Forced convective heat transfer from spheres to Newtonian fluids in steady axisymmetric flow regime with velocity slip at fluid–solid interface

Abstract

The heat transfer phenomenon of spherical particles in Newtonian fluids with velocity slip and uniform thermal boundary condition at the fluid–solid interface has been numerically investigated using a computational fluid dynamics (CFD) based in-house solver. At the interface linear slip velocity boundary condition has been adopted. The dimensionless continuity, momentum and energy equations along with the appropriate non-dimensional boundary conditions are solved by a segregated approach. This numerical procedure is a finite difference method based CFD solver implemented on a staggered grid arrangement in spherical coordinates. The convective and diffusive terms are discretized using the quadratic upstream interpolation for convective kinematics and a second order central differencing scheme respectively. Prior to obtaining new results, the present numerical solver is extensively validated by comparing the present values of the average Nusselt numbers with the existing literature values for either extreme values of the slip conditions, i.e., for fully slip and no-slip conditions. Further new results are obtained over the range of conditions as the Reynolds number, Re = 0.1–200; the Prandtl number, Pr = 1–100; and dimensionless slip parameter, λ = 0.01–100. The effects of these parameters on the isotherm contours and the local and average Nusselt numbers are thoroughly discussed and finally on the basis of present numerical results (196 data points), an empirical correlation is proposed for the average Nusselt numbers of single spheres with velocity slip at the interface as function of Re, Pe, and λ.