Combined effects of fluid shear-thinning and yield stress on heat transfer from an isothermal spheroid

Abstract

In this work, the effect of aspect ratio (polar to equatorial axis) of a spheroid on the flow and heat transfer in shear-thinning viscoplastic fluids characterised by the Herschel–Bulkley fluid model has been analyzed in the forced-convection regime. The momentum and energy equations have been solved numerically in the steady and laminar flow regime over the following ranges of conditions: Reynolds number, 1⩽Re⩽100; Prandtl number, 1⩽Pr⩽100; Bingham number, 0⩽Bn⩽10; power-law index, 0.2⩽n⩽1 and the aspect ratio of the spheroid, 0.2⩽e⩽5. In addition, limited results were also obtained in the low Reynolds number (Re→0) and Peclet number regime to examine the scaling of the Nusselt number with the Peclet number. The effect of particle shape is elucidated on the size and location of yield surfaces, streamline and isotherm contours, wake characteristics (length and separation angle), drag coefficient and the local and average Nusselt numbers over the foregoing ranges of conditions. In general, oblate shapes (e<1) promote heat transfer with reference to that for a sphere (e=1) at fixed values of the Reynolds, Prandtl and Bingham numbers. The tendency for wake formation is, however, reduced by the fluid yield stress. All else being equal, both drag and Nusselt number show a positive dependence on the Bingham number due to the sharpening of the gradients in the thin fluid-like regions existing adjacent to the spheroid. Further augmentation in heat transfer is achieved by introducing shear-thinning fluid behaviour in yield-stress fluids. The paper is concluded by presenting a correlation in terms of the Colburn-j factor as a function of the modified Reynolds number (Re∗), power-law index (n) and aspect ratio (e) thereby enabling the estimation of the Nusselt number for intermediate values of parameters in a new application.