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Transient thermal convection in a spherical enclosure containing a fluid core and a porous shell. (English) Zbl 0932.76082

Summary: We investigate numerically transient natural convection in a spherical enclosure containing a central core fluid and a porous shell fully saturated with the same fluid. Simulations are based on Navier-Stokes equations for the fluid region, on the Brinkmann equation for flow through porous media, on convective diffusion equations for energy transport, and on the Boussinesq approximation for buoyancy. Solutions are obtained by a hybrid spectral method which combines the concepts of Galerkin and collocation methods with Legendre and Chebyshev polynomials employed as basis functions, respectively. Time advancement is accomplished by a combined Adams-Bashforth and backward Euler schemes. The numerical results exhibit remarkable effects along the porous-fluids interface; however, the overall heat flux is only sensitive to the thermal conductivity ratio of the solid matrix to the fluid.

MSC:

76R10 Free convection
76S05 Flows in porous media; filtration; seepage
76M20 Finite difference methods applied to problems in fluid mechanics
76M22 Spectral methods applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
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