Transient natural convection of micropolar fluids in concentric spherical annuli

Abstract

A numerical analysis has been performed to determine the heat transfer of micropolar fluids by natural convection between concentric spheres with isothermal boundary conditions. Calculations were carried out systematically for several radii ratios and a range of Rayleigh numbers broad enough to determine the critical value at which the mode of heat transfer changes from conduction to natural convection. The effects of the micropolar parameter (F) on the flow and temperature fields have been studied graphically. The skin friction stress on the wall has also been studied and discussed. Results indicate that the heat transfer rate of a micropolar fluid is smaller than that of a Newtonian fluid, and the main controlling parameter is the dimensionless vortex viscosity. Expressions were obtained for Nusselt numbers in the transition and convection regions as functions of Rayleigh number and radii ratio. Comparisons between a Newtonian fluid and a micropolar fluid are also made.