Graetz problem for the conjugated conduction-film condensation process

Abstract

We study the condensation process of a saturated vapor in contact with the external surfaces of two vertical thin plates. The condensation is caused by a forced cooling how between the internal surfaces of the plates, The longitudinal heat conduction effects in the plate are considered. By use of perturbation techniques, the governing equations are reduced to a system of integro-differential equations with five nondimensional parameters: the Prandtl number of the condensed fluid Pr-c, the Jakob number Ja, the nondimensional plate thermal conductivity alpha, the aspect ratio of the plate epsilon, and the ratio of the thermal conductance of the condensed layer to the thermal conductance of the forced cooling how beta. The condensed-layer thickness and the temperature of the plates are estimated in the asymptotic limit Ja --> 0 and alpha/epsilon(2) much greater than 1 (thermally thin wall regime).