Natural convection in a horizontal porous cavity filled with a non-Newtonian binary fluid of power-law type

Abstract

This paper investigates the onset of motion and the resulting convective motion in a shallow porous cavity filled with a non-Newtonian binary fluid. The two horizontal walls of the system are subject to constant fluxes of heat and solute while the two vertical ones are impermeable and adiabatic. A power law model is used to characterize the non-Newtonian fluid behavior of the binary solution. The governing parameters for the problem are the thermal Rayleigh number R T , power-law index n, Lewis number Le, buoyancy ratio φ, aspect ratio of the cavity A, normalized porosity ξ, and parameter a defining double-diffusive convection ( a = 0) or Soret induced convection ( a = 1). An analytical solution, valid for shallow enclosures ( A >> 1), is derived on the basis of the parallel flow approximation. Criteria, for supercritical and subcritical onset of motions, are predicted. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations.