Penetrative Brinkman convection in an anisotropic porous layer saturated by a nanofluid

Abstract

The onset of penetrative Brinkman convection in a nanofluid saturated anisotropic porous layer is investigated via uniform internal heating for rigid-rigid, free-free, and lower-rigid and upper-free boundaries. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries and the eigenvalue problem is solved using the Galerkin method. The numerical computations carried out indicated the validity of principle of exchange of stability for all types of velocity boundary conditions. The effect of heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticle concentration Darcy-Rayleigh number and Lewis number is to hasten, while the Darcy number and thermal anisotropy parameter are to delay the onset of convection. In contrast to the regular fluid saturating a Darcy porous medium, the onset of convection for nanofluids is found to be influenced even when the ratio of mechanical anisotropy parameter to thermal anisotropy parameter is unity.