Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Free convection from an isothermal elliptical cylinder in Bingham plastic fluids is studied numerically. This work spans a wide range of aspect ratios of the elliptical cylinder (0.1E10) to delineate the effect of shape on the flowfield close to the heated cylinder. The influence of the relevant parameters, namely, Rayleigh number (102Ra105), Prandtl number (10Pr100), and Bingham number (0.5Bn107), on the momentum and heat transfer characteristics is studied in terms of the yielded/unyielded regions, streamline, isotherm contours, and local Nusselt number for an elliptical cylinder of constant surface area in blunt (E>1) and slender orientations (E<1). The Nusselt number shows a positive dependence on the Rayleigh number, and it correlates negatively with Bingham and Prandtl numbers. The blunt orientations (E<1) enhance heat transfer as compared to that for a circular cylinder (of equal surface area) while slender orientations (E>1) impede it. Using the present numerical results, predictive correlations have been established in terms of the modified Rayleigh number (Ra*) and Prandtl number (Pr*), thereby enabling the prediction of Nusselt number in a new application.