NONLINEAR EIGENVALUE PROBLEM APPROACH IN THE INTEGRAL TRANSFORMS ANALYSIS OF METAL SEPARATION BY POLYMERIC DIFFUSIVE MEMBRANES

摘要

The Generalized Integral Transform Technique (GITT) is a well-established tool in the hybrid numerical-analytical solution of various classes of nonlinear diffusion and convection-diffusion problems. Quite recently, a variant in the GITT approach has been advanced, based on retaining the original nonlinear operator coefficients in the eigenvalue problem proposition, and has been demonstrated in diffusion problems with nonlinear boundary conditions, illustrating the relative gains in convergence enhancement. The present work further demonstrates this nonlinear eigenvalue problem path in the GITT approach, by considering a mass transfer application of metal extraction through a polymeric hollow fiber membrane with diffusive separation. The methodology is here illustrated for this convection-diffusion problem with nonlinear boundary condition coefficient. The novel approach is then critically compared to the methodology employing a linear eigenvalue problem basis, for typical parametric values, but with an alternative convergence enhancement approach based on a nonlinear filter, so as to also demonstrate its convergence enhancement effect with an eventually increased computational effort for a fixed truncation order.