The onset of convection of power-law fluids in a shallow cavity heated from below by a constant heat flux

This paper reports an analytical and numerical study of natural convection in a shallow enclosure filled with a non-Newtonian fluid. Thermal boundary conditions of the Neumann type are applied on the horizontal walls of the enclosure while the vertical walls are assumed adiabatic. A power law model is used to characterize the non-Newtonian fluid behavior of the fluid. The governing parameters for the problem are the thermal Rayleigh number Ra, power-law index n, Prandtl number Pr and cavity aspect ratio A. An analytical solution, valid for an infinite layer, is derived on the basis of the parallel flow approximation. Rigid–rigid, free–free and rigid–free hydrodynamic boundary conditions are considered. It is demonstrated that, for shear-thinning fluids, the onset of convection is subcritical. For shear thickening fluids, convection is found to occur at a supercritical Rayleigh number equal to zero. The effects of the non-Newtonian behavior on the fluid flow, temperature field and heat transfer are discussed. A good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations.

► We examine natural convection in an enclosure filled with a non-Newtonian fluid.
► A power law model is used to characterize the non-Newtonian fluid behavior.
► Both the cases of pseudoplastic and dilatants fluids are investigated.