Laminar film condensation heat transfer on a vertical, non-isothermal,   semi-infinite plate
  This paper gives similarity transformations for laminar film condensation on a vertical flat plate with variable temperature distribution and finds analytical solutions for arbitrary Prandtl numbers and condensation rates. The work contrasts with Sparrow and Gregg assertion that wall temperature variation does not permit similarity solutions. To resolve the long-standing debatable issue regarding heat transfer in the non-isothermal case, some useful formulations are obtained, including a significant dependence of varying Prandtl numbers. Results are compared with the available experimental data. 
Jian-Jun Shu
physics.flu-dyn