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

Abstract

The momentum and thermal energy equations describing the forced convection heat transfer from a heated sphere settling at the axis of a long cylindrical tube filled with a power-law fluid have been solved numerically. The extensive new results reported herein encompass wide ranges of conditions as: Reynolds number, 1≤Re≤100; Prandtl number, 5≤Pr≤100, power-law index, 0.2≤n≤2 and blockage ratio, 0.5≤λ≤0.95. The range of values of the power-law index (n) used here include both the shear-thinning (n<1) and shear-thickening (n>1) fluid behaviours. The overall heat transfer is strongly modulated by Re, n and λ depending upon whether the recirculation region is formed in the rear of the sphere and/or on the proximity of the tube wall. Furthermore, the results reported herein elucidate the effect of the type of thermal boundary condition (isothermal or isoflux) on the surface of the sphere as well as that of the velocity profile (uniform or fully developed Poiseuille profile) in the tube. Overall, the average Nusselt number bears a positive dependence on the Reynolds and Prandtl numbers and blockage ratio. The shear-thinning behaviour (n<1) augments heat transfer over and above the corresponding Newtonian value whereas shear-thickening behaviour (n>1) adversely influences it. The present numerical results (~4000 data) have been consolidated by incorporating the blockage factor into an existing expression valid for λ=0 for Newtonian fluids.