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 (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.

Role of curved walls on efficient thermal convection in porous beds confined within enclosures: heatline and entropy production maps

“…The thermal or natural convection is nontrivial as the combined influence of momentum, and heat transfer effects based on geometries and heating of walls lead to complex fluid flow and heat transfer features. Furthermore, the effect of geometrical intricacies, especially in the case of enclosures (with curved or inclined walls) confining porous bed with various limits of porosities can induce intriguing features of fluid flow and heat transport leading to the extensive research on temperature characteristics (via isotherms) associated with flow visualization (via streamlines) with/without heat flow visualization [via heatlines as first proposed by Kimura and Bejan (1983)] over the past few decades (Murthy et al , 1997; Kumar et al , 1998; Kumar, 2000; Kumar and Shalini, 2003a, 2003b, 2004; Das et al , 2003; Misirlioglu et al , 2005; Misirlioglu et al , 2006; Chen et al , 2007; Khanafer et al , 2009; Basak et al , 2013; Sojoudi et al , 2014; Biswal and Basak, 2017a, 2018; Haq et al , 2018; Cheong et al , 2018; Lukose and Basak, 2020; Saha et al , 2020; Belabid, 2020; Rashed et al , 2021; Rao and Barman, 2021). A number of earlier studies do involve analysis with second law of thermodynamics involving entropy generation rates which elucidate the efficacy of process via entropy production minimization approach [introduced by Bejan (1982)].…”

Numerical heat flow visualization analysis on enhanced thermal processing for various shapes of containers during thermal convection

“…A number of studies were carried out based on natural convection in containers with wavy or curved walls (Das and Mahmud, 2003; Dalal and Das, 2006; Ashjaee et al , 2007; Varol and Oztop, 2008; Oztop et al , 2011; Sompong and Witayangkurn, 2014; Biswal and Basak, 2016; Sheremet et al , 2017; Pop et al , 2017; Biswal and Basak, 2017; Cheong et al , 2017; Esfahani et al , 2017; Biswal and Basak, 2018; Roy, 2018). A few works are explained next.…”

“…Heatfunction is the mathematical representation of heatline. Heatlines were used to analyze the heat flow trajectories for convection in containers [square (Kaluri and Basak, 2010; Mobedi, 2008), tilted square (Singh et al , 2012), parallelogrammic or rhombic (Anandalakshmi and Basak, 2012, 2013), triangular (Basak et al , 2009a, 2010), trapezoidal (Basak et al , 2009b), concave and convex (Biswal and Basak, 2014, 2017, 2018) and right-angled triangle with curved hypotenuse (Basak et al , 2013)]. A recent review on natural convection in non-square shapes by Das et al (2017) provides a few test cases on the application of heatlines in various non-square containers.…”

Analysis of Energy Flux Vector on Natural Convection Heat Transfer in Porous Wavy-Wall Square Cavity with Partially-Heated Surface

“…The results have demonstrated that the use of the wavy-surface geometries can improve the heat transfer effect. Recently, Biswal et al [21] have utilized the energy-flux-vector method to explain the process of heat transport of natural convection within a porous cavity with curved side walls. Their results have shown that given suitable curved-side wall forms with appropriate flow conditions, the heat transfer performance can be enhanced.…”