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An analytic study of bioheat transfer Pennes model via modern non-integers differential techniques

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Abstract

Due to increasing utilization of thermal treatment methods in medical science, the influence of blood’s perfusion has become totally dependent on the heat transfer analysis like heart and neurosurgery need temperature measurement during thermal treatment of the prostate. This manuscript presents the analytical treatment to the bioheat transfer Pennes model via modern fractional derivatives. The heat transfer between blood and tissue is analyzed through temperature distribution based on the arterial blood temperature and the volumetric perfusion rate. The modeling of bioheat transfer equation has been established via Atangana–Baleanu and Caputo–Fabrizio non-integer order fractional derivatives within the order \({\mu }_{1}\in [\mathrm{0,1}]\) and \({\mu }_{2}\in [\mathrm{0,1}]\). The mathematical technique of Laplace transform is invoked on the fractional bioheat transfer equation based on the imposed conditions. The results are demonstrated on the basis of comparison of temperature distribution via Atangana–Baleanu and Caputo–Fabrizio non-integer order fractional derivatives. Finally, the graphical comparison of temperature distribution via both fractional differentiations suggests that the crucial factors to be considered in controlling the characteristics of bioheat transfer Pennes model with the help of non-singular and non-local kernels based on strong memory effects.

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Acknowledgements

The author Kashif Ali Abro is highly thankful and grateful to Mehran university of Engineering and Technology, Jamshoro, Pakistan, for generous support and facilities of this research work.

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Authors and Affiliations

  1. Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

    Kashif Ali Abro & Abdon Atangana

  2. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

    Kashif Ali Abro

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Abdon Atangana

  4. CONACyT-Tecnol´ogico Nacional de M´exico/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca Morelos, Mexico

    Jose Francisco Gomez-Aguilar

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  1. Kashif Ali Abro
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Abro, K.A., Atangana, A. & Gomez-Aguilar, J.F. An analytic study of bioheat transfer Pennes model via modern non-integers differential techniques. Eur. Phys. J. Plus 136, 1144 (2021). https://doi.org/10.1140/epjp/s13360-021-02136-x

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