Laminar Free Convection in Power-Law Fluids from a Heated Hemisphere

Extensive results are presented on the laminar free convection heat transfer in power-law fluids from a heated hemisphere in two orientations, namely, its flat base oriented upward (inverted) or downward (upright). The coupled field equations have been numerically solved over wide ranges of conditions as follows: Grashof number (10 <= Gr <= 10(5)), Prandtl number (0.72 <= Pr <= 100) and power-law index (0.3 <= n <= 1.5). Detailed flow and temperature fields are visualized in terms of the streamline and isotherm contours, respectively. At the next level, the results are analyzed in terms of the total drag coefficient and local Nusselt number variation along the surface of the hemisphere, together with its surface averaged value. The average Nusselt number increases with both the Grashof and Prandtl numbers. Furthermore, for fixed values of the Grashof and Prandtl numbers, and for a given orientation, shear-thinning behavior (n < 1) enhances the rate of heat transfer whereas shear-thickening (n > 1) impedes it with reference to that in Newtonian fluids, especially when there is a reasonable degree of advection. Finally, the present numerical results of drag coefficient and Nusselt number have been correlated using a general composite parameter, which is essentially a modified Rayleigh number. The use of such a Rayleigh number also emphasizes the varying nature of dependence of the average Nusselt number on the Grashof and Prandtl numbers governed by the type of fluid behavior, i.e., shear-thinning (n < 1) or shear-thickening (n > 1).