Analytical, numerical and scale analysis study of thermal diffusion effect on free convection boundary layer flows in a slender porous layer

Abstract

This paper reports an analytical, numerical and scale analysis study of free convective heat and mass transfer flows coupled with thermal diffusion effect in a slender vertical porous cavity subjected to cooperating lateral temperature and concentration gradients. The top and bottom walls of the cavity are assumed to be adiabatic and impermeable to mass transfer. This study aims to analyze the different hydrodynamic, thermal and solutal behaviors developed in laminar boundary layer flow regime reached at high Rayleigh numbers. Based on the parallel flow approximation, an analytical solution of the problem is derived in the extreme case of heat-driven (N≪1) free convection. The obtained analytical results are validated numerically by generating the solutions of the full governing differential equations by means of finite-difference method (FDM). To estimate the order of magnitudes involved in the boundary layer regime, a scale analysis of the conservation equations is performed. The order of magnitudes of boundary layer thickness, Nusselt and Sherwood numbers are derived in this study. For all these quantities, the trends predicted by the scaling law theory are found to be in good agreement with those of the parallel flow approach. The combined effects of Rayleigh and Soret numbers on the boundary layer thickness, flow intensity and heat and mass transfers are illustrated graphically for representative values of N, Le and A_r, and the main results are highlighted and discussed.