Startseite Continuum Modeling Perspectives of Non-Fourier Heat Conduction in Biological Systems
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Continuum Modeling Perspectives of Non-Fourier Heat Conduction in Biological Systems

  • Ákos Sudár , Gergely Futaki und Róbert Kovács ORCID logo EMAIL logo
Veröffentlicht/Copyright: 18. Juni 2021
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

The thermal modeling of biological systems is increasingly important in the development of more advanced and more precise techniques such as ultrasound surgery. One of the primary barriers is the complexity of biological materials: the geometrical, structural, and material properties vary in a wide range. In the present paper, we focus on the continuum modeling of heterogeneous materials of biological origin. There are numerous examples in the literature for non-Fourier thermal models. However, as we realized, they are associated with a few common misconceptions. Therefore, we first aim to clarify the basic concepts of non-Fourier thermal models. These concepts are demonstrated by revisiting two experiments from the literature in which the Cattaneo–Vernotte and the dual phase lag models are utilized. Our investigation revealed that these non-Fourier models are based on misinterpretations of the measured data, and the seeming deviation from Fourier’s law originates from the source terms and boundary conditions.

Award Identifier / Grant number: FK 134277

Funding statement: The research reported in this paper and carried out at BME has been supported by grants from the National Research, Development and Innovation Office (NKFIH FK 134277) and the NRDI Fund (TKP2020 NC, grant No. BME-NC) based on the charter of bolster issued by the NRDI Office under the auspices of the Ministry for Innovation and Technology. This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

Acknowledgment

We dedicate our paper to the memory of our respected colleague, Prof. José Casas-Vázquez, who passed away recently.

References

[1] S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, Dover Publications, 1963.10.1063/1.3050930Suche in Google Scholar

[2] L. Onsager, Reciprocal relations in irreversible processes. I, Phys. Rev. 37 (1931), no. 4, 405.10.1103/PhysRev.37.405Suche in Google Scholar

[3] L. Onsager, Reciprocal relations in irreversible processes. II, Phys. Rev. 38 (1931), no. 12, 2265.10.1103/PhysRev.38.2265Suche in Google Scholar

[4] G. Fichera, Is the Fourier theory of heat propagation paradoxical?, Rend. Circ. Mat. Palermo 41 (1992), no. 1, 5–28.10.1007/BF02844459Suche in Google Scholar

[5] T. Matolcsi, Ordinary Thermodynamics, Akadémiai Kiadó, 2004.Suche in Google Scholar

[6] A. Berezovski and P. Ván, Internal Variables in Thermoelasticity, Springer, 2017.10.1007/978-3-319-56934-5Suche in Google Scholar

[7] H. E. Jackson, C. T. Walker and T. F. McNelly, Second sound in NaF, Phys. Rev. Lett. 25 (1970), no. 1, 26–28.10.1103/PhysRevLett.25.26Suche in Google Scholar

[8] V. Narayanamurti, R. C. Dynes and K. Andres, Propagation of sound and second sound using heat pulses, Phys. Rev. B 11 (1975), no. 7, 2500–2524.10.1103/PhysRevB.11.2500Suche in Google Scholar

[9] T. F. McNelly, Second Sound and Anharmonic Processes in Isotopically Pure Alkali-Halides. 1974. Ph. D. Thesis, Cornell University.Suche in Google Scholar

[10] V. Józsa and R. Kovács, Solving Problems in Thermal Engineering: A Toolbox for Engineers, Springer, 2020.10.1007/978-3-030-33475-8Suche in Google Scholar

[11] D. Y. Tzou, A unified field approach for heat conduction from macro- to micro-scales, J. Heat Transf. 117 (1995), no. 1, 8–16.10.1115/1.2822329Suche in Google Scholar

[12] M. Fabrizio and B. Lazzari, Stability and second law of thermodynamics in dual-phase-lag heat conduction, Int. J. Heat Mass Transf. 74 (2014), 484–489.10.1016/j.ijheatmasstransfer.2014.02.027Suche in Google Scholar

[13] R. Quintanilla and R. Racke, Qualitative aspects in dual-phase-lag heat conduction, Proc. R. Soc., Math. Phys. Eng. Sci. 463 (2007), no. 2079, 659–674.10.1098/rspa.2006.1784Suche in Google Scholar

[14] R. Kovács and P. Ván, Thermodynamical consistency of the Dual Phase Lag heat conduction equation, Contin. Mech. Thermodyn. (2017), 1–8.10.1007/s00161-017-0610-xSuche in Google Scholar

[15] S. A. Rukolaine, Unphysical effects of the dual-phase-lag model of heat conduction, Int. J. Heat Mass Transf. 78 (2014), 58–63.10.1016/j.ijheatmasstransfer.2014.06.066Suche in Google Scholar

[16] S. A. Rukolaine, Unphysical effects of the dual-phase-lag model of heat conduction: higher-order approximations, Int. J. Therm. Sci. 113 (2017), 83–88.10.1016/j.ijthermalsci.2016.11.016Suche in Google Scholar

[17] G. Lebon, From classical irreversible thermodynamics to extended thermodynamics, Acta Phys. Hung. 66 (1989), no. 1-4, 241–249.10.1007/BF03155796Suche in Google Scholar

[18] B. Nyíri, On the entropy current, J. Non-Equilib. Thermodyn. 16 (1991), no. 2, 179–186.10.1515/jnet.1991.16.2.179Suche in Google Scholar

[19] M. Szücs, R. Kovács and S. Simić, Open mathematical aspects of continuum thermodynamics: Hyperbolicity, boundaries and nonlinearities, Symmetry 12 (2020), 1469.10.3390/sym12091469Suche in Google Scholar

[20] T. Fülöp, Cs. Asszonyi and P. Ván, Distinguished rheological models in the framework of a thermodynamical internal variable theory, Contin. Mech. Thermodyn. 27 (2015), no. 6, 971–986.10.1007/s00161-014-0392-3Suche in Google Scholar

[21] A. Berezovski, J. Engelbrecht and G. A. Maugin, Thermoelasticity with dual internal variables, J. Therm. Stresses 34 (2011), no. 5-6, 413–430.10.1080/01495739.2011.564000Suche in Google Scholar

[22] P. Ván, A. Berezovski and J. Engelbrecht, Internal variables and dynamic degrees of freedom, J. Non-Equilib. Thermodyn. 33 (2008), no. 3, 235–254.10.1515/JNETDY.2008.010Suche in Google Scholar

[23] G. A. Maugin and W. Muschik, Thermodynamics with internal variables. Part I. General concepts, J. Non-Equilib. Thermodyn. 19 (1994), no. 3, 217–249.10.1515/jnet.1994.19.3.217Suche in Google Scholar

[24] G. A. Maugin and W. Muschik, Thermodynamics with internal variables. Part II. Applications, J. Non-Equilib. Thermodyn. 19 (1994), no. 3, 250–289.10.1515/jnet.1994.19.3.250Suche in Google Scholar

[25] I. Müller and T. Ruggeri, Rational Extended Thermodynamics, Springer, 1998.10.1007/978-1-4612-2210-1Suche in Google Scholar

[26] T. Ruggeri and M. Sugiyama, Rational Extended Thermodynamics Beyond the Monatomic Gas, Springer, 2015.10.1007/978-3-319-13341-6Suche in Google Scholar

[27] P. Ván, Weakly nonlocal irreversible thermodynamics – the Guyer–Krumhansl and the Cahn–Hilliard equations, Phys. Lett. A 290 (2001), no. 1-2, 88–92.10.1016/S0375-9601(01)00657-0Suche in Google Scholar

[28] V. A. Cimmelli, Different thermodynamic theories and different heat conduction laws, J. Non-Equilib. Thermodyn. 34 (2009), no. 4, 299–333.10.1515/JNETDY.2009.016Suche in Google Scholar

[29] I. Carlomagno, A. Sellitto and V. A. Cimmelli, Dynamical temperature and generalized heat-conduction equation, Int. J. Non-Linear Mech. 79 (2016), 76–82.10.1016/j.ijnonlinmec.2015.11.004Suche in Google Scholar

[30] M. Grmela, Generic guide to the multiscale dynamics and thermodynamics, Comput. Phys. Commun. 2 (2018), no. 3, 032001.10.1088/2399-6528/aab642Suche in Google Scholar

[31] M. Grmela, G. Lebon and C. Dubois, Multiscale thermodynamics and mechanics of heat, Phys. Rev. E 83 (2011), no. 6, 061134.10.1103/PhysRevE.83.061134Suche in Google Scholar PubMed

[32] D. Jou, J. Casas-Vazquez and G. Lebon, Extended irreversible thermodynamics revisited (1988–98), Rep. Prog. Phys. 62 (1999), no. 7, 1035.10.1088/0034-4885/62/7/201Suche in Google Scholar

[33] M. Sauermoser, S. Kjelstrup, N. Kizilova, B. G. Pollet and E. G. Flekkøy, Seeking minimum entropy production for a tree-like flow-field in a fuel cell, Phys. Chem. Chem. Phys. 22 (2020), no. 13, 6993–7003.10.1039/C9CP05394HSuche in Google Scholar

[34] S. Both, B. Czél, T. Fülöp, Gy. Gróf, Á. Gyenis, R. Kovács, et al., Deviation from the Fourier law in room-temperature heat pulse experiments, J. Non-Equilib. Thermodyn. 41 (2016), no. 1, 41–48.10.1515/jnet-2015-0035Suche in Google Scholar

[35] P. Ván, A. Berezovski, T. Fülöp, Gy. Gróf, R. Kovács, Á. Lovas, et al., Guyer-Krumhansl-type heat conduction at room temperature, Europhys. Lett. 118 (2017), no. 5, 50005. arXiv:1704.00341v1.10.1209/0295-5075/118/50005Suche in Google Scholar

[36] T. Fülöp, R. Kovács, Á. Lovas, Á. Rieth, T. Fodor, M. Szücs, et al., Emergence of non-Fourier hierarchies, Entropy 20 (2018), no. 11, 832. arXiv:1808.06858.10.3390/e20110832Suche in Google Scholar PubMed PubMed Central

[37] H. H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol. 1 (1948), no. 2, 93–122.10.1152/jappl.1948.1.2.93Suche in Google Scholar PubMed

[38] M. M. Chen and K. R. Holmes, Microvascular contributions in tissue heat transfer, Ann. N.Y. Acad. Sci. 335 (1980), no. 1, 137–150.10.1111/j.1749-6632.1980.tb50742.xSuche in Google Scholar PubMed

[39] S. Weinbaum, L. M. Jiji and D. E. Lemons, Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer—Part I: Anatomical foundation and model conceptualization, J. Biomech. Eng. 106 (1984), no. 4, 321–330.10.1115/1.3138501Suche in Google Scholar PubMed

[40] W. Wulff, The energy conservation equation for living tissue. IEEE Trans. Biomed. Eng., 6(BME-21):494–495, 1974.10.1109/TBME.1974.324342Suche in Google Scholar

[41] W. Muschik, Objectivity and frame indifference, revisited, Arch. Mech. 50 (1998), no. 3, 541–547.Suche in Google Scholar

[42] T. Fülöp, Objective thermomechanics. arXiv preprint arXiv:1510.08038, 2015.Suche in Google Scholar

[43] T. Matolcsi and P. Ván, Can material time derivative be objective?, Phys. Lett. A 353 (2006), no. 2, 109–112.10.1016/j.physleta.2005.12.072Suche in Google Scholar

[44] H. G. Klinger, Heat transfer in perfused biological tissue – I: General theory, Bull. Math. Biol. 36 (1974), 403–415.10.1016/S0092-8240(74)80038-8Suche in Google Scholar

[45] H. G. Klinger, Heat transfer in perfused biological tissue – II: The “macroscopic” temperature distribution in tissue, Bull. Math. Biol. 40 (1978), no. 2, 183–199.10.1016/S0092-8240(78)80038-XSuche in Google Scholar

[46] A. Taflove and M. E. Brodwin, Computation of the electromagnetic fields and induced temperatures within a model of the microwave-irradiated human eye, IEEE Trans. Microw. Theory Tech. 23 (1975), no. 11, 888–896.10.1109/TMTT.1975.1128708Suche in Google Scholar

[47] D. Tang, N. Araki and N. Yamagishi, Transient temperature responses in biological materials under pulsed IR irradiation, Heat Mass Transf. 43 (2007), no. 6, 579–585.10.1007/s00231-006-0125-7Suche in Google Scholar

[48] A. Fehér and R. Kovács, Novel evaluation method for non-Fourier effects in heat pulse experiments, arXiv:2101.01123, 2021.10.1016/j.ijengsci.2021.103577Suche in Google Scholar

[49] M. Jaunich, S. Raje, K. Kim, K. Mitra and Z. Guo, Bio-heat transfer analysis during short pulse laser irradiation of tissues, Int. J. Heat Mass Transf. 51 (2008), no. 23, 5511–5521.10.1016/j.ijheatmasstransfer.2008.04.033Suche in Google Scholar

[50] G. Tambave, J. Alme, G. G. Barnaföldi, R. Barthel, A. van den Brink, et al., Characterization of monolithic CMOS pixel sensor chip with ion beams for application in particle computed tomography, Nucl. Instrum. Methods Phys. Res., Sect. A, Accel. Spectrom. Detect. Assoc. Equip. 958 (2020), 162626. Proceedings of the Vienna Conference on Instrumentation 2019.10.1016/j.nima.2019.162626Suche in Google Scholar

[51] J. Alme, G. G. Barnaföldi, R. Barthel, et al., A high-granularity digital tracking calorimeter optimized for proton ct, Front. Phys. 8 (2020), 460.10.3389/fphy.2020.568243Suche in Google Scholar

[52] A. Andreozzi, L. Brunese, M. Iasiello, C. Tucci and G. P. Vanoli, Bioheat transfer in a spherical biological tissue: a comparison among various models, J. Phys. Conf. Ser. 1224 (2019), no. 1, 012001.10.1088/1742-6596/1224/1/012001Suche in Google Scholar

Received: 2021-02-27
Revised: 2021-04-29
Accepted: 2021-05-31
Published Online: 2021-06-18
Published in Print: 2021-10-31

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jnet-2021-0016/html
Button zum nach oben scrollen