Theory of heat transfer during condensation in microchannels

A theoretical model for condensation in microchannels takes account of the effects of gravity and streamwise shear stress on the condensate surface as well as the transverse pressure gradient due to surface tension in the presence of change in condensate surface curvature. Numerical solutions of the relevant conservation equations have been obtained for various channel shapes, dimensions, vapor-to-surface temperature differences and vapor mass fluxes. The theory is reviewed and updated. The effect of channel inclination is included and new results are presented. When using boundary conditions of uniform vapor and surface temperature it is found that, over a certain length of channel, the local mean (around the channel perimeter) heat-transfer coefficient is essentially independent of gravity and vapor shear stress. For the surface tension dominated regime, an equation for the Nusselt number as a function of a single dimensionless group, analogous to that occurring in the simple Nusselt theory except that the gravity term is replaced by a surface tension term, has been derived both on the basis of dimensional analysis and by approximate theory. The equation represents all of the data satisfactorily. This is a step towards the goal of representing the solutions, including those conditions where shear stress and gravity play important roles, by relatively simple dimensionless algebraic equations, valid for any fluid and channel geometry, for convenient use in design and optimization.