On the Solution of Non-Isothermal Reaction-Diffusion Model Equations in a Spherical Catalyst by the Modified Adomian Method

Abstract

We investigate the reactant diffusion within a porous catalytic pellet including the heat of reaction. The Lane–Emden boundary value problem with an Arrhenius reaction rate is used to model the reactant concentration. We combine the Volterra integral form with the Adomian decomposition method to solve the equivalent Fredholm–Volterra integral equation. We then estimate the reactant concentration at the center of the catalytic pellet and the iterated Shanks transform is used to improve the accuracy of the approximations. The objective error analysis formulas are used to demonstrate a high accuracy and rapid rate of convergence, which does not depend on a priori knowledge of the exact solution or comparison with an alternate approximation method. Thus low-stage approximations by the Adomian decomposition method are validated for parametric simulations of the reactant concentration profiles and the effectiveness factor profiles. Our approach demonstrates enhancements over previous investigations, and is readily extensible to more general diffusion reaction models in catalytic reactor engineering.

Keywords:

• Adomian decomposition method
• Adomian polynomials
• Arrhenius reaction
• Boundary value problems
• Lane–Emden equation
• Spherical catalyst