A symplectic approach for the fractional heat transfer and thermal damage in 2D biological tissues
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 10 July 2023
Issue publication date: 21 July 2023
Abstract
Purpose
This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral boundary conditions and the quantitative evaluation of the degree of thermal damage and burn depth.
Design/methodology/approach
A symplectic method is used to analytically solve the fractional heat transfer dual equation in the frequency domain (s-domain). Explicit expressions of the dual vector can be constructed by superposing the symplectic eigensolutions. The solution procedure is rigorously rational without any trial functions. And the accurate predictions of temperature and heat flux in the time domain (t-domain) are derived through numerical inverse Laplace transform.
Findings
Comparison study shows that the maximum relative error is less than 0.16%, which verifies the accuracy and effectiveness of the proposed method. The results indicate that the model and heat source parameters have a significant effect on temperature and thermal damage. The pulse duration (Δt) of the laser heat source can effectively control the time to reach the peak temperature and the peak slope of the thermal damage curve. The burn depth is closely correlated with exposure temperature and duration. And there exists the delayed effect of fractional order on burn depth.
Originality/value
A symplectic approach is presented for the thermal analysis of 2D fractional heat transfer. A unified time-fractional heat transfer model is proposed to describe the anomalous thermal behavior of biological tissue. New findings might provide guidance for temperature prediction and thermal damage assessment of biological tissues during hyperthermia.
Keywords
Acknowledgements
This work was supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2022JM-016); the National Natural Science Foundation of China (Grant No. 11702221); the China Postdoctoral Science Foundation (Grant No. 2017M613198); and the Fundamental Research Funds for the Central Universities (Grant No. G2020KY05402).
Declaration of competing interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Citation
Xu, C., Leng, S., Li, D. and Yu, Y. (2023), "A symplectic approach for the fractional heat transfer and thermal damage in 2D biological tissues", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 9, pp. 3073-3093. https://doi.org/10.1108/HFF-01-2023-0013
Publisher
:Emerald Publishing Limited
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