Convective Heat Transfer and Entropy Generation Around a Sphere Within Cuboidal Enclosure

Abstract

The intricate three-dimensional natural convection and entropy generation of a flow between cuboidal enclosure and a spherical surface is numerically examined in this study. The sphere is maintained hot and centrally located in cubical enclosure with four cooled walls, whereas top and bottom walls are perfectly insulated. The effects of inner shape, Rayleigh numbers, and inclination angles on fluid flow and heat transfer characteristics are analyzed in detail for Rayleigh numbers ranging from to and a tilted angle of the enclosure varying from 0 to 90°. The working fluid is air so that the Prandtl number equates to 0.71. The developed mathematical model is governed by the coupled equations of continuity, momentum, and energy and is solved by a finite volume method. Based on numerical results, two correlation expressions for predicting average Nusselt number of lateral walls of the cubical enclosure and the inner sphere are proposed as a function of Rayleigh number and inclination angle under different wake parameters. By comparing inner spherical shape results with that of cylindrical shape, it can be inferred that using a spherical shape provides the highest thermal performance for heat transfer. Moreover, this comparison reveals that the inner spherical shape decelerates the unsteadiness for the considered inclinations. Results indicate also that the optimal average heat transfer rate is obtained for extreme Rayleigh number, , and an inclination of 90° for both cases of the inner sphere and lateral walls of the cuboidal enclosure. The Bejan number and total entropy generation are found to be increased by increasing the inclination angle for the considered Rayleigh numbers. Maximum local entropy generation due to heat transfer and that due to fluid friction decrease gradually by increasing the inclination angle. The results of this investigation find extensive array of applications in several engineering devices, which will be mentioned in the paper content.