Stability of natural convection for a power-law fluid in a vertical porous slab with open boundaries

The natural convection of a non-Newtonian fluid saturating a vertical porous slab is considered. The Ostwald-de Waele rheological model together with the power-law extended form of Darcy’s law is adopted to model the seepage flow of both shear-thinning (pseudoplastic) and shear-thickening (dilatant) fluids. The porous layer is confined by two open boundaries kept at different temperatures. The linear stability of the basic flow is studied by applying small amplitude perturbations. The neutral stability curves and the corresponding threshold values for the onset of convective rolls are presented for sample cases involving pseudoplastic fluids and dilatant fluids. The Newtonian fluid behaviour is also accounted for as a limiting case.