Integral relations for the interfacial heat and mass transfer resistivities and the inverted temperature gradient

Abstract

The occurrence of an inverted temperature gradient in a vapor between two liquids kept at different temperatures was first predicted by Pao [Phys. Fluids 14, 306 (1971)] using kinetic theory. Using integral relations for the interfacial heat and mass transfer resistivities derived in an earlier paper, we show the general validity of a criterion for the occurrence of an inverted temperature gradient for a one-component fluid in the slow evaporation/condensation regime. This criterion was first derived by Pao and subsequently rederived in an equivalent form using nonequilibrium thermodynamics. The general validity of this criterion means that there will always be an inverted temperature gradient in the vapor between a hot and cold liquid. We present numerical solutions of the nonequilibrium van der Waals square gradient model which agree with this general result. The numerical results also show the effects of the magnitude of the evaporation/condensation flux and the excess resistivity in the interfaces. We only consider fluxes and gradients in the direction normal to the interfaces, so the system is in essence one-dimensional.