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Numerical Study on Biological Tissue Freezing Using Dual Phase Lag Bio-Heat Equation

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Trends in Biomathematics: Modeling, Optimization and Computational Problems

Abstract

The most widely used Fourier’s law of heat conduction leads to an unphysical infinite heat propagation speed within the medium, which is clearly in contradiction with the theory of relativity, further CV (Cattaneo and Vernotte) constitutive relation does not describe the microstructural interactions. In present study, dual phase lag model of bio-heat equation is proposed to study the freezing process in biological tissue using temperature dependent enthalpy formulation. Finite difference method is used to solve the mathematical model. Temperature profiles and interface position in tissue are obtained. It is observed that the phase-lag of the heat flux, the phase-lag of the temperature gradient and blood perfusion have significant effect on the transient temperature and phase change interfaces positions. Comparison of DPL model with parabolic and hyperbolic model of heat transport is also made in the study.

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Acknowledgements

The authors Sushil Kumar and Sonalika Singh are thankful to S. V. National Institute of Technology, Surat, India for providing CPDA grant and Senior Research Fellowship, (SRF) respectively, for the research work presented in this manuscript. Sushil Kumar thanks to the International Union of Biological Sciences (IUBS) for partial support of living expenses in Moscow, during the 17th BIOMAT International Symposium, October 29-November 04, 2017.

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Authors and Affiliations

  1. Department of Applied Mathematics and Humanities, S. V. National Institute of Technology, Surat, Gujarat, India

    Sushil Kumar & Sonalika Singh

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  1. Sushil Kumar
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  2. Sonalika Singh
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Correspondence to Sushil Kumar .

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Editors and Affiliations

  1. Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Brazil, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Kumar, S., Singh, S. (2018). Numerical Study on Biological Tissue Freezing Using Dual Phase Lag Bio-Heat Equation. In: Mondaini, R. (eds) Trends in Biomathematics: Modeling, Optimization and Computational Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-91092-5_19

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