Solution of the non-isothermal reaction-diffusion equation in a spherical biocatalyst
DOI:
https://doi.org/10.62486/978-9915-9851-0-7_202645Keywords:
Non-isothermal reaction-diffusion, Biocatalyst pellet, Taylor Series Method, Effectiveness factor, Thiele modulusAbstract
This study develops a comprehensive mathematical model for substrate concentration in a spherical biocatalyst pellet under non-isothermal conditions, capturing the combined effects of heat and mass transfer along with reaction kinetics. Analytical solutions for the concentration profile and effectiveness factor are derived using the Taylor Series Method and validated against numerical simulations, revealing high accuracy and excellent agreement. The research further analyzes how dimensionless parameters, such as the Thiele modulus and Biot number, influence the effectiveness factor, emphasizing the effectiveness of the Taylor Series Method for modeling complex nonlinear bioreaction systems.
References
1. B. Jamal and S. A. Khuri, Non-isothermal Reaction–Diffusion Model Equations in a Spherical Biocatalyst: Green’s Function and Fixed Point Iteration Approach. July 2019, International Journal of Applied and Computational Mathematics 5(4):120
2. M. Danish, S. Kumar and S. Kumar, OHAM solution of a singular BVP of reaction cum diffusion in a biocatalyst, Int. J. Appl. Math., 41(3), 223-227, (2011).
3. M. H. Holmes, Introduction to Perturbation Methods, Springer, 2013.
4. Hristov, I.; Kovac, J.; Kovacova, A. Solving Linear and Nonlinear Problems Using Taylor Series Method. Comput. Appl. Math. 2024, 43, 5. https://www.degruyter.com/document/doi/10.1515/comp-2024-0005/html.
5. Piecewise Analytical Approximation Methods for Initial-Value Problems of Nonlinear Ordinary Differential Equations. Escuela de Ingenierías Industriales, 2025, 13(3), 333; https://doi.org/10.3390/math13030333.
6. S Vinolyn Sylvia, R Joy Salomi, L. Rajendran, M Abukhaled, Poisson–Boltzmann equation and electrostatic potential around macroions in colloidal plasmas: Taylor series approach, Solid State Technology 63(6), 2020, 10090-10106.
7. K Nirmala, MC Devi, L Rajendran, Analysis of Steady-State Behavior of EC′ Catalytic Mechanism at Rotating Disk Electrode: Taylor Series Approach, European Journal of Molecular & Clinical Medicine, 7(11), 2020, 440-447.
8. R.U. Rani, L. Rajendran, MEG Lyons, Steady-state current in product inhibition kinetics in an amperometric biosensor: Adomian decomposition and Taylor series method, Journal of Electroanalytical Chemistry, 886, 2021, 115103.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 R. Rajalakshmi, S. Naganathan, L. Rajendran (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
The article is distributed under the Creative Commons Attribution 4.0 License. Unless otherwise stated, associated published material is distributed under the same licence.
