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Exact analysis for propagation of heat in a biological tissue subject to different surface conditions for therapeutic applications

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  • Kundu, Balaram

Abstract

The thermal therapy to kill cancereous cells is gradually increasing due to no side effect for the treatment. For this therapeutic application, different boundary conditions can be selected to establish the effective heating. In the present study, the separation of variables was used to determine the exact expression for temperature response in a biological tissue under Fourier and non-Fourier heat conduction subject to a therapeutic application. As the thermal therapy is dependent on the surface conditions, isothermal, isoflux, and convective–radiative boundary conditions are taken in the present study. Depending upon the inner core condition, five different boundary conditions were adopted to show the temperature response in a tissue. For every case study, the temperature response was explicitly derived. From the results, it can be highlighted that the temperature distribution in a thermal therapy is a strong function of Fourier number F, Vernetto number Ve, and dimensionless blood flow parameter β. However, the temperature is also strong function of the boundary condition applied to the surface and it is also dependent on the inner core condition. The average temperature response was plotted as a function Fourier number and biological parameters, and is always a sinusoidal nature for a lower value of Fourier number. The ripple of sinusoidal curves is dependent on the therapeutic boundary condition applied.

Suggested Citation

  • Kundu, Balaram, 2016. "Exact analysis for propagation of heat in a biological tissue subject to different surface conditions for therapeutic applications," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 204-216.
    • Handle: RePEc:eee:apmaco:v:285:y:2016:i:c:p:204-216
    DOI: 10.1016/j.amc.2016.03.037
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    References listed on IDEAS

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    1. Deng, Zhong-Shan & Liu, Jing, 2001. "Blood perfusion-based model for characterizing the temperature fluctuation in living tissues," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 521-530.
    2. 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. Angela Camacho de la Rosa & David Becerril & María Guadalupe Gómez-Farfán & Raúl Esquivel-Sirvent, 2021. "Bragg Mirrors for Thermal Waves," Energies, MDPI, vol. 14(22), pages 1-11, November.
    2. Mazhar Hussain Tiwana & Amer Bilal Mann & Muhammad Rizwan & Khadija Maqbool & Shumaila Javeed & Saqlain Raza & Mansoor Shaukat Khan, 2019. "Unsteady Magnetohydrodynamic Convective Fluid Flow of Oldroyd-B Model Considering Ramped Wall Temperature and Ramped Wall Velocity," Mathematics, MDPI, vol. 7(8), pages 1-14, July.
    3. Balaram Kundu & Sujit Saha, 2022. "Review and Analysis of Electro-Magnetohydrodynamic Flow and Heat Transport in Microchannels," Energies, MDPI, vol. 15(19), pages 1-51, September.
    4. Talha Anwar & Ilyas Khan & Poom Kumam & Wiboonsak Watthayu, 2020. "Impacts of Thermal Radiation and Heat Consumption/Generation on Unsteady MHD Convection Flow of an Oldroyd-B Fluid with Ramped Velocity and Temperature in a Generalized Darcy Medium," Mathematics, MDPI, vol. 8(1), pages 1-18, January.

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