Free convection from a single and a pair of spheres in power-law fluids at very small Grashof numbers

Abstract

Laminar free convection in power-law fluids over the range of vanishingly small Grashof number (10−4 ≤ Gr ≤ 10) has been investigated numerically for an isolated sphere and twin spheres for varying centre-to-centre distance (including limiting case of touching spheres). The results of nondimensional total drag (CD), local Nusselt number (Nul), and average Nusselt numbers (Nu) have been examined in detail to understand the momentum and heat transfer characteristics embracing broad ranges of Prandtl number (0.72 ≤ Pr ≤ 1000) and power-law fluid behaviour (0.1 ≤ n ≤ 2 for a single sphere and 0.1 ≤ n ≤ 1.5 for a pair of spheres) for both cases. The gradual decrease of Grashof number has a tendency to flip over the effect of the power-law index on the total drag in both cases, i.e., for a single and twin spheres. On the other hand, an increase in Prandtl number delays this effect to higher Grashof number values. Numerous comparisons with the published approximate, numerical and experimental studies have been carried out to affirm the consistency of the present numerical results. An existing definition of the modified Rayleigh number, captures well the influence of the Grashof and Prandtl numbers and the flow behaviour index on the drag coefficient and mean Nusselt number in both cases studied herein. The behaviour of the twin sphere configurations differs from that of an isolated sphere significantly even at the macroscopic level in terms of the resulting drag and Nusselt number values. Depending upon the separation between the two spheres and the strength of the flow, for the trailing sphere, the drag remains lower while the Nusselt number could be lower or higher than the single sphere and/or than that of the leading sphere over the range of parameters spanned here.