Numerical Solution of Subdiffusion Bioheat equation with Single Phase lag

Jagdish Sonawane; Bhausaheb Sonatakke; Kalyanrao Takale

doi:10.17485/IJST/v17i11.3220

Article

Numerical Solution of Subdiffusion Bioheat equation with Single Phase lag

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i11.3220

Year: 2024, Volume: 17, Issue: 11, Pages: 955-966

Original Article

Numerical Solution of Subdiffusion Bioheat equation with Single Phase lag

Jagdish Sonawane^1*, Bhausaheb Sonatakke², Kalyanrao Takale³

¹Department of Mathematics, GES R. H. Sapat College of Engineering, Management and Research, Nashik, Maharashtra, India
²Department of Mathematics, Pratishthan Mahavidyalaya, Paithan, Aurangabad, Maharshtra, India
³Department of Mathematics, RNC Arts, JDB Commerce and NSC Science College, Nashik Road, Nashik, Maharashtra, 422101, India

*Corresponding Author
Email: [email protected]

Received Date:23 December 2023, Accepted Date:12 February 2024, Published Date:28 February 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The aim of this study is to investigate thermal beheviour of living tissues, for this we use subdiffusion bioheat equation with single phase lag model. Methods: The Crank-Nicolson finite difference scheme is used for subdiffusion bioheat equation with single phase lag by using Caputo fractional derivative. A Python program is used to calculate a numerical solution, which is then visually depicted through graphical representation. Finding: We discuss significance of heat flux time relaxation parameter and fractional parameter. To explore our findings, we conducted comparative analysis of subdiffusion bioheat equation with single phase lag model with classical bioheat model and fractional bioheat model. Moreover, We discussed stability and convergence of developed scheme. Novelty: The bio heat equation can be effectively addressed using the Crank-Nicolson finite difference method of fractional-order. Developed Python program provides effective tool for getting numerical solution of fractional differential equation. Single phase lag model is useful for short time heating process.

Keywords: Fractional Differential Equation, Caputo fractional derivatives, Subdiffusion bioheat equation, Single Phase Lag, Python etc

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Copyright

© 2024 Sonawane et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)