On Paradoxical Phenomena During Evaporation and Condensation between Two Parallel Plates

TL;DR

This paper integrates kinetic theory with continuum models to analyze temperature inversion phenomena during evaporation and condensation between parallel plates, revealing new insights into interfacial temperature jumps and phase behavior.

Contribution

It provides a combined kinetic-continuum framework that rederives the temperature inversion criterion and explains interfacial temperature jumps in evaporation and condensation.

Findings

Temperature inversion can occur with vapor temperature exceeding wall temperatures.

Interfacial temperature jumps follow the external temperature difference direction.

Evaporation and condensation can occur at opposite temperature sides when latent heat is small.

Abstract

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.