Role of heatlines on thermal management during Rayleigh-Bénard heating within enclosures with concave/convex horizontal walls

Abstract

Purpose This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach. Design/methodology/approach The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number ( Nut¯) for various Rayleigh numbers (103 ≤ Ra ≥ 105), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity). Findings The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity). Practical implications The results may be useful for the material processing applications. Originality/value The study of Rayleigh-Bénard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.

Revisit on energy flow: accurate predictions and analysis of heatlines for thermal convection within enclosures of various configurations

“…Energy flow visualization is important for understanding of heat flow within enclosures. While heat flow visualization cannot be carried out via experimental approaches, numerical visualization tool via “heatlines,” first proposed by Kimura and Bejan (1983), has been successfully used to visualize heat flow for various applications of thermal convection within enclosures (Al-Jethelah et al , 2018; Anandalakshmi and Basak, 2013; Biswal and Basak, 2017; Basak et al , 2018; Das and Basak, 2016; Dash, 1996; Ferhi and Djebali, 2020; Hooshmand et al , 2019; Islam et al , 2021; Kaluri and Basak, 2010; Khakrah et al , 2019; Liu et al , 2019; Lukose and Basak, 2020; Manna et al , 2021; Priam and Nasrin, 2022; Rahimi et al , 2019; Rao et al , 2019; Salari et al , 2018; Wang et al , 2020; Zhao et al , 2007). Heat flow trajectories via heatlines follow a few set of rules (Basak et al , 2018).…”

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

“…Natural convection occurs because of the motion and mixing of fluid, induced by the density variations based on the temperature difference within the fluid. Natural convection has been extensively studied in recent works because of its wide variety in various applications (Siddiqa et al , 2015; Shirvan et al , 2017a, 2017b; Rahman et al , 2017; Oztop et al , 2017; Biswal and Basak, 2017; Sheremet et al , 2018a; Sheremet and Pop, 2018; Gerdroodbary et al , 2018; Chen et al , 2018; Pichandi and Anbalagan, 2018; Revnic et al , 2018; Wang et al , 2018; Ismail et al , 2019; Wong et al , 2019). The fluid flow in natural convection is strongly dependent on the shapes of containers.…”

“…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.…”