Flow of Power-Law Fluids Past a Sphere at Intermediate Reynolds Numbers

Abstract

A finite-volume-based numerical approach has been used to solve the equations of motion for the steady and incompressible power-law fluid past a sphere in the two-dimensional symmetric range of conditions. The simulations are verified against previous numerical and experimental results available in the literature. The friction and pressure drag profiles and streamline plots showing the nature of flow and the wake structure are presented. The computed results cover the Reynolds number range of 5 ≤ Re ≤ 500 and the power-law index range of 0.5 ≤ n ≤ 2 (covering both shear-thinning and shear-thickening behavior). Based on the present numerical results, simple predictive correlations, in terms of Re and n values, are proposed to calculate the values of the total drag coefficient (C D) and the ratio of the pressure drag coefficient to the friction drag coefficient (C Dp/C Df) in a new application.

Forced convection heat transfer from a sphere to non‐Newtonian power law fluids

“…The solver used in the present study has already been validated extensively for Newtonian fluids 28 and for power law fluids. 7 The maximum difference between the present drag values for power law liquids from that of the available numerical studies and experimental studies in the literature was found to be around 3 and 10%, respectively. The possible reasons for these deviations have also been discussed and justified elsewhere.…”

“…The detailed flow structure around the sphere for different values of n at different Reynolds numbers also supports the idea of enhanced mobility of the fluid near the sphere. 7 Figures 3a-3i show the relatively large values of the Nusselt number at the front stagnation point ( ϭ 0°), which decreases gradually along the surface of the sphere, to a minimum value at the rear stagnation point. For Re Ͼ 20, that is, when flow separation occurs, Figures 3d-3i show that the Nusselt number decreases from its maximum value at the front stagnation point ( ϭ 0°) to a minimum value near the point of separation, beyond which a gradual increase in the values of the local Nusselt number can be seen up to the rear stagnation point.…”

“…It is important to take a sufficiently large domain so as to simulate the flow over an unconfined sphere. The extensive studies on domain independence carried out previously 7,28 Table 1 for two values of Prandtl number. It can be seen from Table 1 that the variation in Nusselt number for different domain sizes is generally within 1%.…”

“…The possible reasons for these deviations have also been discussed and justified elsewhere. 7 Nusselt Number. The accuracy and the reliability studies of the energy equation solver used in the present study were carried out extensively for the Newtonian case in our previous study.…”

“…4 Little information is available on the prediction of the Nusselt number for a sphere immersed in nonNewtonian fluids, albeit extensive literature is now available on the hydrodynamics of spheres in power law fluids (for example, see Chhabra, 5 Renaud et al, 6 and Dhole et al 7 ). This work is thus concerned with the prediction of heat transfer from a sphere immersed in streaming power law fluids.…”