Steady flow of power-law fluids past a sphere in a tapered tube

Abstract

The flow past a solid sphere constitutes a primary domain in the field of fluid mechanics and has a fundamental importance in several industrially important processes. Thus, the present work endeavours to study the momentum and heat transfer characteristics from a confined sphere inside a cylindrical tube of a converging cross-section with a pressure-driven Poiseuille flow of power-law fluids (only for shear-thinning fluids), different kinematic parameters (Reynolds number, Prandtl number), and geometric parameters (separation ratio, blockage ratio, radius ratio, contraction length, etc.). To achieve this objective, a finite element based numerical approach has been employed to study the flow and thermal characteristics from an isothermal sphere. The numerical results reported herein span the following ranges of parameters: Reynolds number (1 ≤ Re ≤ 100), Prandtl number (1 ≤ Pr ≤ 100), power-law index (0.2 ≤ n ≤ 1), separation ratio (0.1 ≤ SR ≤ 0.7), and blockage ratio (0.4). It can be concluded that the hydrodynamic drag force acting on the sphere and the rate of heat transfer can be increased substantially as the sphere is located towards the exit of the tube, though the enhancement in the drag is much greater than that in heat transfer under otherwise identical conditions.