Analytical solution of film mass-transfer on a partially wetted absorber tube

This work presents a two-dimensional analytical solution of the governing differential equation for falling film vapour-absorption around a plain horizontal tube. The solution of the species transport equation gives the LiBr mass fraction distribution within the liquid absorptive film flowing along the tube surface and can be used to characterize the mass transfer performance of falling film absorbers or generators. By means of the inclusion of partial wetting effects at reduced solution mass flowrates, this study obtains an analytical expression of the mass transfer coefficient of these devices applicable over an extended range of operative conditions. The hypotheses of small penetration for physical absorption and constant heat flux condition are applied at the film interface to reach a closed-form solution. Fourier method is used to solve the problem and the eigenvalues obtained from the characteristic equation depend on Lewis number, Biot number and the dimensionless heat of absorption. Given the boundary condition at the wall, the two-dimensional mass fraction field of the laminar film can be expressed analytically as a function of Schmidt, Reynolds numbers, the tube dimensionless diameter and the ratio of the wetted area to the total exchange surface. Finally, mass transfer coefficient and absorbed mass flux are locally and globally investigated as functions of the influent dimensionless groups to clarify their effects on the physical process and screen the potentiality of the model. Results show notable qualitative and quantitative agreement with previous numerical solutions and experimental results from previous literature. This model constitutes a widely applicable and time-saving tool for actual system simulations, design and control.