Asymptotic Analysis of the Transient Conjugate Heat Transfer Process Between Two Forced Counterflowing Streams

Abstract

In this paper we analyze the transient 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 on the overall heat transfer rates is very important and has been analytically deduced. We present a classification of the solutions of the problem in terms of two main parameters: $\varepsilon $, the ratio of thickness to the height of the wall, which is small in our analysis, and $\alpha $, measuring the ratio of the thermal resistance of one of the boundary layers to the thermal resistance of the wall. Conditions under which longitudinal conduction and transversal temperature variations are important in the solid are clarified. In the asymptotic limit $\alpha \rightarrow \infty $ and using the Lighthill approximation, it can be shown that the balance equations reduce to a single integrodifferential equation with only the parameters $\alpha $, $\beta $, where $\beta $ relat...