Effects of inclination angle on the steady flow and heat transfer of power-law fluids around a heated inclined square cylinder in a plane channel

Abstract

The incompressible Poiseuille flow and heat transfer of a power-law fluid across an inclined long square cylinder confined in a two-dimensional channel is investigated numerically in the steady laminar flow regime. The effects of inclination angle, α, and power-law index, n, on the non-dimensional pumping power and the Nusselt number are studied for the conditions: 1 ⩽ Re ⩽ 40, 0 ⩽ α ⩽ 45, 0.4 ⩽ n ⩽ 1.8, Pr = 50 and blockage ratio β = 1/4. It is verified that the flow is steady in these ranges of conditions and the vortex shedding occurs only for n = 0.4 and α = 45 at Re ⩾ 33. In the steady flow regime the results show that the total drag coefficient on the cylinder increases with an increase in the power-law index and the maximum total lift coefficient occurs at α = 15. Moreover, a decrease in the power-law index and/or an increase in the inclination angle increase the Nusselt number and decrease the non-dimensional local pumping power. Simple correlations are also introduced for drag coefficient, local pressure drop and Nusselt number as functions of n, α and Re.