An analytical solution for the total heat transfer in the thin-film region of an evaporating meniscus

When a liquid wets a solid wall, the extended meniscus may be divided into three regions: a non-evaporating region where liquid is adsorbed on the wall; a thin-film region where effects of long-range molecular forces (disjoining pressure) are felt; and an intrinsic meniscus region where capillary forces dominate. Among these, the thin-film region is characterized by high heat transfer rates because its small thickness results in a very low conduction resistance. In this work, a simplified model based on the augmented Young–Laplace equation is developed and an analytical solution is obtained for the total heat transfer in the thin-film region. The results are consistent with previously published numerical solutions. The present work is valid for a much wider range of fluid thermal conductivity than a previous analytical solution by Schonberg and Wayner, which is only applicable for fluids with very low conductivity. Based on the analytical expression developed, the thin-film heat transfer is found to increase with increasing disjoining pressure, and to decrease with increasing liquid viscosity.