Nguyen, Hoa D.; Paik, Seungho; Pop, Ioan Transient thermal convection in a spherical enclosure containing a fluid core and a porous shell. (English) Zbl 0932.76082 Int. J. Heat Mass Transfer 40, No. 2, 379-392 (1997). 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. Cited in 1 Document 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) Keywords:Adams-Bashforth scheme; backward Euler scheme; Navier-Stokes equations; Brinkmann equation; convective diffusion equations; energy transport; Boussinesq approximation; hybrid spectral method; collocation methods; Legendre and Chebyshev polynomials PDFBibTeX XMLCite \textit{H. D. Nguyen} et al., Int. J. Heat Mass Transfer 40, No. 2, 379--392 (1997; Zbl 0932.76082) Full Text: DOI