This chapter involves a numerical study of coupled heat and mass transfer during the absorption of water vapor by a thin liquid film of an aqueous solution of lithium bromide in a vertical channel. The channel is cooled by a countercurrent flow of water. Ηeat and mass transfer in the liquid film are described by the Navier–Stokes equations, as well as the energy and diffusion equations, along with their associated boundary conditions. Τhe governing equations are discretized using the finite volume method. Τhe resolution of the obtained algebraic equation systems is based on the Thomas algorithm. Validation of the developed computational code has shown good agreement with numerical results available in the literature. Τhe study delves into the impact of operating parameters on the absorption process, and the results have shown that the absorption mass flux is enhanced for a low Reynolds number, high inlet pressure, and concentration. Additionally, the cooling of the liquid film plays a critical role in enhancing absorption, and a low cooling temperature is favorable for the process.