Solving partial differential equations of gas–solid reactions by orthogonal collocation

Abstract

In this work the solution of the coupled partial differential equations for noncatalytic gas–solid reactions has been considered by orthogonal collocation. First of all, by an integral transformation and then by applying the orthogonal collocation method, these partial differential equations are converted to the ordinary differential equations. Then the equations are solved and the conversion–time profiles are obtained. The solution of the equations for volume reaction model, grain model and grain model with product layer resistance, modified grain model, random pore model, nucleation model and reaction of two gas with one solid has been presented in this work. The orthogonal collocation is a rapid method for solving of these equations and shows a good accuracy with respect to other solution techniques in the literature.