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Heat and mass transfer with a uniformly distributed falling liquid desiccant film in a cross-flow parallel plate gas-liquid heat exchanger is predicted, and the results compared with experiment. The process air is in cross-flow over the desiccant film. Refrigerant flows through the heat exchanger tubes and removes the heat of absorption for dehumidification and supplies the heat for regeneration. The governing equations, boundary conditions, and interfacial equilibrium conditions for the concentration, temperature and pressure are presented. The problem is more complex than for cocurrent or countercurrent flow, as it is fully three-dimensional.