Effect of Nonlinear Temperature Profile on Thermal Convection in a Binary Fluid Saturated an Anisotropic Porous Medium

Nur Zarifah  Abdul Hamid; Nor Fadzillah  Mohd Mokhtar; Norihan  Md Arifin; Mohammad Hasan  Abdul Sathar

Authors

Nur Zarifah Abdul Hamid Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
Nor Fadzillah Mohd Mokhtar Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
Norihan Md Arifin Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
Mohammad Hasan Abdul Sathar Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Keywords:

anisotropic, binary, Galerkin method, nonlinear temperature profile, thermal convection

Abstract

The thermal convection in a horizontal binary fluid layer saturated an anisotropic porous medium with the effect of non-uniform temperature profile is studied analytically by linear stability analysis. The generalized eigenvalues problem subjected to various boundaries conditions are solved numerically using Galerkin method. The effects of solute Rayleigh number, Lewis number, mechanical anisotropy and thermal anisotropy parameters corresponding to the six basic temperature profiles on the stationary thermal convection are shown graphically. It is found that the effects of thermal anisotropic parameter, Lewis number and solute Rayleigh number are to reinforce the stability of the system while the effect of mechanical anisotropic parameter is to advance the onset of convection.