Conjugate natural convection heat transfer between two fluids separated by a horizontal wall: Steady-state analysis

Abstract

The conjugate heat transfer across a thin horizontal wall separating two fluids at different temperatures is investigated both numerically and asymptotically. The solution for large Rayleigh numbers is shown to depend on two non-dimensional parameters

alpha/epsilon(2), with alpha being the ratio of the thermal resistance of the boundary layer in the hot medium to the thermal resistance of the wall and epsilon the aspect ratio of the plate, and beta, the ratio of the thermal resistances of the boundary layers in the two media. The overall Nusselt number is an increasing function of alpha/epsilon(2) taking a finite maximum value for alpha/epsilon(2) --> infinity and tending to zero for alpha/epsilon(2) --> 0.