The method of Ilias and Govind for modeling ultrafiltration was modified to model a flat sheet air gap membrane distillation module with empty channels. In the membrane distillation process, there is mutual dependence of the momentum and heat transport processes. It complicates the solution of the governing equations and often leads to using simplifications. The developed method allows solving hydrodynamic and heat transport equations without additional assumptions for decoupling the equations with permeation taken into account. Velocity and temperature distributions inside the membrane feed channel were obtained, as well as the concentration profiles of a sparingly soluble salt (barium sulfate). Severe temperature polarization, occurring under poor mixing conditions, has been shown. Supersaturation profiles of barium sulfate are shown to be dependent on the inlet temperature of the membrane channel, and at certain conditions a maximum value of the barium sulfate concentration lies in the bulk of the channel, rather than at membrane surface.