Efficiency of Heat Exchanger: Description and Formula

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The term efficiency of heat exchanger is not defined as a unique concept in scientific resources. However, to determine the efficiency of any system, an ideal state is considered, based on which the degree of proximity of the system to that state is defined as efficiency. In the case of a heat exchanger, the ideal state is not definitively determined. But methods are provided for this purpose, which we will discuss below.

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How We Write this Blog Post about How to Calculate the Efficiency of Heat Exchangers?

Heat exchangers are devices that transfer heat between two or more fluids. They are used in many industrial applications, such as power plants, chemical plants, and refrigeration systems. The efficiency of a heat exchanger is a measure of how well it transfers heat from one fluid to another. It is essential to calculate the efficiency of a heat exchanger to ensure that it is operating correctly and efficiently. A poorly performing heat exchanger can lead to increased energy consumption, reduced productivity, and even equipment failure.

Writing a blog post about calculating the efficiency of heat exchangers requires some experience in the field. We had knowledge about the types of heat exchangers and their applications. We also had experience in calculating the efficiency of heat exchangers using different methods such as LMTD (Logarithmic Mean Temperature Difference) and NTU (Number of Transfer Units). We also provide tips and tricks for calculating the efficiency of heat exchangers and discuss common mistakes that people make when calculating efficiency.

Analysis of a Heat Exchanger

There are generally two ways to evaluate the performance of heat exchangers. One is Log Mean Temperature Difference, abbreviated as LMTD, and the other is the Effectiveness NTU-method, denoted by ε-NTU.

Meanwhile, by defining the efficiency of heat exchangers, another general method can be considered as a method for analyzing the performance of heat exchangers. This criterion shows how far the heat exchanger is from its best and most ideal design point and how much change it needs to reach this desired state.

Definition of Efficiency of a Heat Exchanger

The heat exchange process between two fluids with different temperatures using solid walls occurs in various engineering applications. The tool to achieve this exchange is a heat exchanger. Some applications like air conditioning, power generation, waste heat recovery, and chemical processing use this device.

The basis of the work of a heat exchanger is that the hot fluid enters the heat exchanger at temperature T₁ and its heat capacity is C_hot. Also, the cold fluid with the heat capacity of C_cold enters temperature t₁; in the meantime, the hot fluid loses its heat, and its temperature drops to T₂. It delivers heat to the cold fluid to increase its temperature to t₂ and leave the heat exchanger at this temperature.

In general, the efficiency of heat exchange is defined as the ratio of the amount of heat transferred in the actual case to the amount of heat in the ideal case, in the optimal case (equation below).

$\eta =\frac{q_{act}}{q_{ideal}}$

The heat transfer rate in the actual state is defined as the basis of the rate of change of cold or hot fluid temperature.

$q_{act}=C_{hot}\left(T_1-T_2\right)$

$q_{act}=C_{cold}\left(t_2-t_1\right)$

Also, the optimal heat transfer can be calculated as the following equation.

$q_{ideal}=UA\left(\overline{T}-\overline{t}\right)$

We denote the surface at which heat exchange takes place by A. Also, the overall average heat transfer coefficient is equal to U. The phrase in parentheses is called the Arithmetic Mean Temperature Difference (abbreviated as AMTD) and is calculated as follows.

$\overline{T}-\overline{t}\mathrm{=}\frac{T_1+T_2}{2}-\frac{t_1+t_2}{2}$

The best heat transfer occurs in the case of the counter flow heat exchanger.

Also, to find the overall average heat transfer coefficient (U) we can use the following relationship.

$\frac{1}{UA}=\frac{1}{U_{hot}A_{hot}}=\frac{1}{U_{cold}A_{cold}}$

A general equation can be used to calculate the efficiency of heat exchanger developed for a number of known exchangers.

$\eta =\frac{{\mathrm{tanh} \left(Fa\right)\ }}{Fa}$

In the equation above, Fa is the fin analogy number which can be evaluated for some common heat exchanger as what follows. In the following section, we refer to counter flow and parallel flow heat exchangers.

Counter Flow Heat Exchanger

The direction of flow of hot and cold fluids in counter flow converters is the opposite. In this can we have the following relation to calculate Fa.

$Fa=NTU\frac{(1-C_r)}{2}$

In this equation, NTU is the number of transfer units and is equal to:

$NTU=\frac{UA}{C_{min}}$

$C{_{min}}=min(C{_{hot}},C{_{cold}})$

Also, C_r is the capacity ratio and defined as:

$C_r=\frac{C_{min}}{C_{max}}$

Parallel Flow Heat Exchanger

In a parallel flow heat exchanger, hot and cold fluids move in the same direction. To find Fa the following relation is suggested.

$Fa=NTU\frac{(1+C_r)}{2}$

Evaluating the Heat Exchanger Using LMTD Method

Consider q is the rate of heat transfer within a heat exchanger between the hot and cold fluids. Because heat transfer between the exchanger and its surroundings is negligible, we rewrite the transferred heat based on the parameters we defined in previous parts as following.

$q=C_{hot}\left(T_1-T_2\right)=C_{cold}\left(t_2-t_1\right)$

The temperatures in the equations point to the mean fluid temperatures at the designated sections.

To write the heat transfer using the overall heat transfer coefficient, we consider another expression as follows.

$\mathrm{\Delta }\mathrm{T}=T_{hot}-T_{cold}$

Since ΔT varies with location through the heat exchanger, it is important to deal with an equation in the form of:

$q=UA\mathrm{\Delta }T_m$

ΔT_m is mean temperature difference. Now, we need to establish an expression for this parameter. It is shown in the references that the appropriate temperature difference should be expressed based on the logarithmic mean temperature difference, which is defined as follows.

$\mathrm{\Delta }T_m=\mathrm{\Delta }T_{lm}=\frac{\mathrm{\Delta }T_1-\mathrm{\Delta }T_2}{{\mathrm{ln} \left(\frac{\mathrm{\Delta }T_1}{\mathrm{\Delta }T_2}\right)\ }}=\frac{\mathrm{\Delta }T_2-\mathrm{\Delta }T_1}{{\mathrm{ln} \left(\frac{\mathrm{\Delta }T_2}{\mathrm{\Delta }T_1}\right)\ }}$

Thus,

$q=UA\mathrm{\Delta }T_{lm}$

In the definition of logarithmic mean temperature difference (LMTD), indices 1 and 2 are related to the sections from which entry or exit occurs. This means that one of the following two conditions happens.

Parallel Flow Heat Exchanger

In this type of heat exchangers, as two fluids enter and exit in the same directions, we have:

$\mathrm{\Delta }T_1=T_1-t_1$

$\mathrm{\Delta }T_2=T_2-t_2$

Counter Flow Heat Exchanger

Since in counter flow heat exchangers, hot and cold fluid flows enter or leave in opposite directions:

$\mathrm{\Delta }T_1=T_1-t_2$

$\mathrm{\Delta }T_2=T_2-t_1$

Based on these equations, the calculation of the actual heat transfer can be performed.

Evaluating the Heat Exchanger Using ε-NTU Method

Based on this method, the effectiveness of the exchanger is defined. Of course, it is necessary to determine the maximum allowable heat transfer rate from a heat exchanger. This amount can be achieved by a counter flow heat exchanger of infinite length. In such an exchanger, one of the two fluids will have the maximum allowable temperature change; that’s mean:

${\mathrm{\Delta }T}_{max}=T_1-t_1$

The first case is to assume C_c<C_h. Then we have:

$q_{max}=C_c\left(T_1-t_1\right)$

And if C_c>C_h, the maximum allowable heat transfer is:

$q_{max}=C_h\left(T_1-t_1\right)$

After summarizing the last two relationships, we can write:

$q_{max}=C_{min}\left(T_1-t_1\right)$

$C_{min}={\mathrm{min} \left\{C_c,C_h\right\}\ }$

The efficiency of the heat exchanger or its effectiveness can now be defined as follows:

$\varepsilon =\frac{q}{q_{max}}$

It can be shown for each heat exchanger:

$\varepsilon =f\left(NTU,\ C_r\right)$

Both NTU and C_r are introduced in the previous sections. There are some relations developed to calculate the function mentioned above. Each expression belongs to a specific class of exchangers. In the following, some of these classes and the related equations are presented.

Parallel Flow Heat Exchanger

Efficiency of heat exchanger with the parallel arrangement is:

$\varepsilon =\frac{1-{\mathrm{exp} [-NTU\left(1+C_r\right)]\ }}{1+C_r}$

Counter Flow Heat Exchanger

Efficiency of heat exchanger with the parallel pattern is:

(C_r<1)

$\varepsilon =\frac{1-{\mathrm{exp} [-NTU\left(1-C_r\right)]\ }}{1-C_r{\mathrm{exp} [-NTU\left(1-C_r\right)]\ }}$

(C_r=1)

$\varepsilon =\frac{NTU}{1+NTU}$

Shell and Tube Heat Exchanger

Efficiency of heat exchanger with the shell and tube structure (n shell passes) is:

$\varepsilon =\left[{\left(\frac{1-{\varepsilon }_1C_r}{1-{\varepsilon }_1}\right)}^n-1\right]-\left[{\left(\frac{1-{\varepsilon }_1C_r}{1-{\varepsilon }_1}\right)}^n-C_r\right]$

Where ε₁ is the efficiency of heat exchanger with one pass shell and tube structure.

${\varepsilon }_1=2{\left[1+C_r+{\left(1+C^2_r\right)}^{\frac{1}{2}}\times \frac{1+{\mathrm{exp} {\left[-(NTU\right)}_1{\left(1+C^2_r\right)}^{\frac{1}{2}}]\ \ }}{1-{\mathrm{exp} {\left[-(NTU\right)}_1{\left(1+C^2_r\right)}^{\frac{1}{2}}]\ \ }}\right]}^{-1}$

Cross Flow Heat Exchanger

To calculate the efficiency of heat exchanger with cross flow formation, usually, a correction factor is regarded for the logarithmic mean temperature difference. This means:

$\mathrm{\Delta }T_{lm}=F\mathrm{\Delta }T_{lm.counter\ flow}$

The correction factor is determined using diagrams for different types of heat exchangers.

In the following figure, you can see the curves to find the effectiveness of a cross flow heat exchanger for different values of NTU and C_r.

Heat Exchangers with C_r=0

The efficiency of heat exchanger is calculated with the following equation.

$\varepsilon =1-{\mathrm{exp} \left(-NTU\right)\ }$

What Factors Affect the Efficiency of Heat Exchangers?

Heat exchanger efficiency is highly influenced by the velocity of the operating fluid, so increasing the flow rate is recommended from time to time. The increased turbulence prevents fouling tendencies that would otherwise damage the heat exchangers and impede fluid flow.

Which Is the Most Efficient Heat Exchanger?

Plate exchangers are the most efficient because they have turbulent flow on both sides. High heat transfer coefficient and turbulence caused by the even distribution of flow are important. Regenerative plate heat exchangers, however, are limited to low viscosities. It may be necessary to use a special tubular for high viscosities.

FAQs about How to Calculate the Efficiency of Heat Exchangers

What affects heat exchanger efficiency?

The opening temperature of the heat pipe, the rate of fluid filling, the physical properties of the liquid refrigerant, the work temperature of the tube, the angle, the tube spacing, the tube length, the hot and cold fluid flow, and wind speed are just a few of the variables that affect how well a heat pipe heat exchanger transfers heat.

What is the best efficiency of heat exchanger?

Even when such characteristics are taken into account in estimates made by the industry, plate heat exchangers are still routinely proven to be the most efficient of all heat exchangers. They frequently reach efficiency levels of around 90%.

How do you prevent a heat exchanger from failing?

The majority of failures in steam-heated exchangers are caused by fluid thermal expansion. In the heated fluid system, relief valves can be placed to help avoid failure brought on by thermal expansion and cycling. It’s also a good idea to provide a way to handle fluid expansion.

Why is the efficiency of a heat exchanger important?

It is often suggested to increase the flow rate because the speed of the working fluid has a big effect on how well the heat exchanger works. Increased turbulence reduces the likelihood of fouling, which might harm heat exchangers and obstruct fluid flow.

How efficient is a heat exchanger temperature?

The ratio between the actual heat transfer in a heat exchanger and the ideal heat transfer rate is known as the heat exchanger efficiency.

How can thermal efficiency be improved?

The thermal efficiency of gasoline engines may be improved by diluting and increasing the compression ratio. Slow combustion, greater cooling loss, and engine banging are among the problems that are related to increased compression ratios.

Conclusion

In this article, we reviewed the efficiency of heat exchanger, explained the methods introduced to calculate this parameter, and mentioned the equations for different types of heat exchangers.