Surface tension effects on a conjugate laminar filmcondensation process for a vertical fin placed in a porous medium

In this work we treat theoretically the conjugate film-condensation process on a vertical fin embedded in a homogeneous porous medium filled with a saturated vapor. The presence of the solid matrix results in the occurrence of a two-phase flow region governed by gravity and capillarity. In order to predict the influence of surface tension on the condensed thickness, an overall energy balance in the liquid, the two-phase region, and through the fin was conducted. Therefore, the conservation equations of mass, momentum, and energy for the condensed film, together with the energy equation in the fin are reduced to a nonlinear system of two differential equations containing five dimensionless numbers: the Bond number, Bo; the Jakob number, Ja; the Rayleigh number Ra; a conjugate heat transfer parameter, α, which represents the competition between the heat conducted by the fin in the longitudinal direction and the heat conducted through the condensate film, and the aspect ratio of the fin, η. Using the limit of Ja 蠐 1 with Ra 蠑 1, and finite values of Bo, together with the boundary layer approximation for the film condensation process, the non-dimensional heat transfer or Nusselt number and the overall mass flow rates of the condensed fluid have been obtained as functions of the involved dimensionless parameters.