Mixed convection from a heated semi-circular cylinder to power-law fluids in the steady flow regime

Steady mixed convection heat transfer from a heated semi-circular cylinder immersed in power-law fluids is considered here with its curved surface facing upstream. The imposed flow and the buoyancy act in the same direction thereby resulting in the so-called aiding-buoyancy configuration. The momentum and thermal energy equations have been solved numerically over the following ranges of conditions: image, image, image and image. The combined effects of the forced and free convection on the flow and thermal fields are visualized in terms of the streamline and isotherm contours. Further insights are provided in terms of the distribution of pressure coefficient and local Nusselt number along the cylinder surface. Finally, the overall macroscopic characteristics are reported in terms of the individual and total drag coefficients and the average Nusselt number as functions of the pertinent dimensionless parameters. The influence of the power-law index is strongly modulated by the value of the Reynolds number. Broadly, drag coefficient shows a monotonic increase as the value of the Richardson number or Reynolds number increases. At low Reynolds numbers, such as Re = 1, the local value of the Nusselt number is found to be maximum at corners and for high values of the Reynolds number, it shifts towards the front stagnation point. The average Nusselt number increases with an increase in the value of the Reynolds number, Prandtl number and Richardson number. Broadly, shear-thinning viscosity facilitates heat transfer whereas shear-thickening has an adverse effect on it.