Approximate analytical and numerical investigation of Oseen-type forced convection around a sphere in a low Reynolds number slip flow

Abstract

Convective heat transfer around a spherical particle submerged in a viscous heat-conducting fluid at very low Reynolds numbers is analytically investigated using Oseen’s theory. The size of the sphere is assumed to be small enough so that the temperature jump condition of dilute gas dynamics is valid on the sphere surface. Approximate analytical formulations are presented for the mean Nusselt number, the local Nusselt number and the temperature field. The presented formulations outperform the existing analytical solutions for the Oseen-type heat transfer around the sphere for both no-slip and slip flows. The new formulations do not diverge by increasing the Reynolds number and are capable of predicting acceptable results even up to Reynolds numbers beyond the validity of the Oseen’s theory. While the existing asymptotic solutions only give the mean Nusselt number, the proposed solutions additionally yield the local Nusselt number and the temperature field. A numerical solution of Oseen’s equation is also conducted for comparison. Based on the results presented, recommendations are made on the use of various formulations to achieve accurate results.