Heatlines visualization of convective heat flow during differential heating of porous enclosures with concave/convex side walls

TLDR: In this paper, the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Prm) and Darcy numbers (Dam) at Rayleigh number, Ram = 106, involving various wall curvatures.

Abstract: Purpose This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach. Design/methodology/approach The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Prm) and Darcy numbers (Dam) at Rayleigh number, Ram = 106, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation. Findings Smooth end-to-end heatlines are seen at the low Dam involving all the cases. At the high Dam, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number (Nur¯) at the low Dam for all Prm. At the high Dam, Nur¯ for the Case 1 (concave) is the largest involving the low Prm, whereas Nur¯ is the largest for Case 1 (convex) involving the high Prm. Practical implications Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications Originality/value The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.