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

Abstract

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.

Mixed convection from a hemisphere in Bingham plastic fluids

“…Finally, included in these figures are also the yield surfaces (shown as broken lines) predicted by the bi-viscous approximation of the true Bingham fluid model, as given by Eq. (12). Notwithstanding the minor differences in the size of the fluid-like cavity, the two predictions are seen to be in fair agreement with each other thereby lending credibility to the present results.…”

“…This would be indeed so in the forced convection regime as has been demonstrated in the case of a sphere [11,12] and a cylinder [20]. Additional complications arise in the present case due to the coupled nature of the velocity and temperature fields thereby bringing in the influence of Richardson and Prandtl numbers even on the fluid mechanical aspects of the problem.…”

“…were used as inputs for pre-chosen values of the Richardson number, Prandtl number, Bingham number, Reynolds number, etc., but these specific values are of no particular consequence as the final results are expressed in their dimensionless forms. More detailed discussions of the numerical solution methodology can be found elsewhere [11,12,38].…”

“…Much has been written in the literature in general and in our recent studies in particular [11,12,30,31,38] about the influence of the optimal values of the relevant numerical computational parameters. In the present context, these include the size of the computational domain (D 1 /d), quality of numerical mesh (number of nodes on the surface of the hemi-sphere, N p , finest cell size and the total number of cells, N) and the value of the regularization parameter m or the value of yielding viscosity l Y /l B in the Bingham constitutive equation.…”

Laminar forced convection heat transfer from a two-dimensional transverse plate in Bingham plastic fluids

“…Under these conditions, the drag force is determined solely by the geometry of the immersed surface and the yield stress of the fluid and the only mechanism of heat transfer is conduction. These limiting trends are well documented in the literature for a sphere [7][8][9][10], for a two dimensional square bar [11] and a circular cylinder [12][13][14]. In contrast, very little is known about the momentum and heat transfer aspects from a heated two-dimensional plane surface oriented transverse to a free stream of Bingham plastic fluids.…”