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

摘要

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 (Nu_t) 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 Nu_t at the low Ra for all Pr. At the high Ra, Nu_t 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.