Heat transfer in vacuum membrane distillation: Effect of velocity slip

A two-dimensional, boundary layer model is presented, for describing the heat transfer in the feed channel of a vacuum membrane distillation (VMD) module. The model formulation allows for variations of viscosity with temperature, and introduces an 'effective' slip coefficient so as to account for the possible deviation of the flow and heat transfer characteristics over a liquid-gas interface, from those at a solid surface. The model solution provides the temperature field in the feed channel and its dependence on the bulk velocity and temperature, as well as the vapor mass flux across the membrane. While the effect of a temperature variable viscosity becomes increasingly apparent at higher temperatures, its effect on the evaporation mass flux is not substantial. The relative contribution of transverse convection to the evaporation mass flux is shown to be insignificant, within the range of parameters examined. In the presence of an 'effective' velocity slip, the degree of temperature polarization is reduced and a corresponding increase in the evaporation mass flux is observed. Calculated results are in good agreement with experimental data. The presented results suggest that the effect of alternating solid and gas interfaces, encountered by the fluid, on the flow field and resulting heat transfer, should be accounted for if accurate predictions are to be made.