TRANSIENT THERMAL-CONVECTION IN A SPHERICAL ENCLOSURE CONTAINING A FLUID CORE AND A POROUS SHELL

Transient natural convection in a spherical enclosure containing a cen tral core fluid and a porous shell fully saturated with the same fluid is investigated numerically. Simulations are based on a mathematical model consisting of the Navier-Stokes equations for the fluid region, the Brinkman equation for flow through porous media, a convective diff usion equation for energy transport, and the Boussinesq approximation for buoyancy. Solutions are obtained by a hybrid spectral method which combines the concepts of Galerkin and collocation methods with Legend re and Chebyshev polynomials employed as basis functions, respectively . Time advancement is accomplished by a combined Adams-Bashforth and b ackward Euler schemes. The numerical results exhibit remarkable effect s along the porous-fluids interface;however, the overall heat flux is only sensitive to the thermal conductivity ratio of the solid matrix t o the fluid. Copyright (C) 1996 Elsevier Science Ltd.