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A Fibonacci Wavelet Method for Solving Dual-Phase-Lag Heat Transfer Model in Multi-Layer Skin Tissue during Hyperthermia Treatment

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  • Hari Mohan Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, Baku AZ1007, Azerbaijan)

  • Mohd. Irfan

    (Department of Mathematics, South Campus, University of Kashmir, Anantnag 192101, India)

  • Firdous A. Shah

    (Department of Mathematics, South Campus, University of Kashmir, Anantnag 192101, India)

Abstract

In this article, a novel wavelet collocation method based on Fibonacci wavelets is proposed to solve the dual-phase-lag (DPL) bioheat transfer model in multilayer skin tissues during hyperthermia treatment. Firstly, the Fibonacci polynomials and the corresponding wavelets along with their fundamental properties are briefly studied. Secondly, the operational matrices of integration for the Fibonacci wavelets are built by following the celebrated approach of Chen and Haiso. Thirdly, the proposed method is utilized to reduce the underlying DPL model into a system of algebraic equations, which has been solved using the Newton iteration method. Towards the culmination, the effect of different parameters including the tissue-wall temperature, time-lag due to heat flux, time-lag due to temperature gradient, blood perfusion, metabolic heat generation, heat loss due to diffusion of water, and boundary conditions of various kinds on multilayer skin tissues during hyperthermia treatment are briefly presented and all the outcomes are portrayed graphically.

Suggested Citation

  • Hari Mohan Srivastava & Mohd. Irfan & Firdous A. Shah, 2021. "A Fibonacci Wavelet Method for Solving Dual-Phase-Lag Heat Transfer Model in Multi-Layer Skin Tissue during Hyperthermia Treatment," Energies, MDPI, vol. 14(8), pages 1-20, April.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:8:p:2254-:d:537988
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    References listed on IDEAS

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    1. Falcón, Sergio & Plaza, Ángel, 2009. "On k-Fibonacci sequences and polynomials and their derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1005-1019.
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    Cited by:

    1. Mikhail A. Sheremet, 2023. "Numerical Simulation of Convective Heat Transfer," Energies, MDPI, vol. 16(4), pages 1-3, February.
    2. Robert Frontczak & Hari Mohan Srivastava & Živorad Tomovski, 2021. "Some Families of Apéry-Like Fibonacci and Lucas Series," Mathematics, MDPI, vol. 9(14), pages 1-10, July.
    3. Manohara, G. & Kumbinarasaiah, S., 2024. "Numerical approximation of fractional SEIR epidemic model of measles and smoking model by using Fibonacci wavelets operational matrix approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 358-396.

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