Approximate Solution of Non-Linear Reaction-Diffusion in A Thin Membrane: Taylor Series Method

J Visuvasam, Et Al

doi:10.17762/turcomat.v12i1s.1934

Abstract

The nonlinear reaction-diffusion cycle in the thin membrane that describes the chemical reactions involving three species is studied. The model consists of the system of on nonlinear reaction-diffusion equations. The closed type of analytical expression of concentrations for the enzyme was developed by solving equations using the Taylor series formula. This results in the mixed Dirichlet and Neumann boundary conditions. Taylor series method similar to exponential function method. This technique provides approximate and simple solutions that are quick, easy to compute, and efficiently correct. These estimated findings are compared to the nuxmerical results. There is a good agreement with the simulation results.

Highlights

According to the reaction mechanism product, a diffusion-controlled chemical reaction between two species A and B is considered to be a product
The corresponding non-steady state system of this problem was perceived by Haario Seidman [5] to describe the reactions in the film for the gas/liquid interface under the complex boundary conditions
In that paper a simple and efficient approach is introduced to solve the system of nonlinear reactiondiffusion equation in a thin membrane

Summary

Introduction

According to the reaction mechanism product, a diffusion-controlled chemical reaction between two species A and B is considered to be a product. The reaction path consists of a coupled pair of simple, irreversible and fast reaction mechanisms [4]. Where and denote the binary reaction rates. Seidman et al [2, 3] and Kalacheve et al [ 4] presented a detailed singular perturbation analysis of the steady-state problem. The corresponding non-steady state system of this problem was perceived by Haario Seidman [5] to describe the reactions in the film for the gas/liquid interface under the complex boundary conditions. [8] and Ananthaswamy et al [9] developed approximate analytical expressions for steady-state concentrations using the homotopy perturbation and homotopy analysis methods Rajendranet al. [8] and Ananthaswamy et al [9] developed approximate analytical expressions for steady-state concentrations using the homotopy perturbation and homotopy analysis methods

Methods

Findings

Discussion

Conclusion