Forced Convection from a Heated Equilateral Triangular Cylinder in Bingham Plastic Fluids

Abstract

The momentum and forced convection heat transfer characteristics of a heated equilateral triangular cylinder immersed in a Bingham plastic fluid have been studied numerically. The governing equations (continuity, momentum, and thermal energy) are solved for both vertex-upstream and vertex-downstream orientations, over wide ranges of the pertinent parameters, such as Reynolds number: 0.1 ≤ Re ≤30; Prandtl number: 1 ≤ Pr ≤100; and Bingham number: 0 ≤ Bn ≤200. Over the range of conditions, the flow is expected to be steady and symmetric. Detailed analysis of the flow and heat transfer phenomena in the vicinity of the cylinder is performed by a thorough inspection of the streamline and isotherm contours. Furthermore, due to the presence of the yield stress, the flow domain consists of yielded (or fluid-like) and unyielded (or solid-like) zones. The effect of Reynolds number and Bingham number on the shape and size of these zones has been thoroughly examined in terms of the detailed velocity and shear rate profiles. At the next level, the functional dependence of the drag and Nusselt number on the Reynolds number, Bingham number, and Prandtl number is explored and developed. The heat transfer results spanning the above-noted ranges of parameters are consolidated by developing a correlation in terms of the Colburn j _h factor as a function of the modified Reynolds number.