Effects of Uniform Heat Flux and Velocity-Slip Conditions at Interface on Heat Transfer Phenomena of Smooth Spheres in Newtonian Fluids

Abstract

The effects of the uniform heat flux and a linear velocity-slip on the heat transfer phenomena of spheres in Newtonian fluids are numerically investigated using semi-implicit marker and cell (SMAC) method implemented on a staggered grid arrangement in spherical coordinates. The solver is thoroughly benchmarked through domain independence, grid independence, and comparison with literature. Further extensive results are obtained in the range of conditions as: Reynolds number, Re = 0.1–200; Prandtl number, Pr = 1–100; and dimensionless slip number, λ = 0.01–100. The results are presented and discussed such that the isotherm contours and the local and average Nusselt numbers of isoflux spheres with velocity-slip at the interface are compared with their isothermal spheres counterparts under identical conditions. Briefly, the results indicate that the average Nusselt numbers of isoflux spheres are large compared to those of isothermal spheres under identical conditions. Finally, an empirical correlation is developed for the average Nusselt numbers of the spheres in Newtonian fluids with velocity-slip and the uniform heat flux conditions along the fluid–solid sphere interface.