Heat transfer in Bingham plastic fluids from a heated elliptical cylinder

The forced convection heat transfer characteristics in Bingham plastic fluids from a heated elliptical cylinder of various aspect ratios E (=a/b) have been investigated numerically. The momentum and energy equations have been solved here by using the finite element method over wide ranges of rheological and kinematic parameters as: 0.01 ⩽ Bn ⩽ 100 (Bingham number), 0.01 ⩽ Re ⩽ 40 (Reynolds number), 1 ⩽ Pr ⩽ 100 (Prandtl number) and 0.1 ⩽ E ⩽ 10 (aspect ratio) thereby approaching the limiting conditions of a plate aligned with and transverse to the direction of mean flow. Furthermore, the influence of the type of thermal boundary condition, i.e., constant wall temperature (CWT) and constant heat flux (CHF) prescribed on the surface of the elliptical cylinder has also been examined. Extensive numerical results are reported herein in terms of the isotherm contours, variation of the Nusselt number on the surface of the cylinder for the two above-noted thermal boundary conditions and finally, the overall results are presented in terms of the surface averaged Nusselt number. Irrespective of the boundary condition prescribed on the surface of the cylinder, the Nusselt number shows a positive dependence on the both Reynolds number and Prandtl number while the effect of Bingham number is somewhat dependent on the Reynolds number range. The average Nusselt number has also been interpreted and correlated in terms of the Colburn heat transfer factor (j). Empirical correlations for the Colburn factor as functions of the Bingham number and aspect ratio have been proposed based on the present numerical results.