Flow Past a Porous Permeable Sphere: Hydrodynamics and Heat-Transfer Studies

Abstract

Flow past a porous permeable sphere has been studied using standard computational fluid dynamics (CFD) software (FLUENT) for a wide range of Reynolds numbers. Brinkman’s extension of Darcy’s law in the inner region and Navier–Stokes equations in the outer region of the porous permeable sphere were employed to solve the fluid flow phenomena. The results are presented in terms of three dimensionless parameters, e.g., the particle Reynolds number, the permeability ratio, and the drag ratio. The computed drag ratio asymptotically approaches zero at high permeability ratios and unity at low permeability ratios. A peak in the drag ratio versus permeability ratio plot is observed at high particle Reynolds number and in the intermediate range of permeability ratio. The drag ratios obtained from CFD simulation show good agreement with the experimental data available in the literature at different Reynolds numbers and permeability ratios. The results of heat transfer from porous permeable sphere are presented in terms of four dimensionless parameters: the particle Reynolds number (Re), permeability ratio, the Prandtl number (Pr), and the Nusselt number (Nu). The correlation obtained from the CFD simulation data for heat transfer from a porous permeable sphere is useful in predicting Nu for a wide range of Re and Pr at different permeability ratios.