Thermal effects of the micropolar fluid parameters on the laminar free convection in spherical annuli with mixed boundary conditions

The effects of micro-rotation and vortex viscosity in micropolar fluids have been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with specified mixed boundary conditions. Calculations were carried out systematically for several different eccentricities and a range of modified Rayleigh numbers to determine the average Nusslet numbers which are affected by the micropolar parameters (F) of the flow and temperature fields. The skin friction stress on the walls has also been studied and discussed. The governing equations, in terms of vorticity, stream function, temperature and angular momentum are expressed in a spherical polar coordinate system. Results were obtained for steady heat-transfer in spherical annuli at a Prandtl number of 0.7, with the modified Rayleigh number ranging from 10³ to 5 × 10⁵, for a radius ratio of 2.0 and eccentricities varying from −0.625 to +0.625. Comparisons are attempted between the Newtonian fluid and micropolar fluid.