Analysis of differential versus Rayleigh–Bénard heating via heat flow visualization for thermal convection due to heating at enclosures with concave/convex walls

Abstract

Natural convection within enclosures in the presence of isothermal curved walls involving (a) differential heating and (b) Rayleigh–Bénard heating is considered for investigation. The two heating strategies are compared based on the distributions of fluid flow, heat flow and local or average heat transfer rates for various Da_m (modified Darcy number) and Pr_m (modified Prandtl number) at the high Ra_m (modified Rayleigh number). Unidirectional circulation cells occur for differential heating whereas four (combination of clockwise and anticlockwise) circulation cells occur for Rayleigh–Bénard heating. Consequently, unidirectional heatline cell occurs at the center for differential heating and four heatline circulation cells occur for Rayleigh–Bénard heating specially at the high . Multiple heatline cells lead to larger thermal mixing for Rayleigh–Bénard heating. The heat transfer rate is larger for differential heating case and the percentage enhancement of Nusselt number is calculated in terms of the gain in heat transfer rate for differential heating (E). The gain in heat transfer rate in terms of E involving concave and convex cavities (cases 1 and 2) is found to be the strong function of Da_m and Pr_m at the high Ra_m.