T_{B1})$
${\dot {Q}}={\dot {m}}_{A}*(C_{p})_{A}*(T_{A2}-T_{A1})$
${\dot {Q}}=U*A_{ex}*\Delta {T?}$
The first two are well-defined, since the quantities $(T_{B2}-T_{B1})$ and $(T_{A2}-T_{A1})$ don't change over the course of the heat exchanger. Unfortunately, the third expression's value does depend on where in the heat exchanger you evaluate it, since the change in temperature there is the difference in temperature between the two fluids A and B. Our goal now is to show how we can use the temperature information we have to calculate the total flow of heat or, more usefully, take the total amount of heat that's flowed and calculate the area of the heat exchanger.