Numerical study of thermal wall boundary effects for transient natural convection between concentric and vertically eccentric spheres

Transient analysis has been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with specified constant heat flux wall boundary conditions. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. The alternating direction implicit method and the successive over-relaxation techniques are applied to solve the finite difference form of governing equations. Results were obtained for steady and transient heat-transfer in vertically eccentric spheres at a Prandtl number of 0.7, with the modified Rayleigh number ranging from 10(3) to 5 x 10(5), for a radius ratio of 2.0 and eccentricities varying from -0.625 to +0.625. Comparisons are attempted between the isothermal boundary condition and the present computations for constant heat flux boundary condition.