Free convection in power-law fluids from a heated sphere

Abstract

In this work, the governing field equations describing heat transfer from a heated sphere immersed in quiescent power-law fluids have been solved numerically. In particular, consideration has been given to elucidate the role of Grashof number (Gr), Prandtl number (Pr) and power-law index (n), on the value of the Nusselt number (Nu) for a sphere in the natural convection regime. Further insights are provided by presenting streamline and constant temperature contours. The results presented herein encompass the following ranges of conditions: 10≤Gr≤10⁷; 0.72≤Pr≤100 and 0.4≤n≤1.8 thereby covering both shear-thinning and shear-thickening types of fluid behaviours. Broadly, all else being equal, shear-thinning behaviour can enhance the rate of heat transfer by up to three-fold where as shear-thickening can impede it up to I30-40% with reference to that in Newtonian fluids. The paper is concluded by presenting detailed comparisons with the scant experimental data and the other approximate treatments of this problem available in the literature.