Dead-core solutions to fast diffusion–reaction equation for catalyst slabs with power-law reaction kinetics and external mass transfer resistance

Abstract

This paper investigates semi-analytic approaches used to solve a two-point boundary value problem for nonlinear fast diffusion–reaction equation for catalytic slabs with external mass resistance. The kinetics considered is the power-law type having a fractional reaction exponent. The semi-analytic approach for dead-core problems with Fickian diffusion is generalized to models with non-Fickian diffusion. The dimensionless steady-state equation for mass conservation in the catalyst slab for a single n-th order chemical reaction and the non-Fickian diffusion model is derived and studied. We show that the dead zone can appear close to the pellet center under certain combinations of the following parameters: slab size, effective diffusivity, mass transfer coefficient, bulk reactant concentration, reaction order, reaction rate constant, and diffusion exponent. We also study the effects of the process parameters on the concentration profiles and length of dead zones. Analytical findings are verified by numerical simulations.