Soret driven thermosolutal convection in a shallow porous layer with a stress-free upper surface

摘要

Purpose - Thermodiffusion or Soret effect is a phenomenon that can be encountered in many applications. However only little is known about this phenomenon, particularly in the case of sparsely packed media (i.e. Brinkman media). The aim of this paper is to study numerically and analytically the effect of thermodiffusion on the onset of natural convection in a horizontal Brinkman porous layer with a free-stress upper boundary. Design/methodology/approach - The study is performed by solving numerically the governing equations for different combinations of the governing parameters. An analytical solution is also developed in the case of a shallow layer using the approximation of a parallel flow in the core region to predict the critical conditions corresponding to the onset stationary, subcritical and Hopf convection. Findings - The results obtained show that, in the presence of Soret effect, the numerical and analytical solutions agree well for long enough layers. The thermodiffusion parameter can affect considerably the supercritical and sub-critical Rayleigh numbers and heat and mass transfer characteristics in the layer. It is also shown that the plane Le-φ can be divided into three main regions with specific and different behaviours. Originality/value - The Soret effect can play a stabilizing or a destabilizing role and this, depending on the sign of the separation parameter, φ.