A new approximate analytical method for solving some non-linear boundary value problems in Reaction-Diffusion model

Document Type : Research Paper

Authors

1 Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India.

2 Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India.

Abstract

The applications of a Reaction-Diffusion boundary value problems are found in science, biochemical applications, and chemical applications. The Ananthaswamy-Sivasankari method (ASM) is employed to solve the considered specific models like non-linear reaction-diffusion model in porous catalysts, spherical catalysts pellet, and catalytic reaction-diffusion process in a catalyst slab. An accurate semi-analytical expression for the concentrations and effectiveness factors are given in the explicit form. Graphical representations are used to display the impacts of several parameters, including the Thiele modulus, characteristic reaction rate, concentration of half-saturation, reaction order and dimensionless constant in Langmuir-Hinshelwood kinetics. The impact of numerous parameters namely the Langmuir-Hinshelwood kinetics and Thiele modulus on effectiveness factors are displayed graphically. Our semi-analytical findings shows good match in all parameters when compared to numerical simulation using MATLAB. Many non-linear problems in chemical science especially, the Reaction-Diffusion equations, Michaelis-Menten kinetic equation, can be resolved with the aid of the new approximate analytical technique, ASM.

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Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 2
March 2025
Pages 432-449

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History

  • Receive Date: 06 February 2024
  • Revise Date: 08 April 2024
  • Accept Date: 21 April 2024

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