Effect of Non-Uniform Temperature Gradients on the Onset of Convection in a Couple-Stress Fluid-Saturated Porous Medium

The effect of different forms of basic temperature gradients on the criterion for the onset of convection in a layer of an incompressible couple-stress fluid-saturated porous medium is investigated. It is shown that the principle of exchange of stability is valid, and the eigenvalue problem is solved numerically using the Galerkin technique. The parabolic and inverted parabolic basic temperature profiles have the same effect on the onset of convection and similar is the case between piecewise linear temperature profiles heating from below and above. Amongst the various basic temperature profiles, the linear temperature profile is found to be more stabilizing on the onset of instability. In addition, the influence of thermal depth on the criterion for the onset of convection is assessed in the case of piecewise linear temperature profiles. Moreover, an increase in the value of couple-stress parameter is found to delay the onset of convection and to increase the width of convection cells. It is also noted that the critical wave numbers are slightly affected by the nature of basic temperature profiles.