Free convection from a heated circular cylinder in Bingham plastic fluids

Abstract

In this work, the equations of motion and energy have been solved numerically using Comsol Multiphysics (version 4.3a) for the laminar free convection heat transfer from a horizontal heated cylinder to Bingham plastic fluids over the range of conditions as: Rayleigh number, 102 ≤ Ra ≤ 106; Prandtl number, 30 ≤ Pr ≤ 100 and Bingham number, 0 ≤ Bn ≤ 104. Extensive results on the streamline and isotherm contours, yielded/unyielded regions, local and average Nusselt numbers are presented and discussed. Owing to the presence of the fluid yield stress, both fluid-like (yielded) and solid-like (unyielded) regions coexist in the flow domain depending upon the prevailing stress levels vis-a-vis the value of the fluid yield stress. Naturally, heat transfer in the solid-like regions occurs purely by conduction and convection is thus restricted to the fluid-like regions. Furthermore, the yielded regions progressively diminish with the increasing value of the Bingham number and/or the decreasing value of the Rayleigh number as the buoyancy-induced flow weakens. All in all, the overall rate of heat transfer is determined by the gradients on the surface of the heated cylinder. Finally, the present numerical values of the average Nusselt number have been correlated in terms of the modified Rayleigh number (Ra∗) and Prandtl number (Pr∗).