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• RBF-DG was a novel prediction for absorption process in falling film and membrane based absorbers. • RBF-DG method provided excellent solutions. • Comparison with analytical solutions and experiments provided good agreements. • It becomes possible to predict accurately the absorption rate of falling film and membrane. The present investigation is intended to develop an understanding of how the vapor pressure and inlet temperature of the solution affect the absorption rate, which is helpful for the design of absorption heat pump systems. Many conjugated heat and mass transfer processes in falling film and membrane during lithium bromide (LiBr) absorption have not been well addressed. This paper proposes combining the meshless Radial Basis Function (RBF) and Discontinuous Galerkin (DG) methods to solve the conjugated heat and mass transfer in falling film and membrane-based absorption problems. The derivatives in the transverse direction are discretized using the RBF method. Owing to the parabolic nature of the governing equations, the DG methods can be used to discretize the derivatives in the streamwise direction. The efficacy of the proposed method is shown by comparing its results with analytical solutions and experimental data available in the literature. Furthermore, the proposed method is used to evaluate the analytical solutions of the heat and mass transfer problem in a membrane-based absorber. The previous published works simplified the problem to obtain the analytical solutions by providing the mean temperature and concentration values as the boundary conditions at the membrane-solution interface. The comparison of the RBF-DG method and the analytical solutions reveals that there are minor changes in temperature and local concentration values along the streamwise direction, but the profiles and trends are relatively similar across the film. A comparison of mass absorption rate calculations shows that RBF-DG and analytical solutions are compatible. The advantage of the numerical method is that various types of boundary conditions can be handled easily without any simplifications. Moreover, the numerical results of the proposed method are compared with experimental data, and they present good agreement. As a results, the absorption rate of falling film and membrane becomes capable of being accurately predicted. [ABSTRACT FROM AUTHOR]