APPLICATION OF THE PARTIAL ELIMINATION ALGORITHM FOR SOLVING THE COUPLED ENERGY EQUATIONS IN POROUS MEDIA

Abstract

This article discusses the solution of coupled energy equations in local thermal nonequilibrium models for porous media. The decoupled solution approach, in which the interaction between the solid and the fluid temperature fields is treated in an explicit manner, converges very slowly when the interface heat transfer coefficient and/or the specific surface area of the porous medium are large (large Biot number). An attractive alternative to the decoupled approach is the partial elimination algorithm, proposed by D. B. Spalding. In this algorithm, the discretization equations are rearranged so that the resulting equations are more implicit and take directly into account the coupling between the two phases. The convergence rates of these two solution procedures are studied with reference to convective heat transfer in a two-dimensional channel filled with a porous medium. The partial elimination algorithm converges much more quickly than the decoupled procedure, with the number of iterations required for convergence becoming constant for large Biot numbers.