Lagging heat models in thermodynamics and bioheat transfer: a critical review

Shomali, Zahra; Kovács, Róbert; Ván, P.; Кудинов, И. В.; Ghazanfarian, Jafar

doi:10.1007/s00161-022-01096-6

Cited by 24 publications

(11 citation statements)

References 301 publications

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“…The authors reported similar work for the one‐dimensional semi‐infinite domain with boundaries subjected to sudden temperature change 32 . Different theories for extended CIT have been proposed to analyze the compatibility of non‐Fourier models with the thermodynamics second law, but these theories are conditionally valid 33 . So, it motivated us to compare the equilibrium and nonequilibrium EPR to detect any unphysical behavior in the living tissue irradiated by laser due to the non‐Fourier model‐based BHTE.…”

Section: Introductionmentioning

confidence: 99%

“…32 Different theories for extended CIT have been proposed to analyze the compatibility of non-Fourier models with the thermodynamics second law, but these theories are conditionally valid. 33 So, it motivated us to compare the equilibrium and nonequilibrium EPR to detect any unphysical behavior in the living tissue irradiated by laser due to the non-Fourier model-based BHTE. Thus, it is one of the objectives of the current study to compare the equilibrium with the nonequilibrium EPRs.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic stability analysis of non‐Fourier model‐based bio‐heat transfer in laser‐irradiated cylindrical‐shaped multilayered biological tissue

Kishore

Kumar

2023

Heat Trans

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The present research focuses on examining the thermic response of living tissue in the form of a triple‐layered cylindrical structure when subjected to laser light and the compatibility analysis of non‐Fourier heat transfer with thermodynamics second law. The temperature field in the triple‐layered cylindrical living tissue subjected to laser light is determined by numerically solving the transient radiative transfer equation in conjunction with the dual phase lag (DPL) based bioheat equation. Once the temperature field is known, the equilibrium and nonequilibrium entropy production rate (EPR) is calculated based on the hypothesis of classical irreversible thermodynamics and extended irreversible thermodynamics, respectively. The present results are verified against the data from the literature and found a good match between them. A comparative analysis of the Fourier and non‐Fourier models is accomplished. The equilibrium and nonequilibrium EPR values for the Fourier model are found to be positive. While the equilibrium EPR is negative for non‐Fourier heat conduction and does not satisfy the thermodynamics second law, nonequilibrium EPR is always a positive value for Fourier, DPL, and hyperbolic models and satisfies thermodynamics second law. It has been investigated how thermal relaxation times affect the temperature field and EPRs in tissue are subjected to laser light.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamic stability analysis of non‐Fourier model‐based bio‐heat transfer in laser‐irradiated cylindrical‐shaped multilayered biological tissue

Kishore

Kumar

2023

Heat Trans

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“…[2][3][4][5][6][7][8][9] The accurate prediction of temperature in the above fields is highly desirable for pathological and medical applications. It has been observed by various authors [10][11][12][13][14][15][16] that the heat transfer related to the above-mentioned applications cannot be accurately modeled through the Fourier heat conduction model due to the heterogeneous nature of skin tissue, bone, and blood. Heat transfer in such cases involves finite heat propagation speed (i.e., thermal wave propagation) and thermal resistance via the effect of thermal inertia and microstructural inertia, respectively.…”

Section: Introductionmentioning

confidence: 99%

A closed‐form solution of DPL bioheat transfer problem with time‐periodic boundary conditions

Biswas,

Singh,

Srivastava

2023

Heat Trans

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A closed‐form (long‐time) solution of one‐dimensional dual‐phase lag bioheat transfer problem with consistent time‐periodic boundary conditions (BCs) is presented in this paper for planar, cylindrical, and spherical skin tissue for a newly developed solution methodology. The steady‐periodic solution is composed of a steady‐state part and an oscillating part; corresponding to the constant and oscillating parts of BCs, respectively. Using the superposition principle, these two parts are split into two problems, which are solved separately. The steady‐state part is fairly straightforward to obtain, while for the oscillating part, an alternate Laplace transform (LT) approach is proposed in this work. It is demonstrated that for sinusoidal BCs, a closed‐form solution in the time domain can be obtained by evaluating an approximate convolution integral, which emulates the effect of the inverse LT. The obtained closed‐form solution is free of any series summation or numerical inversion, thereby, making it computationally very efficient compared with conventional LT and eigenfunctions‐based approaches. The current methodology is verified with the established eigenfunctions expansion‐based methodology. It can be seen that the long‐time solutions obtained by these two approaches are almost identical. The verified methodology is further extended for the time‐periodic nonsinusoidal BCs. The ease of implementation and simplicity of the new methodology for both sinusoidal and nonsinusoidal BCs is demonstrated using a few test cases. It is evident from the results that the developed methodology leads to an efficient and accurate solution.

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“…Besides the Cattaneo-Vernotte and the dual-phase lag models, other models can be derived from a linear irreversible thermodynamic framework, such as the Guyer-Krumhansl equation, the Jeffreys and the Green-Nahdi type equations [30]. All of these falls in the general category of heat transport equations with a lagging behavior [31][32][33]. The DPL model has also been tested experimentally by Tang [34] that reported the temperature profile as a function of time in biological tissue.…”

Section: Introductionmentioning

confidence: 99%

“…The non-Fourier behavior is an important topic in applications such as photo-thermal therapy, where it is important to understand the temperature profile around nanoparticles that are heated by an external source [32,[42][43][44]. In micro and nanofluidics also a non-Fourier behavior is observed [45,46].…”

Section: Introductionmentioning

confidence: 99%

Causality in non-fourier heat conduction

Rosa

Esquivel‐Sirvent

2022

J. Phys. Commun.

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We present a study of the causal response of non-Fourier heat conduction by introducing a dispersive generalized thermal susceptibility and show it obeys Kramers-Kronig relations. In particular, we discuss the Cattaneo-Vernotte and the dual-phase lag models. The constitutive equations are written as a linear response theory and determine the conditions for which the dual-phase lag model does not satisfy Kramers-Kronig relations. An alternative model is presented to describe non-Fourier transport using the similarity with the causal response of viscoelastic materials to avoid this unphysical issue.

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Lagging heat models in thermodynamics and bioheat transfer: a critical review

Cited by 24 publications

References 301 publications

Thermodynamic stability analysis of non‐Fourier model‐based bio‐heat transfer in laser‐irradiated cylindrical‐shaped multilayered biological tissue

Thermodynamic stability analysis of non‐Fourier model‐based bio‐heat transfer in laser‐irradiated cylindrical‐shaped multilayered biological tissue

A closed‐form solution of DPL bioheat transfer problem with time‐periodic boundary conditions

Causality in non-fourier heat conduction

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