Longitudinal heat conduction effects on a vertical thin plate in a steady laminar condensation process

Abstract

In this paper, we analyze the steady-state condensation process of a saturated vapor in contact with one side of a vertical thin plate, caused by an uniform cooling rate on the other surface of the plate. The effects of both longitudinal and transverse heat conduction in the plate are considered. The momentum and energy balance equations are reduced to a system of three differential equations with four parameters: the Prandtl (Pr) and Jakob (Ja) numbers, a nondimensional plate thermal conductivity alpha, and the aspect ratio of the plate epsilon. To obtain the 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 Ja --> O, including the cases of very good and poor conducting plates. The results obtained indicate that the effect of the longitudinal heat conduction through the plate on the condensed layer thickness changes from a profile x(1/4) for a good conducting plate to x(1/3) for a poor conducting plate.