Explicit Solution to Predict the Temperature Distribution and Exit Temperatures in a Heat Exchanger Using Differential Transform Method

Abstract

In this paper, a simple mathematical model based on energy transfer between the hot and cold fluids in a single-pass cross-flow plate-type heat exchanger is considered and the governing equations are solved using the differential transform method (DTM). DTM transforms the governing equations and its boundary conditions into a set of recurrence relations with some algebraic equations. These relations are further reduced, and then from the inverse transform, the dependent variable (temperature distribution) is obtained as a series solution in explicit form. The temperature distribution and the exit temperatures inside a single-pass cross-flow heat exchanger under steady state are obtained successfully for a single channel. The results obtained are then compared with those derived from Laplace Adomian decomposition method, finite difference method and the effectiveness-NTU approach. The comparison of the solution by DTM with other widely used industrial solutions is also shown, and the merits of the proposed method are presented. The predicted temperature distribution by the DTM is accurate, and it has excellent agreement with the effectiveness-NTU results and other well-known published results.