Effects of the Finite Thermal Conductivity of the Condensed Phase on Evaporation and Condensation Flows of Its Vapor: Existence of the Maximum Mass and Energy Flows

Abstract

Transient to steady motions of a vapor due to evaporation and condensation processes between the plane condensed phases with temperature fields as their internal structures have been studied in detail based on the new governing system at the ordinary fluid dynamic level, i.e., fluid dynamic formulation, which consists of the compressible Navier-Stokes equations and the boundary conditions appropriate for evaporation and condensation problems derived earlier from the kinetic theory analysis. The previous studies based on the Boltzmann equation of BGK type have shown that the mass and energy flows may take their maximum values at a certain value of the latent heat parameter when the condensed phases have temperature fields as their internal structures; the internal structure is a reflection of the thermal conductivity of the condensed phase being finite compared to that of its vapor. This is a striking feature in contrast to the case in which no internal structures exist in the condensed phases. Particular attention, therefore, is paid to the quantitative aspect of this behavior of the mass and energy flows. Incidentally, the comparison between the present results and the corresponding ones from the Boltzmann equation of BGK type has been made and found to be quite good, indicating that the fluid dynamic formulation works satisfactorily in the present case with temperature fields as the internal structures of the condensed phases.