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Natural convection in a heat generating hydrodynamically and thermally anisotropic non-darcy porous medium. (English) Zbl 1154.80327
Summary: Natural convection in a two-dimensional square cavity containing hydrodynamically and thermally anisotropic porous medium with internal heat generation is analyzed numerically by generalized non-Darcy approach. The properties considered for the study are permeability ratio \((K^{*})\), inclination of the principal axes \((\theta )\), ratio of Forchheimer constants \((F^{*})\) and thermal conductivity ratio \((k^{*})\). Results are presented in terms of isotherms, streamlines and maximum temperature in the cavity to understand the flow physics. It is observed that the anisotropic properties have significant influence on the flow behaviour and heat transfer. A correlation for maximum temperature in the cavity for a wide range of parameters (\(10^{7}\leqslant Ra\leqslant 10^{8}, 10^{ - 6}\leqslant Da\leqslant 10^{ - 3}, 0^\circ \leqslant \theta \leqslant 90^\circ \), 1 \(\leqslant F^{*}\leqslant 100, 0.1 \leqslant K^{*}\leqslant 10\) and \(0.1 \leqslant k^{*}\leqslant 10)\) is developed.

MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
76R10 Free convection
76S05 Flows in porous media; filtration; seepage
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