Onset of thermal convection in a horizontal porous layer saturated by a power-law fluid

A horizontal porous layer saturated by a non-Newtonian fluid is taken into account. The fluid is a Ostwald-De Waele type of fluid. The layer is heated from below while the upper boundary is isothermal. The lower boundary is impermeable and the upper one is free. A fully developed basic throughflow is considered. The basic state is perturbed by employing small amplitude perturbations such that a linear stability analysis is performed. The disturbances are assumed to be normal modes and a system of ordinary differential equations governing the perturbation dynamics is obtained. These ODEs form an eigenvalue problem that is solved numerically: both the neutral stability curves and the threshold values for the onset of convection are presented.