Thermosolutal convection in a darcy porous medium with anisotropic permeability and thermal diffusivity

Abstract

A problem of thermosolutal convection with reaction in an anisotropic porous medium of Darcy type is investigated. The Darcy model is employed as the momentum equation with the density being a linear function in temperature and salt concentration. Two cases are considered: heated below and salted above system and heated and salted below system. We allow the permeability and thermal diffusivity to be anisotropic tensors. Particularly, we restrict consideration to horizontal isotropy in mechanical and thermal properties of the porous medium. The energy method is used to study the non-linear stability aspect of the problem. The D2 Chebyshev Tau method is implemented to solve the associated system of equations, with the corresponding boundary conditions, and to obtain the non-linear stability boundaries below which the solution of the system is globally stable. The effect of the reaction rate, the mechanical anisotropy parameter, and the thermal anisotropy parameter on the stability of the system is discussed and presented graphically. We find that the thermal anisotropy parameter has the opposite effect to that of the mechanical anisotropy parameter on the stability of the system.