Onset of convection in a couple-stress fluid-saturated porous medium: effects of non-uniform temperature gradients

Abstract

Onset of convection in a layer of couple-stress fluid-saturated porous medium is investigated for different types of basic temperature gradients. The boundaries are considered to be adiabatically insulated to temperature perturbations. The eigenvalue equations of the perturbed state obtained from the normal mode analysis are solved analytically using a regular perturbation technique with wave number as a perturbation parameter and also numerically using the Galerkin technique. The critical stability parameters obtained from these two techniques are in excellent agreement and an increase in the value of couple-stress parameter is found to delay the onset of convection. The results also indicate that the piecewise linear temperature profile hastens the onset of convection when compared to linear, parabolic, and inverted parabolic temperature profiles. In addition, the influence of thermal depth on the critical conditions is assessed in the case of piecewise linear temperature profiles, and it is observed that the critical thermal depth decreases marginally with an increase in the couple-stress parameter.