An analytical solution for heat and mass transfer in falling film absorption with arbitrary thermal boundary conditions

Absorption, the process of capturing the absorptive component in the volume of the absorbent, is essential for various industrial applications. Several analytical solutions exist for falling film absorbers, which is the most common absorber used in industrial applications. However, in existing models, the temperature of the heat transfer fluid has been assumed to be constant, while the design of falling film absorbers for absorption heat pumps requires an analytical model accounting for the variation in the heat transfer fluid temperature changes. This study presents a new and comprehensive analytical solution for non-volatile absorbents using the Laplace transform method, where an arbitrary heat flux is applied to the heat exchanger wall in contact with the heat transfer fluid. For the first time, this study provides analytical solutions for various wall boundary conditions, including arbitrary heat flux, isothermal, as well as mean, linear, and exponential temperature variation of the heat transfer fluid. The present model is validated with experimental data available in the literature with a relative difference of 11% for several absorber configurations. Considering a case study of an absorber with a length of 1 m, it is shown that assuming an average temperature for the heat transfer fluid overestimates the optimal length of the absorber and results in up to 3 times the absorption rate at the outlet region of the absorber compared to a linear and an exponential temperature estimation.