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

Sushil Kumar () and Sonalika Singh
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Sushil Kumar: S. V. National Institute of Technology, Department of Applied Mathematics and Humanities
Sonalika Singh: S. V. National Institute of Technology, Department of Applied Mathematics and Humanities

A chapter in Trends in Biomathematics: Modeling, Optimization and Computational Problems, 2018, pp 283-300 from Springer

Abstract: 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.

Keywords: Phase Change Interface; Hyperbolic Model; Freezing Process; Interface Position; Blood Perfusion (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-91092-5_19

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DOI: 10.1007/978-3-319-91092-5_19

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