On the extremum dissipation for steady state incompressible flow past a sphere at low Reynolds number

Abstract

A methodology based on sound non-equilibrium thermodynamics principles is developed to estimate the extremum dissipation point for steady-state incompressible flow past a sphere at low Reynolds numbers. It is shown, that the extremum dissipation point appears at the point when both the shear stress and the pressure at the surface of the sphere are equal to zero. The Reynolds number and the position of the extremum dissipation flow past a sphere were further estimated with the aid of a mathematical model for pressure distribution on the sphere surface, accounting for both creeping and ideal flow. The parameters of the model were determined by comparison of the calculated pressure distribution at the surface with the available literature data. The conditions at which the separation angle and the extremum dissipation angle coincide were also investigated. It is believed that this work could be used to further elucidate the flow past a sphere.