Effect of blockage on heat transfer from a sphere in power-law fluids

This work endeavors to elucidate the influence of confining walls on the convective heat transfer from a sphere to power-law fluids. The governing equations (mass, momentum, and thermal energy) have been solved numerically over the following ranges of conditions: power-law index, 0.2-1, i.e., only for shear-thinning fluid behavior; sphere Reynolds number, 5-100; sphere-to-tube-diameter ratio, 0-0.5; and Prandtl number, 1-100. Extensive results of the local and surface averaged values of the Nusselt number are presented herein to delineate the influence of each of the aforementioned parameters on the rate of heat transfer from a sphere. Broadly speaking, the Nusselt number shows positive dependence on both the Reynolds and Prandtl numbers. All else being equal, shear-thinning fluid behavior is seen to facilitate heat transfer with reference to that in Newtonian fluids. Indeed, it is possible to augment the rate of heat transfer by up to 60-70% under appropriate conditions. However, the imposition of confining walls is seen to limit the enhancement in heat transfer, especially at low Reynolds and/or Prandtl numbers. Therefore, the severity of confinement together with the values of the Reynolds and Prandtl numbers influences the value of the Nusselt number in an intricate manner