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Analytical and numerical model of transient heat transfer in a single tube row heat exchanger

Taler D.

Archives of Thermodynamics

2007

Vol. 28, no. 1

51-64

Cross-flow tubular heat exchangers are widely applied as condensers and evaporators in air conditioners and heat pumps or as air heaters in heating systems. There are analytical and numerical mathematical models of heat exchangers of that type to determine the steady state temperature distribution of fluids. In this paper the transient response of a single-row tubular cross-flow tube - and - fin heat exchanger is analyzed. Partial differential equations for both hot and cold fluid are solved by the Laplace transform method with numerical inversion and by the finite-difference (finite-volume) method. The transient response of one-row tube - and - fin heat exchanger due to step change of air temperature is calculated using both developed approaches. Good agreement between the analytical predictions (the Laplace transform method and analytical exact steady state solution) and the finite difference solution has been found. After eliminating the time, using the Laplace transform, a simpler system of partial equations is formed, which can be solved analytically. In view of the complex form of the achieved solutions, the inverse Laplace transform is obtained numerically by the method due to Crump improved by de Hoog. The solutions presented in the paper can be used to analyze the operation of heat exchangers in transient conditions and can find application in systems of automatic control or in the operation of heat exchangers.