Steady-state analysis of the conjugate heat transfer between forced counterflowing streams

Abstract

In this article we analyze the steady-state conjugate heat transfer process between two counterflowing forced streams separated by a wall with finite thermal conductivity, The influence of the longitudinal heat conduction through the wall is very important on the overall heat transfer rates and has been analytically deduced, The most important parameters are denoted by alpha, beta, and epsilon. The parameter alpha corresponds to the ratio of the solid heat conduction in the longitudinal direction to the convected heat towards the hotter fluid, beta is the relationship between the thermal boundary-layer thickness of both fluids, and epsilon is the aspect ratio of the plate. In the asymptotic limit alpha --> infinity and using the Lighthill approximation, it can be shown that the balance equations reduce to a single integro-differential equation with only the parameters alpha and beta. This limit is analyzed using regular perturbation techniques, On the other hand, for alpha --> 0, the governing equations can also be solved using asymptotic methods. The distribution of the temperature of the plate as well as the overall heat transfer rates have been obtained in closed form and compared with the numerical solution for different values of the parametric set, In general, close to the analyzed limits, a good agreement is achieved.