Mixed convection from a heated sphere in power-law fluids

Abstract

In this work, the steady, laminar, mixed convection heat transfer from a heated sphere immersed in power-law fluids has been investigated in the so-called aiding-buoyancy configuration. The momentum and thermal energy equations have been solved numerically over the following ranges of conditions: Richardson number, 0≤Ri≤2, power-law index, 0.2≤n≤2, sphere Reynolds number, 1≤Re≤100 and the generalized Prandtl number, 1≤Pr≤100. The detailed kinematics of the flow and temperature fields are visualized in terms of the streamline (stream trace) and isotherm contours in the close proximity of the heated sphere. Further insights are provided in terms of the distribution of pressure coefficient and local Nusselt number along the surface of the heated sphere over wide ranges of conditions from weak to strong free convection flow. Finally, the overall macroscopic characteristics are reported in terms of the individual and total drag coefficients and the surface average Nusselt number as functions of the pertinent dimensionless parameters. The drag coefficient is seen to increase monotonically with the Richardson and Prandtl numbers at low Reynolds numbers and the type of dependence changes at a critical Richardson number. Similarly, the average Nusselt number shows a positive dependence on the Reynolds number, Prandtl number and Richardson number. Broadly, shear-thinning viscosity (n<1) promotes heat transfer over and above that in Newtonian fluids otherwise under identical conditions and, as expected, shear-thickening behaviour (n>1) somewhat impedes it. Finally, the present numerical results have been correlated in terms of the modified Reynolds and Prandtl numbers thereby enabling interpolation of the present results for the intermediate values of the governing parameters.