Drag Effect on Prats Problem Using Power-Law Saturating Fluid: Convective Instability

The paper focuses on the study of the onset of thermal instability in a horizontal porous layer saturated by power-law fluid and undergoing a throughflow. The lower impermeable wall is supposed to have a uniform constant temperature while the upper free surface is held at uniform heat flux. The saturating fluid in a solid matrix flows according to the Forchheimer model where the non-Newtonian fluid density fulfills the theory of the Oberbeck-Boussinesq approximation. The normal modes approach is applied to obtain the eigenvalues problem. An analytical solution is developed to solve the resulting ordinary differential equations. The finding shows the effect of the drag number on the stability of the power law fluid in both cases of weak and strong flow rates.