Analytical solution for combined heat and mass transfer in laminar falling film absorption using first type boundary conditions at the interface

摘要

Since the late seventies of the 20th century, several analytical models for combined heat and mass transfer in laminar falling film absorption have been proposed. Nevertheless the analytical solutions obtained with the Fourier method for the coupled process are complex and for short flow length a certain instability occurs which have been explained with the inconsistency of the initial and boundary conditions. Therefore boundary layer models have been justified in order to solve the transfer problem for short flow length. Moreover a linear approximation of the phase equilibrium is required. The analytical solutions for heat and mass transfer presented in this paper are obtained by using the Laplace transform to solve the partial differential equations for an isothermal as well as impermeable wall. An originally unknown constant temperature and mass fraction boundary condition at the interface are set. The temperature and mass fraction profile across the film are obtained formally independently. In order to determine the yet unknown interface temperature and mass fraction the phase equilibrium and the interface energy balance are applied, using averaged gradients with regard to the streamwise coordinate. The interface temperature and mass fraction obtained with this procedure are interpreted and treated as mean values. From the known evolution of the mean interface temperature and mass fraction, the local values are derived by inverting the first mean value theorem for integration. The results show very good agreement to the established analytical solutions. The solving procedure does not depend on the input parameters such as the Lewis number for instance, which is needed in order to determine the eigenvalues within the Fourier method. Moreover arbitrary correlations for the phase equilibrium are applicable. The present solution is mathematically stable and offer explicit expressions in order to calculate the mean heat and mass fluxes directly. Therefore this solution is favourable to implement entire absorption process simulation, yet describing the coupled heat and mass transfer process comprehensively.