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Transient free convection in a square cavity filled with a porous medium. (English) Zbl 1106.76457

Summary: Transient free convection in a two-dimensional square cavity filled with a porous medium is numerically studied in this paper. The left vertical wall is suddenly heated to a constant temperature \(T_{\text h}\), while the right wall is suddenly cooled to a constant temperature \(T_{\text c}\) by equal amount relative to an initially uniform temperature distribution. Both the horizontal walls are adiabatic. The finite volume numerical method is used to solve the non-dimensional governing equations. The results are obtained for the initial transient state up to the steady state, and for Rayleigh number values of \(10^2-10^4\). It is observed that the average Nusselt number showing an undershoot during the transient period and that the time required to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

MSC:

76R10 Free convection
76S05 Flows in porous media; filtration; seepage
76M12 Finite volume methods applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
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