Heat Exchangers Study Notes for Chemical Engineering

By Vineet Vijay|Updated : August 21st, 2017

Classification of Heat Exchangers

Heat exchangers are generally classified according to the relative directions of hot and cold fluids:

Cross flow:  Fluids passes perpendicular to each other (figure 5.1 (a))

Counter Flow – the two fluids flow through the pipe but in opposite directions. A common type of such a heat exchanger is shown in Fig. 5.1(b). By comparing the temperature distribution of the two types of heat exchanger

Parallel Flow – the hot and cold fluids flow in the same direction. Fig 5.1 (c)  depicts such a heat exchanger where one fluid (say hot) flows through the pipe and the other fluid (cold) flows through the annulus.


Fig: Orientation of fluid stream in heat exchanger (a) cross flow   (b) counter current flow (c) parallel flow

Counter flow and parallel flow heat exchangers are most common type of heat exchanger and we will focus on only these two types in detail. 

Let  are the  mass flow rate of hot fluid and cold fluid respectively

are the heat capacity of the hot fluid and the cold fluid respectively

are the inlet and outlet temperature of hot fluid fluid respectively .

And are the  inlet and outlet temperature of cold fluid respectively

Figure 5.2 shows an important parameter, mcp, the product of mass flow rate (m) and the specific heat, cp, of the fluids. The product mcp is called the rate of heat capacity.
The overall energy balance of the heat exchanger gives the total heat transfer between the fluids, q, expressed by

The figure also demonstrates the relative variation of the two fluid temperatures through the heat exchanger, which is influenced by whether http://nptel.ac.in/courses/103103032/module8/images/16.jpg is greater or less than http://nptel.ac.in/courses/103103032/module8/images/17.jpg.

In particular, for counter flow, examination of the sketches in fig 5.2  shows that limiting condition for maximum heat transfer is determined by whether http://nptel.ac.in/courses/103103032/module8/images/16.jpg is greater or less than http://nptel.ac.in/courses/103103032/module8/images/17.jpg.

When, http://nptel.ac.in/courses/103103032/module8/images/16.jpghttp://nptel.ac.in/courses/103103032/module8/images/17.jpgthe maximum possible heat transfer is determined by the fact that the hot fluid can be cooled to the temperature of the cold fluid inlet. Thus, for http://nptel.ac.in/courses/103103032/module8/images/16.jpghttp://nptel.ac.in/courses/103103032/module8/images/17.jpg





Figure :Temperature profiles of (a) parallel flow, and (b) counterflow, for different map  inequalities

For the other case when the limit is determined as the cold fluid is heated to the inlet temperature of the hot fluid.


http://nptel.ac.in/courses/103103032/module8/images/21.jpgThus for the counter flow exchanger, the above two set equations show that the maximum possible heat exchanger is determined in terms of the inlet parameters. The maximum possible heat exchange may be determined (eq. 5.1) by the fluid stream having low heat capacity rate. Thus for counter current flow we have

The  is for the fluid having lower value of .

In case of parallel flow, regardless of the relative sizes of the two stream the limiting heat transfer condition is determine by the fact that the two fluid streams approach the same outlet temperature. Thus, Tho → Tco condition can be found out by the weighted average of the inlet streamhttp://nptel.ac.in/courses/103103032/module8/images/26.jpgFrom the above equations (5.1 and 5.2) it can be calculated for a given inlet conditions the counter current flow arrangement always has a better potential for heat transfer as compared to parallel flow arrangement.

We find that the temperature difference between the two fluids is more uniform in counter flow than in the parallel flow. Counter flow exchangers give the maximum heat transfer rate and are the most favored devices for heating or cooling of fluids.

Log Mean Temperature Difference (LMTD)

The rate of heat exchange between the hot fluid and the cold fluid can be calculated from the equation below 

 Q = U A s ΔTlm   

Where, U = over all heat transfer coefficient ,As = area of heat transfer and ΔTlm     = log mean temperature difference

Figure 5.7: Temperature profile (a) parallel flow   (b) counter flow

The driving force of heat exchange in a heat exchanger is generally not uniform through the heat exchanger and this must be taken into account in the analysis. From the heat exchanger equations shown earlier, it can be shown that the integrated average temperature difference for either parallel or counter flow may be written as.

 The effective temperature difference calculated from this equation is known as the log

Fouling Factors in Heat Exchangers

Heat exchanger walls are usually made of single materials. Sometimes the walls are bimettalic (steel with aluminium cladding) or coated with a plastic as a protection against corrosion, because, during normal operation surfaces are subjected to fouling by fluid impurities, rust formation, or other reactions between the fluid and the wall material. Material deposits on the surfaces of the heat exchanger tubes may add more thermal resistances to heat transfer. Such deposits, which are detrimental to the heat exchange process, are known as fouling. Fouling can be caused by a variety of reasons and may significantly affect heat exchanger performance. With the addition of fouling resistance, the overall heat transfer coefficient, Uc, may be modified as:

 where Rf is the fouling resistance or the fouling factors.

The Equivalent diameter

Figure: flow through annulus

Heat Exchangers Effectiveness - Useful Parameters

In the design of heat exchangers, the efficiency of the heat transfer process is very important. The method suggested by Nusselt and developed by Kays and London is now being extensively used. The effectiveness of a heat exchanger is defined as the ratio of the actual heat transferred to the maximum possible heat transfer.

Let  and  be the mass flow rates of the hot and cold fluids, ch and cc be the respective specific heat capacities and the terminal temperatures be Th and Th for the hot fluid at inlet and outlet,  and  for the cold fluid at inlet and outlet. By making an energy balance and assuming that there is no loss of energy to the surroundings, we write


From Eq. (10.13), it can be seen that the fluid with smaller thermal capacity, C, has the greater temperature change. Further, the maximum temperature change of any fluid would be  and this Ideal temperature change can be obtained with the fluid which has the minimum heat capacity rate. Thus,


Or, the effectiveness compares the actual heat transfer rate to the maximum heat transfer rate whose only limit is the second law of thermodynamics. An useful parameter which also measures the efficiency of the heat exchanger is the 'Number of Transfer Units', NTU, defined as

NTU = Temperature change of one fluid/LMTD.

Thus, for the hot fluid: NTU = , and

for the cold fluid:


we have  and

The heat exchanger would be more effective when the NTU is greater, and therefore,

  NTU = UA/Cmin  

An another useful parameter in the design of heat exchangers is the ratio the minimum to the maximum thermal capacity, i.e., R = Cmin/Cmax,

where R may vary between 1 (when both fluids have the same thermal capacity) and 0 (one of the fluids has infinite thermal capacity, e.g., a condensing vapour or a boiling liquid).

Effectiveness - NTU Relations

For any heat exchanger, we can write: . In order to determine a specific form of the effectiveness-NTU relation, let us consider a parallel flow heat exchanger for which . From the definition of effectiveness , we get


 for a parallel flow heat exchanger, we have




Similarly, for a counter flow exchanger,



Heat Exchanger Effectiveness Relation


Fin Efficiency and Fin Effectiveness

  • Fins or extended surfaces increase the heat transfer area and consequently, the amount of heat transfer is increased. The temperature at the root or base of the fin is the highest and the temperature along the length of the fin goes on decreasing Thus, the fin would dissipate the maximum amount of heat energy if the temperature all along the length remains equal to the temperature at the root. Thus, the fin efficiency is defined as:

 ηfin = (actual heat transferred) / (heat which would be transferred if the entire fin area were at the root temperature)

  • In some cases, the performance of the extended surfaces is evaluated by comparing the heat transferred with the fin to the heat transferred without the fin. This ratio is called 'fin effectiveness' E and it should be greater than 1, if the rate of heat transfer has to be increased with the use of fins.

For a very long fin, effectiveness

  • E = with fin / without fin

= (hpkA)1/2θo /hAθo =  (kp/hA)1/2

And ηfin = (hpkA)1/2θo (hpLθo) = (hpkA)1/2 / (hpL)


i.e., effectiveness increases by increasing the length of the fin but it will decrease the fin efficiency.

 Expressions for Fin Efficiency for Fins of Uniform Cross-section

  • Very long fins:

  • For fins having insulated tips:


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