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Steady natural convection flow in a square cavity filled with a porous medium for linearly heated side wall(s). (English) Zbl 1124.80363
Summary: In this paper natural convection flows in a square cavity filled with a porous matrix has been investigated numerically when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Darcy–Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for a range of parameters (Rayleigh number $$Ra, 10^{3}\leqslant Ra\leqslant 10^{6}$$, Darcy number Da, $$10^{- 5}\leqslant Da\leqslant 10^{-3}$$, and Prandtl number $$Pr, 0.2\leqslant Pr \leqslant 100)$$ in terms of stream functions and isotherm contours, and local and average Nusselt numbers.

##### MSC:
 80A20 Heat and mass transfer, heat flow (MSC2010) 76R10 Free convection 76S05 Flows in porous media; filtration; seepage 76M10 Finite element methods applied to problems in fluid mechanics 80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
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