Laminar natural convection in power-law liquids from a heated semi-circular cylinder with its flat side oriented downward

In this work, laminar free convection heat transfer from a heated semi-circular cylinder, with its flat base facing downward, submerged in quiescent power-law fluids has been studied. The coupled momentum and energy equations have been solved numerically in the following ranges of dimensionless parameters: Grashof number (10⩽Gr⩽105), Prandtl number (0.72⩽Pr⩽100) and power-law index (0.2⩽n⩽1.8). The detailed flow and temperature fields in the vicinity of the heated object are visualized in terms of the streamline and isotherm contours respectively. The rate of heat transfer is described in terms of the local Nusselt number variation along the surface of the cylinder together with its average value over the above-mentioned ranges of parameters. As expected, the value of the local Nusselt number increases from the front stagnation point up to the sharp corner and then decreases all the way up to the rear stagnation point. Broadly, over the range of conditions spanned here, the flow remains attached to the surface of the cylinder. The average Nusselt number increases with both the Grashof and Prandtl numbers and it decreases with the increasing power-law index. Furthermore, shear-thinning behavior (n < 1) enhances heat transfer whereas shear-thickening behavior (n > 1) impedes it with reference to that in Newtonian fluids otherwise under identical conditions. The numerical results obtained herein are correlated using a composite parameter consistent with the boundary layer analysis and these are contrasted with the results for the other two-dimensional shapes thereby suggesting the general usefulness of the composite parameter.