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

The buoyancy-induced flows of non-Newtonian fluids in a horizontal flu id saturated porous layer is studied analytically and numerically usin g the power-law model to characterize the non-Newtonian fluid behavior . A constant heat flux is applied for heating and cooling the two oppo sing walls of the layer while the other two walls are insulated. On th e basis of a modified Darcy equation the problem is solved analyticall y, in the limit of a thin layer, using a parallel flow approximation a nd an integral form of the energy equation. Solutions for the flow and temperature fields, and Nusselt numbers are obtained explicitly in te rms of the modified Rayleigh number R and the power-law index n. A num erical 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.