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The purpose of this paper is to analyse the dynamic behaviour of a three-fluid heat exchanger subjected to a step change in the temperature and velocity of the fluids at the inlet.

The analysis is carried out using the finite element methodology, adopting the Galerkin’s approach, using implicit method for transient behaviour.

The effect of step changes in the inlet temperature of hot and cold fluids show that an increase in the fluid inlet temperatures leads to increased outlet temperatures of all fluids and decreased hot fluid effectiveness. The exit temperatures of the fluids do not show any response initially for a certain period of time with the step changes. The time to reach steady state is independent of the step change in inlet temperature of the hot and the cold fluids.

The findings of this paper is limited to constant property situations.

The findings will be useful in designing control and regulation systems of heat exchangers used in different industrial processes and operations, such as in nuclear reactors, cryogenic and petrochemical process plants.

The analysis provides a time frame in which the controls and regulation systems work, so that the necessary safety precautions for the people working in the surrounding area can be taken care of.

As per the best knowledge of the authors, none of the papers so far have discussed the effect of the change in the inlet temperature and velocity of both the fluids. Performance parameters such as effectiveness, time to reach steady state, etc. have not been studied so far.

Heat exchangers working in cryogenic temperature ranges are strongly affected by heat ingression from the ambient. This paper aims to investigate the effect of ambient heat-in-leak on the performance of a three-fluid cross-flow cryogenic heat exchanger.

The governing equations are derived for a three-fluid cross-flow cryogenic heat exchanger based on the conservation of energy principle. For given fluid inlet temperatures, the governing equations are solved using the finite element method to obtain exit temperatures of the three-fluid exchanger. The performance of the heat exchanger is determined using effectiveness-number of transfer units (e-NTU) method. In the present analysis, the amount of ambient heat-in-leak to the heat exchanger is accounted by two parameters H_t and H_b. The variation of the heat exchanger effectiveness due to ambient heat-in-leak is analyzed for various non-dimensional parameters defined to study the heat exchanger performance.

The effect of ambient heat in leak to the heat exchanger from the surrounding is to increase the dimensionless exit mean temperature of all three fluids. An increase in heat in leak parameter (H_t = H_b) value from 0 to 0.1 reduces hot fluid effectiveness by 32 per cent for an NTU value of 10.

The effect of heat-in-leak on a three-fluid cross-flow cryogenic heat exchanger is significant, but so far, no investigations are carried out. The results establish the efficacy of the method and throw light on important considerations involved in the design of such heat exchangers.

The purpose of this paper is to attain higher effectiveness with an introduction of Joule–Thomson effect on a three-fluid heat exchanger with two communications. It also gives a range of parameter values that have to be maintained for achieving effectiveness above 0.85. Attaining effectiveness above 0.85 is very important for the heat exchanger to perform the liquefaction of hot fluid.

The analysis is conducted using Galerkin’s method, a finite element approach.

This investigation determines crucial values for the cryogenic heat exchanger to achieve effectiveness above 0.85. The important findings are as follows: effectiveness above 0.85 is attained if the heat exchanger size is within the range of 8–10; ratio of heat flow resistance between intermediate and hot stream to heat flow resistance between cold and hot stream should be maintained between 1 and 10; the intermediate fluid temperature should be maintained between 0 and 0.2; the ratio of thermal capacity of the hot fluid relative to a cold fluid should be maintained between 1.25 and 1.42; and the ratio of thermal capacity of the hot fluid relative to an intermediate fluid should be maintained between 2 and 2.5.

The investigation has presented a finding for improving the effectiveness of the cryogenic heat exchanger. Higher the Joule–Thomson pressure drop effect, more is the drop in temperature of the fluid resulting in additional cooling or lowering of the fluid temperature. The practical implementation is also explained, i.e. to achieve practically the Joule–Thomson pressure drop in a cryogenic heat exchanger.

To the best of the authors’ knowledge, no investigations were carried out previously on Joule–Thomson investigation on a three-fluid heat exchanger with two communications, for different values of Joule–Thomson pressure drop.