Using Generalized Dimensional Analysis to Obtain Reduced Effective Model Equations for Condensation in Slender Tubes With Rotational Symmetry

In this paper, we study the continuum physics model equations for condensation (two phase flow problems) in vertical tubes with small diameter and obtain reduced model equations. We found that generalization of dimensional analysis to multiple spatial dimensions is an excellent tool for that purpose, so that a review of this method is also part of the paper. We obtain the nondimensional numbers of the problem and derive reduced bulk and interface equations. The problem is characterized by three length scales, tube radius R, tube length L, and initial film thickness H. For small ratio $ɛ=H/L$⁠, we derive a single ordinary differential equation for the condensate film thickness as function of axial position with tube radius as parameter, which agrees well with commonly used (parametric) models from literature. Our model is based on the physical dimensions of the problem which gives a greater geometrical flexibility and a wider range of applicability. We also discuss the effect of surface tension and the limit of the model.