Transient Melting of a Solid Heated by a Condensing Saturated Vapor—Case I: Negligible Interface Curvature

Abstract

A transient analysis has been performed to analytically determine the instantaneous dimensionless thickness of a vertically suspended solid at its melting temperature upon which a saturated vapor is condensing. The spatial variation and transient behavior of the melt-condensate liquid film, which is continuously drained, has also been obtained from the closed form analytical solution of the uncoupled equations for the solid-liquid and liquid-vapor interface motions under the condition of assumed negligible interface curvature. Classical boundary layer assumptions were applied to the convection process in the subcooled liquid film which was analyzed using integral techniques. From the analytic solution to the resultant interface motion equations in terms of characteristic curves, the functional dependence of the melting solid and the liquid layer thicknesses on the time and space variables was established. The liquid mass flux and heat transfer coefficient were then obtained analytically.