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

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 (Pr_m) and Darcy numbers (Da_m) at Rayleigh number, Ra_m = 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 Da_m involving all the cases. At the high Da_m, 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 Da_m for all Pr_m. At the high Da_m, Nur¯ for the Case 1 (concave) is the largest involving the low Pr_m, whereas Nur¯ is the largest for Case 1 (convex) involving the high Pr_m.

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.

Citation

Biswal, P. and Basak, T. (2018), "Heatlines visualization of convective heat flow during differential heating of porous enclosures with concave/convex side walls", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 7, pp. 1506-1538. https://doi.org/10.1108/HFF-12-2016-0502