Industrial equipment for drying polymeric coatings normally consists of a series of zones, each with a controlled temperature and airflow. Drying of a polymer-solvent solution is strongly affected by the variation of diffusivity, solvent vapor pressure, and solvent activity with temperature and composition. The equations of mass transfer by diffusion and of heat transfer by conduction and radiation describe changes in composition and temperature within the shrinking coating. This system of equations is solved by Galerkin’s method with finite element basis functions. The boundary conditions on dryer airflow and temperature change at the entrance to each zone. In a few test cases, the predictions show how evaporative cooling can slow drying in early zones where the coating temperature drops below the dryer temperature, whereas in later zones the coating temperature rapidly approaches the dryer temperature. Infrared heating can be used to reduce the extent of evaporative cooling. In the test cases and experiments, "blistering" occurs in later zones where high oven temperature causes the solvent partial pressure to rise; dryer parameters can be chosen to maintain solvent partial pressure just below ambient pressure in order to avoid "blistering" with least sacrifice of process speed.