Coupling between laminar film condensation and natural convection on opposite sides of a vertical plate

Theoretical analyses which incorporate one-dimensional heat conduction along a plate and transverse heat conduction approximations are presented to predict the net heat transfer between laminar film condensation of a saturated vapour on one side of a vertical plate and boundary layer natural convection on the other side. It is assumed that countercurrent boundary layer flows are formed on the two sides. The governing boundary layer equations of this problem and their corresponding boundary conditions are all cast into dimensionless forms by using a non-similarity transformation. Thus the resulting system of equations can be solved by using the local non-similarity method for the boundary layer equations and a finite difference method for the heat conduction equation of the plate. The plate temperature and the heat flux through the prate are repetitively determined until the solutions for each side of the plate match. The predicted results show that the effect of Pr-c is not negligible for larger values of A* (thermal resistance ratio between natural convection side and condensing film side) and the approximation of transverse heat conduction overpredicts the plate temperature for lower values of R(t) (thermal resistance ratio between plate and condensing film). However, no significant differences are observed between the two different approximations for higher values of R(t).