Stability of a condensate film flowing down a vertical plane
The mathematical problem governing the motion and temperature in a two dimensional condensate film are formulated. The linearized stability problem is derived under the parallel flow assumption. A second—order perturbation solution of the stability problem is presented using the Nusselt solution as base flow. The boundary layer equations of laminar film condensation are solved to first-order by using perturbation methods. A first-order perturbation solution of the stability problem is determined using the first-order solution of the boundary layer equations as base flow. The first-order solutions of the stability problem lead to approximate closed form expressions for the neutral stability curve. A nonlinear algebraic equation for the neutral stability curve is found from the second-order solution of the stability problem which is solved numerically.
It is found that decreasing the temperature drop across the condensate film has a stabilizing effect. This is observed to be in qualitative agreement with the previous experimental studies. It is also found that increasing the Prandtl number or the surface tension has a stabilizing effect on the condensate film. Critical distances up to which the condensate film is completely stable are predicted. The predictions are discussed with reference to the previous experimental studies. The critical distance and neutral stability predictions disagree with the results from the previous stability analyses. The reasons for this disagreement are discussed. The results indicate that the effects of acceleration and convection in the base flow are negligible in the linearized stability problem for almost all practical situations.