Effect of Orientation on the Steady Laminar Free Convection Heat Transfer in Power-Law Fluids from a Heated Triangular Cylinder

Abstract

In this work, the influence of orientation on the steady laminar free convection heat transfer from a heated triangular cylinder (flat side facing downward and upward) in quiescent power-law fluids has been investigated. In particular, the coupled momentum and energy equations have been solved numerically over wide ranges of the relevant dimensionless parameters as: Grashof number (10 ≤ Gr ≤ 10⁵), Prandtl number (0.72 ≤ Pr ≤ 100), and power-law index (0.3 ≤ n ≤ 1.8). The detailed flow and temperature fields in the vicinity of the heated cylinder are visualized in terms of the streamline and isotherm contours, respectively. At the next level, the influence of each of the governing parameters, namely, Grashof number (Gr), Prandtl number (Pr), and power-law index (n) on the local and average Nusselt number and drag coefficient, is examined. The flow separation was found to occur at high Grashof numbers and low Prandtl numbers, but only in shear-thickening and Newtonian fluids (n ≥ 1) for the cylinder orientated with its flat side facing upward. Over the range of conditions spanned here, for equal surface area, the rate of heat transfer and drag coefficient are always higher for the cylinder oriented with its flat side facing upward. Broadly speaking, over the range of conditions embraced here, shear-thinning fluid behaviour enhances heat transfer and shear-thickening impedes it. Finally, the present numerical values of the Nusselt number and drag coefficient have been correlated via a simple expression using a composite parameter consistent with the boundary layer analysis. Naturally, this parameter is more effective only at large values of the Grashof and Prandtl numbers, an assumption inherent in the boundary layer approximation.