Effect of Prandtl number on thermo-fluidic transport characteristics for mixed convection past a sphere

Abstract

In this paper, we numerically investigate the influence of Prandtl number on the thermo-fluidic transport characteristics for steady laminar mixed convection from a sphere in an assisting flow configuration. The stream function-vorticity formulation with a higher order finite difference compact scheme in spherical polar coordinates has been used to solve the governing transport equation of motion and thermal energy. The fluid flow and heat transfer characteristics are presented in terms of streamline and isotherm contours in close proximity to the sphere together with local Nusselt number along the sphere surface and average Nusselt number for the Reynolds number in the range 5 ≤ Re ≤ 200, Richardson number in the range 0 ≤ Ri ≤ 1.5 and Prandtl number ranging from 0.72 to 40. Critical Richardson number has been identified for different values of Reynolds number and Prandtl number, signifying the strength of the force of streamwise acceleration due to the buoyancy and externally imposed flow field relative to the combined viscous resistance and pressure force, for which the flow separation phenomenon occurring in the downstream region of the sphere gets suppressed. It reveals that for lower values of Reynolds number, the average Nusselt number monotonically increases with Richardson number for any particular value of Prandtl number. At higher values of Reynolds number, contrasting features have been observed. For lower values of Prandtl number, the average Nusselt number increases monotonically with Richardson number, while for higher values of Prandtl number the variation is non-monotonous.