On New High Order Quasilinearization Approaches to the Nonlinear Model of Catalytic Reaction in a Flat Particle

A novel computational approach known as pseudospectral quasilinearization (SQLM) is employed to tackle the two-point boundary value problem describing the reactivity behaviour of porous catalyst particles subject to both internal mass concentration gradients and temperature gradients, in endothermic or exothermic catalytic reactions. A comparison with the numerical results generated using the inbuilt MATLAB boundary value solver, bvp4c, for different values of the governing physical parameters is performed and an excellent agreement is achieved. A systematic way of improving the convergence of the SQLM is also presented. 1. Introduction In many engineering and industrial applications, catalytic processes in chemical reactors are often considered to be very useful. This induces particular attention to the study of catalytic reactions at the single-particle level [1]. Moreover, the problem of how the intraparticle diffusion of molecules would modify the overall reaction behaviour of porous catalyst particles had been studied over nearly a quarter of a century [2–4]. Majority of chemical reactions are accompanied by heat transfer effects; they either release or absorb heat. This can lead to appreciable increase (or decrease) of temperature toward the particle centre [5–7]. Since chemical reaction rates vary rapidly (exponentially) with temperature, this effect could radically change the behaviour of the catalyst particles from that which we would otherwise expect. Analysis of chemical kinetics with diffusion effects usually leads to solving highly nonlinear differential equations. Detailed reviews of mathematical models describing reactions in a porous catalyst particle can be found in [8]. Assuming a flat geometry for the particle and that conductive heat transfer is negligible compared to convective heat transfer, Hlavácek et al. [9] derived a dimensionless nonlinear two-point boundary value problem for catalytic reaction in a flat particle as with boundary condition where is the reactant concentration, is a coordinate measured along the particle, is the Thiele modulus or the reaction rate parameter, is the activation energy parameter that expresses the sensitivity of the reaction rate to temperature, and is the heat evolution parameter that shows the maximum temperature variation which could exist within the particle relative to the boundary temperature. The main objective of the current research is to solve the nonlinear problem described in (1)-(2) using the pseudospectral quasilinearization method (SQLM). This method is formed by blending the