False diffusion in convection and diffusion with chemical reaction

Abstract

The method of moments is used to obtain the false diffusion coefficient as D f a l s e = u Δ x 2 ( 1 − u Δ t Δ x 1 1 − k Δ t ) for the unsteady state ‘reactor-and-tube’ model with a first-order chemical reaction. A comparison is made between the upwind finite difference solution (i.e. the continuous stirred chemical reactor in series) and the exact solution with a false diffusion coefficient.