Transient natural convection of micropolar fluids between concentric and vertically eccentric spheres

Micropolar fluids in transient analysis have been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with specified isothermal boundary conditions. Calculations were carried out systematically for several different eccentricities and a range of Rayleigh numbers to determine the average Nusselt numbers which are affected by the micropolar parameters (F) on 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 and transient heat-transfer in vertically eccentric spheres at a Prandtl number of 0.7, with the Rayleigh number ranging from 103 to 5 × 105, for a radius ratio of 2.0 and eccentricities varying from −0.625 to +0.625, and for the value of micropolar parameters are 0, 1 and 5 respectively. Comparisons are attempted between the Newtonian fluid and micropolar fluid.