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# Analysis of a Heat Exchanger

What are the problems associated with a heat exchanger? What is fouling? What do LMTD and NTU methods imply? How can the outlet temperatures of the heat exchanger be determined?

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__Table of Contents:__In the last __post__, we got to know the importance of a heat exchanger and then we also dealt in deep with all the possible classifications of heat transfer. We move a further step in this post. During its due course of time, heat exchanger performance might deteriorate. One of the reasons for this could be fouling. We will be covering fouling along with the analysis of the heat exchanger, that is, determining the effectiveness of a heat exchanger. This can be achieved by two methods - the log mean temperature difference method (LMTD) as well as the number of transfer units (NTU) method.

**Fouling**

With time, on the heat transfer surfaces of the heat exchangers, there could possibility of deposits accumulation. These accumulated deposits could directly affect the performance of the heat exchanger by posing as resistance and thereby slowing down the heat transfer rate.

This process is termed fouling and the net effect on the performance of heat exchanger due to the deposit accumulation is determined by fouling factor, also defined as the additional thermal resistance incurred due to fouling.

**Types of fouling**

Precipitation - In this type of fouling, solid particles suspended in the fluid get deposited on the heat transfer surfaces. This is a very common type of fouling and is more prominent in regions with hard water. A heat exchanger might have fine tubes and accumulation of such deposits may adversely affect the performance of the heat exchanger. The way to avoid precipitation is by treating the water so as to remove all the solid components before allowing it to flow through the heat exchanger.

Corrosion - Corrosion is another common form of fouling and is more prominent in chemical industries. The fouling here occurs due to the accumulation due to products resulting from the chemical reaction on the heat transfer surfaces. To avoid this type of fouling, generally, the coating is provided to the metal surfaces or the metal surfaces are replaced by plastic.

Biological fouling - This type of fouling occurs due to algae formation, especially in the warm fluid zones. To avoid biological fouling, chemical treatments are usually recommended.

The fouling factor depends on the fluid velocity in the heat exchangers and the operating temperatures. Fouling factor is large when fluid velocity is low and/or when the operating temperatures are high.

**Analysis of heat exchangers**

The overall purpose of a heat exchanger is to transfer heat between two fluids at different temperatures. Hence, it is very important to know the temperature change to be achieved in the fluid or to know the outlet temperatures of the hot and cold fluid streams. In order to achieve each of the above tasks, methods namely the log mean temperature difference method (LMTD) and a number of transfer units (NTU) method are used respectively.

**Assumptions**

To analyse the effectiveness of the heat exchanger, the following assumptions are considered.

Heat exchangers are modelled as steady-flow devices since the operating conditions do not change with respect to time.

The mass flow rate of hot and cold fluid is constant

The inlet and outlet temperature, as well as the velocity, is assumed to be constant.

The changes in potential and kinetic energy are negligible

Specific heat of the fluid is assumed constant over a specified temperature range

The outer surface of the heat exchanger is considered as perfectly insulated with no heat loss to the surrounding.

**Log mean temperature difference method (LMTD)**

Inside the heat exchanger, the temperature difference between the hot and the cold fluid varies at different points. At the inlet of the heat exchanger, this temperature difference is large while at the outlet, the temperature difference is relatively less. The temperature difference is exponential, hence it is advisable to consider a mean temperature difference for calculating the heat transfer rate. The mathematical expression for the rate of heat transfer is given as

where U and As represent the overall heat transfer coefficient and total heat transfer surface area respectively. The Delta T1 and T2 represent the temperature difference between the two fluids at the inlet and at the outlet. The calculations for either a condenser or a boiler can be derived using this expression. Thus, the method comes handy in use for heat exchanger analysis once we know the inlet and the outlet temperatures of the hot and cold fluids. However, while designing a specific heat exchanger wherein the outlet temperatures are not known, the LMTD method is quite tedious and hence we go for the alternative method given by Kays and London called as effectiveness-NTU method or simply the NTU method.

**Number of transfer units method (NTU)**

NTU method is derived from a nondimensional parameter 'heat transfer effectiveness' defined as the ratio of actual rate of heat transfer to the maximum possible rate of heat transfer. Here, the actual rate of heat transfer is calculated by performing energy balance on the hot/cold fluids while the maximum possible rate of heat transfer is calculated by determining the maximum possible temperature difference in the heat exchanger, which is usually the difference of temperature between hot and cold fluid at the inlet.

The mathematical expression for NTU is given as

where U and As represent the overall heat transfer coefficient and total heat transfer surface area respectively while Cmin represent a smaller heat capacity ratio.

The effectiveness is usually expressed as a function of NTU and c, where c is the capacity ratio defined as the ratio of the smaller heat capacity ratio to the larger heat capacity ratio. Typically we use effectiveness relations and charts extensively while using NTU methods.

**Important conclusions from effectiveness relations and charts**

Discussing the charts and effectiveness relations would steal the essence of this topic and would seem to be very technical. Hence, these lengthy relations and elaborative graphs have been avoided but the necessary conclusions driven from them have been discussed in brief below.

The effectiveness value ranges between 0 and 1.

Counter-flow heat exchangers have the highest value of effectiveness amongst all other types for the same NTU and capacity ratio.

For NTU less than 0.3, effectiveness does not depend on the capacity ratio.

The capacity ratio value ranges from 0 to 1.

**Summary**

The solid particles suspended in fluid get accumulated on the heat transfer surface, thereby impacting the performance of the heat exchanger. This process is fouling.

LMTD and NTU methods are adopted for the analysis of heat exchangers.

Effectiveness relations and charts are used in NTU methods which help in predicting the outlet temperatures of the heat exchanger