Film condensation generated by a forced cooling fluid

Abstract

In this paper we analyze the condensation process of a saturated Vapor in contact with one side of a vertical thin plate, caused by a forced flow on the other surface of the plate. The effects of both longitudinal and transversal heat conduction in the plate are considered. Due to the finite thermal conductivity of the plate, a longitudinal temperature gradient arises within it changing the mathematical character of the problem from parabolic to elliptic. The momentum and energy balance equations are reduced to a system of integro-differential equations with five parameters: the Prandtl (Pr-c) and a Jakob (J alpha) numbers, a non-dimensional plate thermal conductivity alpha, the aspect ratio of the plate epsilon and beta defined by the ratio of the thermal resistance of the condensed layer to the thermal resistance of the forced cooling how. In order to obtain the spatial evolution of the condensed layer thickness and the related temperature of the plate as a function of the longitudinal coordinate position, the coupled balance equations are integrated in the asymptotic limit J alpha --> 0, including the cases of very good and poor conducting plates. For finite values of the parameters alpha and beta, this paper shows that effect of the heat conduction through the plate modifies the classical Nusselt solution substantially. Two terms of the asymptotic expansions, for the limiting case of alpha --> infinity and finite beta, are enough to reproduce the temperature distribution and the condensed layer thickness evolution with high accuracy even for values of or of order unity.