Thermosolutal convection within a vertical porous enclosure in the case of a buoyancy ratio balancing the separation parameter

The present work deals with an analytical solution based on the parallel flow assumption obtained in the case of a vertical porous layer heated and salted from the long vertical sides with uniform fluxes of heat and mass, respectively. The study concerns a specific case for which the buoyancy ratio and the separation coefficient are identical. For this particular situation, the external mass flux is compensated by the Soret effect, which leads to zero concentration gradient on the vertical walls. The problem is first analyzed by solving numerically the full governing equations and the aspect ratio required to satisfy numerically the parallel flow conditions is determined. Analytical solutions for the pseudo-conductive and boundary layer regimes are proposed and discussed. The N – Le plane is divided into regions with specific behaviors and the results obtained are presented in terms of boundary layer thickness, heat transfer (Nusselt number), and mass transfer (Sherwood number) versus the main governing parameters.