Thermal instability of a power-law fluid-saturated porous layer with an internal heat source and vertical throughflow

The thermal instability of internally heated convection in a porous medium saturated by a power-law (PL) fluid is studied. The governing dimensionless equations are solved using the normal mode approach, which leads to an eigenvalue problem for the linear stability theory. The neutral curves are obtained for different prescribed values of the other physical parameters. The effect of the PL index, internal heat source parameter, and Peclet number on the onset of instability was analyzed. Furthermore, an analytical solution is obtained for the regime of small wave numbers by using asymptotic analysis.