Mixed convection from a spheroid in Bingham plastic fluids: Effect of buoyancy-assisted flow

In this work, laminar mixed convection from an isothermal spheroidal particle immersed in a Bingham plastic fluid is studied numerically in the buoyancy-assisted regime. The results reported herein encompass the following ranges of conditions: Reynolds number, 0.1 ≤ Re ≤ 100; Prandtl number, 10 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 100; Richardson number, 0 ≤ Ri ≤ 8; and aspect ratio of the spheroid, 0.2 ≤ e ≤ 5. In particular, consideration is given to the effect of shape and orientation of the particle on the detailed flow and temperature fields (in terms of streamlines, iso-vorticity, and isotherm contours), morphology of the yielded–unyielded regions, and the local and surface-averaged Nusselt number. All else being equal, the propensity for flow separation is seen to be greater for oblates (e < 1) than that for prolates (e > 1). In both cases, this reduces with the increasing Bingham number and/or the Richardson number. Both drag coefficient and the Nusselt number show a positive dependence on the Bingham number as well as on the Richardson number. Overall, the drag coefficient increases as the particle shape changes from an oblate to prolate, whereas the reverse trend is obtained for the average Nusselt number, which is in line with the general inference that more drag corresponds to more heat transfer. Finally, the average Nusselt number is correlated with the pertinent dimensionless parameters (Re, Pr, Bn, Ri, e) via a simple correlation, thereby enabling its prediction for intermediate values of the parameters and/or in a new application.