Effect of Shear-Thinning Behavior on Heat Transfer from a Heated Sphere in Yield-Stress Fluids

The present study deals with the prediction of drag and forced convection heat transfer behavior of a heated sphere in shear-thinning yield-stress fluids over wide ranges of conditions: plastic Reynolds number, 1 ≤ Re ≤ 100; Prandtl number, 1 ≤ Pr ≤ 100; Bingham number, 10–³ ≤ Bn ≤ 10; and shear-thinning index, 0.2 ≤ n ≤ 1. The momentum and energy equations have been solved numerically together with the Papanastasiou regularization method for viscosity to circumvent the discontinuity inherent in the Herschel–Bulkley constitutive equation. Extensive results on the flow and heat transfer characteristics are presented in order to delineate the influence of the aforementioned dimensionless parameters. Thus, for instance, the flow characteristics are presented in terms of the streamlines, morphology of the yielded/unyielded regions, recirculation length, shear rate magnitude over the surface of the sphere, and drag coefficient. Similarly, heat transfer characteristics are examined in terms of isotherm contours in the close proximity of the sphere and the average Nusselt number as a function of the relevant dimensionless groups. Furthermore, the present results are compared with the available experimental and numerical results in order to establish the reliability and precision of the numerical solution methodology employed in this work. Finally, the average Nusselt number and drag values are correlated in terms of the shear-thinning index (n) and the modified Reynolds number (Re*) via simple expressions, thereby enabling their interpolation for intermediate values of the modified Reynolds number. All else being equal, in addition to Bingham number, shear-thinning behavior of yield stress fluids enhances the rate of heat transfer over and above that observed in Newtonian fluids.