Transient laminar-film condensation on a vertical plate

Abstract

This work addresses the problem of transient, laminar-film condensation onto a vertical surface. It examines the behavior of the liquid film in response to changes in the temperature drop across the film or in the interfacial shear stress. Numerical solutions of the governing equations are compared with a simpler quasisteady analysis. The quasisteady analysis is adequate in many cases (e.g., atmospheric water). However, as the Jakob number or Jakob divided by Prandtl number approaches unity, the full equations and the quasisteady analysis yield significantly different predictions for heat transfer and mass flux during the transient. This reflects the increasing importance of accounting for the development of the temperature and velocity profiles. Nomenclature Cp = liquid specific heat D2 = finite-difference form of the Laplacian operator g = gravitational acceleration hfg = latent heat of vaporization Ja = Jakob number, Cp AT+ /hfg k = liquid thermal conductivity L = plate length Pr = liquid Prandtl number, v/a q = interfacial heat flux T = temperature t = time u = streamwise velocity v = cross-stream velocity x = streamwise coordinate y = cross-stream coordinate a = liquid thermal diffusivity T = liquid mass flux per unit width of plate d = film thickness d yy = film thickness at x + = L using Nusselt theory A = difference or increment fj. = liquid dynamic viscosity v = liquid kinematic viscosity p = liquid density i = interfacial shear stress