Role of thermal and flow characteristics on entropy generation during natural convection in porous enclosures with curved walls subjected to Rayleigh-Bénard heating

Abstract

The comprehensive analysis of natural convection within various enclosures with the concave and convex horizontal walls involving the classical Rayleigh-Bénard heating (hot bottom wall, cold top wall and adiabatic side walls) is carried out via the entropy generation approach. Galerkin finite element method is employed to obtain the solutions in terms of the isotherms (θ), streamlines (ψ), entropy generation (Sθ,Sψ and Stotal) and average heat transfer rates (Nut‾) for a selected range of Darcy numbers (10-5⩽Dam⩽10-2), Prandtl numbers (Prm=0.015 and 7.2) at Rayleigh number, Ram=106 with various test cases with different wall curvatures (concave and convex). The magnitudes and spatial locations of local entropy generation due to heat transfer and fluid friction are studied for various thermal and geometrical parameters. The active zones with larger Sθ are found along near core region and middle portions of the curved walls with less and moderate concavities whereas, those are found only near the middle portions of the curved walls with the high concavity at the low Dam involving all Prm. In the convex domain, the active zones with larger Sθ are seen near the corner regions for the low Dam at all Prm. The zones prone to the entropy generation with the high Sθ are seen along the mid-horizontal axis of the cavity involving all the concave and convex domains at the high Dam and all Prm. Also, the left and right portions of the curved walls act as the active zones with the high Sθ for the concave domains at the high Dam and all Prm. The larger values of Sψ are seen near all the solid walls (at all Dam) and at the interior zone (at the high Dam) for all Prm involving all concave and convex cases. Based on the comparison of all the concave and convex cases, the concave case with the high wall concavity may be preferred over the specific concave cases (with the less and moderate wall concavities) and all the convex cases due to the larger Nut‾ and less Stotal values for the entire range of Dam and Prm.