TRANSIENT NATURAL-CONVECTION HEAT-TRANSFER BETWEEN CONCENTRIC SPHERES

The transient laminar natural convection heat transfer of fluids between two concentric isothermal spheres is investigated theoretically. The fluid is initially at rest and then the inner wall is subjected to a step change of temperature. The stream function/vorticity formulation is employed for the analysis because of the symmetry of the problem. The transient behavior of the flow field and its subsequent effect on the temperature distribution for different Rayleigh numbers and radius ratios are analyzed by finite difference methods. Forward differences are used for the time derivatives and second-order central differences for the space derivatives. The alternating direction implicit method is used for solution of the discretization equations. The results show that the Rayleigh number and radius ratio have a profound influence on the temperature and flow fields. The results of average Nusselt numbers are also compared with those of previous experimental and numerical investigations. Excellent agreement is obtained.