Transient analysis of the natural laminar convection heat transfer process between two fluids separated by a thin horizontal wall

Abstract

The transient conjugate heat transfer across a thin horizontal wall separating two fluids at different temperatures is investigated using both numerical and asymptotic techniques. The solution for large Rayleigh numbers is shown to depend on three nondimensional parameters

alpha is the ratio of the thermal resistance of the laminar boundary layer in the hot medium to the thermal resistance of the wall in the longitudinal direction, epsilon is the aspect ratio of the plate, and beta, corresponds to the ratio of the thermal resistances of the boundary layers in the two media. The nondimensional evolution time is obtained, showing a minimum for finite values of alpha such as epsilon(2) much less than alpha much less than 1.