Concentration-dependent diffusion in a finite slab with and without chemical reaction

Abstract

Concentration-dependent diffusion in symmetrical and asymmetrical geometrical systems is investigated in this work. Also included is the chemical reaction of general order. Different types of concentration dependence of diffusion coefficient are considered. The governing nonlinear diffusion equation is solved by the orthogonal collocation method which involves the approximation of the spatial derivative term by an orthogonal polynomial of the Legendre type. The main advantage of the orthogonal collocation method is that the resulting ordinary differential equations can be integrated with precision and stability. Due to these advantages, a wide range of nonlinear diffusion problems can be tackled without much difficulty.