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 fates is very important and has been analytically deduced. We present a classification of the solutions of the problem in terms of two main parameters: epsilon, 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 --> infinity 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 relates the boundary layer thicknesses. This limit is analyzed using regular perturbation techniques. On the other hand, for alpha --> 0, the governing equations can be solved using asymptotic techniques. The evolution in time and space of the temperature of the plate has been obtained in closed form and compared with the numerical solution for different values of the parametric set. In general, close to the studied limits, a very good agreement is achieved.