Analysis of Mass Transfer in Hollow-Fiber Membrane Separator via Nonlinear Eigenfunction Expansions

Abstract

The Generalized Integral Transform Technique (GITT) is a well-established hybrid numerical-analytical method applicable to the solution of linear or non-linear convection-diffusion problems, which presents relatively low computational cost and automatic error control. Here, this hybrid method is employed in the analysis of mass transfer in hollow-fiber mass separators. The adopted model considers fully developed laminar flow of a Newtonian fluid with diffusion and reaction transport effects of the solute through the membrane pores. The diffusive-reactive process at the membrane is represented through a nonlinear boundary condition. A hybrid numerical-analytical solution is obtained, based on retaining the original nonlinear boundary condition coefficients in the eigenvalue problem proposition. The developed nonlinear eigenfunction expansion is then thoroughly analyzed in terms of convergence behaviour. The novel approach is also critically compared against previously reported numerical results for typical parametric values and with an alternative convergence enhancement approach based on the proposition of a nonlinear filter, that makes the boundary condition homogeneous and allows for an integral transform solution through the proposition of a linear eigenvalue problem.