NATURAL-CONVECTION OF NON-NEWTONIAN FLUIDS IN A HORIZONTAL POROUS LAYER

The buoyancy-induced flows of non-Newtonian fluids in a horizontal fluid saturated porous layer is studied analytically and numerically using the power-law model to characterize the non-Newtonian fluid behavior. A constant heat flux is applied for heating and cooling the two opposing walls of the layer while the other two walls are insulated. On the basis of a modified Darcy equation the problem is solved analytically, in the limit of a thin layer, using a parallel flow approximation and an integral form of the energy equation. Solutions for the flow and temperature fields, and Nusselt numbers are obtained explicitly in terms of the modified Rayleigh number R and the power-law index n. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also conducted. A good agreement is found between' the analytical prediction and the numerical simulation.