  Kinetic theory has long predicted that temperature inversion may happen in
the vapor-phase for evaporation and condensation between two parallel plates,
i.e., the vapor temperature at the condensation interface is higher than that
at the evaporation interface. However, past studies have neglected transport in
the liquid phases, which usually determine the evaporation and condensation
rates. This disconnect has limited the acceptance of the kinetic theory in
practical heat transfer models. In this paper, we combine interfacial
conditions for mass and heat fluxes with continuum descriptions in the bulk
regions of the vapor and the liquid phases to obtain a complete picture for the
classical problem of evaporation and condensation between two parallel plates.
The criterion for temperature inversion is rederived analytically. We also
prove that the temperature jump at each interface is in the same direction as
externally applied temperature difference, i.e., liquid surface is at a higher
temperature than its adjacent vapor on the evaporating interface and at a lower
temperature than its adjacent vapor on the condensing interface. We explain the
interfacial temperature jump and temperature inversion using the interfacial
cooling and heating processes, and we predict that this process can lead to a
vapor phase temperature much lower than the lowest wall temperatures and much
higher than the highest wall temperature imposed. When the latent heat of
evaporation is small, we found that evaporation can happen at the low
temperature side while condensation occur at the high temperature side,
opposing the temperature gradient.
