The mass transfer rates into wavy falling films are larger than those predicted by smooth-film theory. Inertial, roll waves in the falling film flowing over a vertical tube are responsible for the largest enhancement. Transient, two-dimensional (2-D) governing equations were formulated for simultaneous heat and mass transfer in the film, with roll wave hydrodynamics as input. The equations, coupled nonlinearly at the vapor-liquid interface, were solved by an iterative finite-difference scheme. Average heat and mass transfer coefficients were extracted from the results and compared to experimental as well as theoretical data from the literature. Excellent agreement with penetration theory was obtained for the smooth film, but in the roll wave regime, the model predicted much higher transport rates than those possible with a smooth film. The model results indicate that the normal convective flux attributable to the transverse velocity in its inward phase, coupled with the effect of the corresponding streamwise velocity, is responsible for transport enhancement in such wavy films.