Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

Abstract

In the present work, the forced convection momentum and heat transfer aspects of isothermal spheroidal particles (both prolates and oblates) in Bingham plastic fluids have been numerically investigated in the steady axisymmetric flow regime. Extensive results on the detailed structures of the flow and temperature fields are presented and analyzed in terms of the streamline and isotherm contours, and the yield surfaces as well as their dependence on the pertinent influencing parameters, namely, Reynolds number (1 ≤ Re ≤ 100), Prandtl number (1 ≤ Pr ≤ 100), and Bingham number (0 ≤ Bn ≤ 100) are delineated. Five values of aspect ratio, e = 0.2 and 0.5 (oblates) and e = 2 and 5 (prolates), and the limiting case of a sphere, i.e., e = 1, are considered here to elucidate the effect of shape on both drag and Nusselt number values. Broadly, for a given shape (value of e), drag shows the classic inverse dependence on the Reynolds number and a positive correlation with the Bingham number. Similarly, the mean Nusselt number bears a positive dependence on each of these parameters, Re, Pr, and Bn, due to the sharpening of the temperature gradient in the thin thermal boundary layer. The present drag results have been correlated via the use of a modified Reynolds number whereas the heat transfer results have been consolidated in terms of the Colburn jH factor, thereby enabling their prediction in a new application.