Significance of the inconstant viscosity and internal heat generation on the occurrence of Darcy-Brinkman convective motion in a couple-stress fluid saturated porous medium: An analytical solution

In this analysis, the collective effect of temperature-reliant viscosity and internal heat generation on the appearance of convective motion in couple-stress fluids saturated a thin porous layer is investigated employing linear stability principle. The significant influences of viscosity deviation parameter Q, internal heat generation parameter H-S, couple-stress parameter C-s and Darcy number Da on the stability of the arrangement are obtained analytically and presented graphically in term of the critical thermal Darcy-Rayleigh number R-t,R-c. Below the critical values, no convective motion arises in the considered system. It is recognized that the viscosity deviation parameter Q and internal heat generation parameter H-S have destabilizing effect, while the couple-stress parameter C-s and the Darcy number Da show stabilizing effect on the stability of the fluidic system. By increasing the couple-stress parameter C-s from 0.2 to 0.4 and the Darcy number Da from 0.25 to 0.50, the critical thermal Darcy-Rayleigh number R-t,R-c increased approximately 21% and 51%, respectively.