Momentum and heat transfer from a heated circular cylinder in Bingham plastic fluids

In this work, heat and momentum transfer characteristics of a heated circular cylinder submerged in Bingham plastic fluids over wide ranges of conditions as: plastic Reynolds number, 1 ⩽ Re ⩽ 40, Prandtl number, 1 ⩽ Pr ⩽ 100 and Bingham number, 0 ⩽ Bn ⩽ 104 have been studied numerically. The governing equations in conjunction with the Papanastasiou regularization for the discontinuous-viscosity behavior of a Bingham fluid have been solved using the finite element method. Extensive new results on streamlines, distribution of shear rate and velocity, morphology of yielded/unyielded regions and drag coefficient are presented and discussed to delineate the influence of the fluid yield stress on the structure of flow field. As expected, while the yield stress acts to stabilize the flow by suppressing the phenomenon of flow detachment, the inertial forces act to destabilize the flow. A delicate balance thus exists between the viscous and yield stress effects on one hand and the inertial effects on the other. For a fixed Reynolds number, there exists a critical Bingham number beyond which no flow separation is observed. Also, the laminar forced convection heat characteristics have been analyzed in terms of the isotherm contours, local Nusselt number and average Nusselt number. In order to facilitate the estimation of drag coefficient and Nusselt number in a new application, the present numerical values have been correlated in terms of the pertinent dimensionless parameters with acceptable levels of accuracy. Finally, due to the occurrence of steeper gradients in Bingham plastic fluids otherwise under identical conditions (same Reynolds and Prandtl numbers), the drag is augmented by 37-100% and the Nusselt number by ∼30-57% over and above its value in Newtonian fluids (Bn = 0) over the range of conditions spanned here.