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Finite Element Analysis of Nonlinear Bioheat Model in Skin Tissue Due to External Thermal Sources

Author

Listed:
  • Marin Marin

    (Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania)

  • Aatef Hobiny

    (Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21521, Saudi Arabia)

  • Ibrahim Abbas

    (Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21521, Saudi Arabia
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

Abstract

In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments.

Suggested Citation

  • Marin Marin & Aatef Hobiny & Ibrahim Abbas, 2021. "Finite Element Analysis of Nonlinear Bioheat Model in Skin Tissue Due to External Thermal Sources," Mathematics, MDPI, vol. 9(13), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1459-:d:579450
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    References listed on IDEAS

    as
    1. Ghazanfarian, J. & Saghatchi, R. & Patil, D.V., 2015. "Implementation of Smoothed-Particle Hydrodynamics for non-linear Pennes’ bioheat transfer equation," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 21-31.
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    Cited by:

    1. Mohamad Hosein Rasekhmanesh & Gines Garcia-Contreras & Juan Córcoles & Jorge A. Ruiz-Cruz, 2022. "On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    2. Nicolae Pop & Marin Marin & Sorin Vlase, 2023. "Mathematics in Finite Element Modeling of Computational Friction Contact Mechanics 2021–2022," Mathematics, MDPI, vol. 11(1), pages 1-5, January.

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