Laminar forced convection heat transfer from a heated square cylinder in a Bingham plastic fluid

In this work, the momentum and heat transfer characteristics of a heated cylinder of square cross-section immersed in a streaming Bingham plastic medium have been studied. The governing differential equations (continuity, momentum and thermal energy) have been solved numerically over wide ranges of conditions as: plastic Reynolds number, 0.1⩽Re⩽40, Prandtl number, 1⩽Pr⩽100 and the Bingham number, 0⩽Bn⩽100. Over this range of conditions, the flow is expected to be symmetric and steady. The detailed flow and temperature fields in the vicinity of the cylinder surface are examined in terms of streamline and isotherm profiles respectively. In particular, owing to the presence of the yield stress, the so-called yielded (fluid-like) and unyielded (solid-like) regions are delineated in the flow domain as functions of the Reynolds and Bingham numbers. This objective is accomplished by a detailed examination of the velocity profiles and shear rate profiles along the center planes. Further insights are developed in terms of the distribution of the pressure and local Nusselt number along the cylinder surface together with their average values in terms of drag coefficients and mean Nusselt number. The present numerical results on drag and Nusselt number (in the form of j-factor) have been correlated to the modified Bingham and Reynolds numbers via simple expressions thereby enabling their interpolation for the intermediate values of these dimensionless parameters.