Compressible Low Reynolds Number Flow around a Sphere

Abstract

The low Reynolds number flow past a sphere is studied for cases involving significant variation in density and temperature. An order of magnitude analysis of the governing equations for a continuum flow indicates the relative importance of compressibility, variable transport properties, and viscous dissipation. The order of magnitude of the nondimensional impressed temperature difference τ is shown to be useful as a guide for distinguishing problems with different governing physical characteristics. The cases τ = O(1) and τ = O(Re), where Re is the Reynolds number, are analyzed in detail. Inner and outer asymptotic expansions are derived for each of the flow variables in terms of the parameters Re τ and Mach number M∝. For τ = O(Re) the solutions are developed up to and including the first effect of nonzero M∞. For τ = O(1) the velocity expansions are calculated to zeroth order and the temperature expansions to order Re. Drag and heat transfer coefficients are calculated for each case