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.

Citation

Biswal, P. and Basak, T. (2017), "Role of heatlines on thermal management during Rayleigh-Bénard heating within enclosures with concave/convex horizontal walls", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 9, pp. 2070-2104. https://doi.org/10.1108/HFF-04-2016-0143