Pseudosteady-state natural convection inside spherical containers partially filled with a porous medium

A computational study of the pseudosteady-state two-dimensional natural con vection within spherical containers partially filled with a porous medium i s presented. The computations are based on an iterative, finite-volume nume rical procedure using primitive dependent variables, whereby the time-depen dent continuity, momentum and energy equations in the spherical coordinate system are solved within the composite system. The natural convection effec t is modeled via the Boussinesq approximation, whereas the Darcy Law is uti lized to treat the porous medium. For a reference case, flow and temperatur e field details during the transient evolution to the pseudosteady-state ar e presented. It is shown that the dominant transport mechanism at the early stages is due to heat conduction and natural convection plays no role. A p arametric study was performed with the values of the Rayleigh number (Ra), Darcy number (Da) and the thermal conductivity ratio varying one ata time. The dependence of the flow and thermal fields on these parameters was eluci dated. For low Ra and Da numbers, the flow field is restricted within the c entral fluid core. Only for high Rn and Da numbers, one can observe compara ble fluid motion in both the porous medium and central fluid core regions. The local Nusselt number on the surface and interface temperature exhibit n early uniform variations for low Ra and Da numbers, signifying little devia tion from the limiting pure conduction case. For high Ra and Da numbers, ma rked heat transfer is observed on the bottom of the sphere. The interface t emperature is also seen to deviate from uniform variation for high Ra and D a numbers. Only the intensity of the recirculating flow in the central flui d core region was seen to depend on the thermal conductivity ratio. The the rmal conductivity ratio modifies the time scale of the thermal transport an d only the relative magnitudes of the monitored quantities are affected. (C ) 1999 Elsevier Science Ltd. All rights reserved.