Parallel Flow Convection in a Shallow Horizontal Cavity Filled with Non-Newtonian Power-Law Fluids and Subject to Horizontal and Vertical Uniform Heat Fluxes

Natural convection heat transfer in a shallow horizontal rectangular enclosure is considered. The enclosure contains non-Newtonian fluids and is exposed to cross-gradients of temperatures. The power-law model is used to characterize the non-Newtonian fluid behavior. Analytical solution is obtained in the central region of the cavity in terms of stream function and temperature fields, assuming a parallel flow in the central part of the enclosure. The analytical results are compared against the numerical solution, obtained by solving the full governing equations using a finite difference method. It is demonstrated that multiple steady state convective flows are possible.