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.
Date of this Version
H. Wang, S. V. Garimella and J. Y. Murthy, “An Analytical Solution for the Total Heat Transfer in the Thin-Film Region of an Evaporating Meniscus,” International Journal of Heat and Mass Transfer Vol. 51, pp. 6317-6322, 2008.