Heat transfer to a sphere in tube flow of power-law liquids

Extensive new results on forced convection heat transfer from an isothermal heated sphere exposed to the fully developed laminar velocity profile of power-law fluids in a tube are reported herein. In particular, these results endeavor to elucidate the influence of the pertinent dimensionless governing parameters, namely, Reynolds number (5 ⩽ Re ⩽ 100), Prandtl number (1 ⩽ Pr ⩽ 100), power-law index (0.2 ⩽ n ⩽ 1) and sphere-to-tube diameter ratio (0.05 ⩽ λλ ⩽ 0.5). The heat transfer characteristics are analyzed in terms of the local as well as surface averaged values of the Nusselt number. Broadly, all else being equal, shear-thinning behavior promotes heat transfer, though confinement limits such an increase in shear-thinning fluids depending upon the value of the power-law index. Similarly, all else being equal, confining walls also enhance the rate of heat transfer which is, however, maximum in the case of Newtonian fluids. Possible reasons for such counter-intuitive trends are advanced. The present numerical results have been approximated by simple expressions thereby enabling their interpolation for the intermediate values of the governing parameters like Reynolds number, Prandtl number, diameter ratio and power-law index.