Thermal instability and heat transfer in a multi-layer system subjected to uniform heat flux from below

Abstract

Thermal instability and heat transfer in a system consisting of multiple layers separated by solid partitions are studied. A closed form solution is derived when the system is subjected to a uniform heat flux from below and adiabatic boundary conditions at two ends. For limiting cases of single and double layers, the critical Rayleigh numbers agree with previously published results. The solid partitions are found to be most effective in suppressing flow and heat transfer when they are equally distributed in a single fluid. The equivalent Rayleigh number is shown to be the weighted average of the product of the thermal conductivity and the height of each layer.