Conservation Equations for a Nonsteady Flow of a Compressible Viscous Single-Phase Fluid in Various Coordinate Systems

Abstract

Abstract : Based on a generalization of the Reynolds transport theorem the mass, momentum and energy conservation equations for a nonsteady flow of a compressible viscous single-phase fluid (expressed in vector and dyadic notations) are first formulated in integral form (in terms of moving volume and surface elements), next converted into differential form and then transformed in terms of orthogonal curvilinear coordinates. Specialized equations are obtained for three dimensional flows in Cartesian, cylindrical and spherical coordinates. These equations can then be reduced to corresponding equations for one and two dimensional flows in various coordinates. Equations for the vorticity, entropy and enthalpy and Bernoulli equation are also summarized.