We study the conjugate condensation-heat conduction process of a saturated vapor in contact with a vertical fin, including both longitudinal and transversal heat conduction effects. The momentum and energy balance equations are reduced to a nonlinear system of partial differential equations with four parameters: the Prandtl number, Pr-c, Jakob number, Ja, a nondimensional fin thermal conductivity alpha and the aspect ratio of the plate epsilon. Using the small Jakob limit and the boundary layer approximation, the total mass flow rate of condensed fluid has been obtained for all possible values of the involved parametric space.