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Journal articles on the topic 'Non-Fourier heat conduction'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 June 2025

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1

Pysarenko, O. "NON-FOURIER HEAT CONDUCTION IN TWO-DIMENSIONAL MEDIA." Mechanics And Mathematical Methods 7, no. 1 (2025): 90–102. https://doi.org/10.31650/2618-0650-2025-6-1-90-102.

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Real-time heat distribution and phase transformation based on operating conditions and material properties can be estimated using heat equations. The corresponding characteristic functions are used to analyze heat conduction processes in various fields, including laser and electron beam processing. A powerful universal analytical and numerical method that transforms partial differential equations into a coupled system of ordinary differential equations is the wavelet transform method. Fourier and non-Fourier heat equations can be implemented for both equilibrium and non-equilibrium thermodynamic processes, including a wide range of processes such as the two-temperature model, ultrafast laser irradiation, and biological processes. The ultrafast laser heating process of nanofilms is characterized by ultrashort duration and ultrasmall spatial size, in which the classical Fourier law based on the local equilibrium hypothesis is no longer applicable. Based on the Cattaneo-Vernotte model and the double phase delay model, two-dimensional analytical solutions of thermal conductivity in two-dimensional structures under the action of ultrafast laser are obtained using the integral transform method. The results show that there is a thermal wave phenomenon inside the film, which becomes increasingly obvious as the temperature gradient delay time elapses. In this paper, non-Fourier heat conduction problems with temperature and heat flux relaxations are studied based on the wavelet finite element method and solved by the central difference scheme for one-dimensional and two-dimensional media. The heat wave model and the double phase delay model are used to formulate the finite elements, and a new formulation of the wavelet finite element solution is proposed to solve the computational optimization problem. Compared with the current methodologies for the heat wave model and the dual phase delay model, the present model is a direct model that describes the thermal behavior with a single equation with respect to temperature. The developed method can be used for arbitrary shapes. A new iteration update methodology is also proposed for the dual phase delay model to solve the computationally efficient problems. The time iteration algorithms do not use the global stiffness matrix. This allows for optimized calculations. Numerical calculations were performed in comparison with the classical finite element method and the spectral finite element method. The comparisons in accuracy, efficiency, flexibility and applicability confirm that the developed method is an effective and alternative tool for thermal analysis of local volumes of two-dimensional materials.
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2

Fülöp, Tamás, Róbert Kovács, Ádám Lovas, et al. "Emergence of Non-Fourier Hierarchies." Entropy 20, no. 11 (2018): 832. http://dx.doi.org/10.3390/e20110832.

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The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs, and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier’s law for room-temperature phenomena in modeling of heterogeneous materials. The second approach provides an interpretation of generalized heat conduction equations using a simple thermo-mechanical background. Here, Fourier heat conduction is coupled to elasticity via thermal expansion, resulting in a particular generalized heat equation for the temperature field. Both aforementioned approaches show the size dependency of non-Fourier heat conduction. Finally, a third approach is presented, called pseudo-temperature modeling. It is shown that non-Fourier temperature history can be produced by mixing different solutions of Fourier’s law. That kind of explanation indicates the interpretation of underlying heat conduction mechanics behind non-Fourier phenomena.
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3

Wang, Fei Fei, and B. Wang. "Current Research Progress in Non-Classical Fourier Heat Conduction." Applied Mechanics and Materials 442 (October 2013): 187–96. http://dx.doi.org/10.4028/www.scientific.net/amm.442.187.

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Classical Fourier law can accurately describe most heat conduction problems. But for ultrafast heat conduction process and micro/nanoscale heat conduction problems, non-classical Fourier (non-Fourier) effect may become dominated. The paper gives a review on the current progress on non-Fourier heat conduction in engineering. It includes basic concept, physical models, thermal relaxation effect, and related experiments. Also introduced are the solution methods of non-Fourier heat conduction equations, including closed-form solution, finite difference method, finite element method, molecular dynamics simulation, variational method, and other hybrid methods. Some challenging issues are discussed at the conclusion of the paper.
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4

Zhang, Jingjie, Xiangfei Meng, Jin Du, et al. "Modelling and Prediction of Cutting Temperature in the Machining of H13 Hard Steel of Transient Heat Conduction." Materials 14, no. 12 (2021): 3176. http://dx.doi.org/10.3390/ma14123176.

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Cutting heat conduction undergoes three stages that include intensity transient-state, transient-state, and steady-states. Especially during machining with coated cutting tools, in the conduction process, cutting heat needs to pass through a few micron thick coatings and then flow into the tool body. This heat conduction presents typical non-Fourier heat conduction characteristics. This paper focuses on the cutting temperature in transient heat conduction with a coated tool. A new analytical model to characterize the thermal shock based on the non-Fourier heat conduction was proposed. The distribution of cutting temperature in mono-layer coated tools during the machining was then illustrated. The cutting temperature distribution predicted by the Fourier heat conduction model was employed to compare with that by non-Fourier heat conduction in order to reveal the non-Fourier heat conduction effect in transient heat conduction. The results show that the transient heat conduction analytical model is more suitable for the intensity transient-state and transient-state in the process of cutting heat conduction.
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5

Guo, Zeng-Yuan, and Yun-Sheng Xu. "Non-Fourier Heat Conduction in IC Chip." Journal of Electronic Packaging 117, no. 3 (1995): 174–77. http://dx.doi.org/10.1115/1.2792088.

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Instead of the classic Fourier equation based on diffusion, a hyperbolic equation based on a wave model has been used to predict the rapid transient heat conduction in IC chips. The peak temperature, spatial difference, and time variation of temperature, which are critical to thermal reliability of the chip, are given and compared with that obtained from the Fourier equation. Analytical and numerical results show that non-Fourier effects, including the higher peak temperature and thermal stress, greater temperature difference between components, and stronger thermal noise, are significant to IC chip reliability.
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6

Zhang, Xiaomin, Song Peng, Long Zhang, Zimin Yan, Yuan Liang, and Bo Yan. "VARIATIONAL EQUATION OF NON-FOURIER HEAT CONDUCTION." Heat Transfer Research 49, no. 3 (2018): 275–85. http://dx.doi.org/10.1615/heattransres.2018015988.

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7

Izadpanah, E., S. Talebi, and M. H. Hekmat. "Numerical simulation of non-Fourier effects in combined heat transfer." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 2 (2010): 429–36. http://dx.doi.org/10.1243/09544062jmes2001.

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The non-Fourier effects on transient and steady temperature distribution in combined heat transfer are studied. The processes of coupled conduction and radiation heat transfer in grey, absorbing, emitting, scattering, one-dimensional medium with black boundary surfaces are analysed numerically. The hyperbolic heat conduction equation is solved by flux splitting method, and the radiative transfer equation is solved by P1 approximate method. The transient thermal responses obtained from non-Fourier heat conduction equation are compared with those obtained from the Fourier heat conduction equation. The results show that the non-Fourier effect can be important when the conduction to radiation parameter and the thermal relaxation time are larger. Further, the radiation effect is more pronounced at small values of single scattering albedo and conduction to radiation parameters. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature.
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8

Herwig, H., and K. Beckert. "Fourier Versus Non-Fourier Heat Conduction in Materials With a Nonhomogeneous Inner Structure." Journal of Heat Transfer 122, no. 2 (1999): 363–65. http://dx.doi.org/10.1115/1.521471.

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Distinct non-Fourier behavior in terms of finite propagation velocity and a hyperbolic wave like character of heat conduction has been reported for certain materials in several studies published recently. However, there is some doubt concerning these findings. The objective of this note is to present experimental evidence for a perfectly Fourier-like behavior of heat conduction in those materials with nonhomogeneous inner structure that have been under investigation in the other studies. This controversy needs to be settled in order to understand the physics of heat conduction in these materials. [S0022-1481(00)00102-X]
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9

Ipilakyaa, Tertsegha Daniel, Sebastine Aondover Bam, and Livinus Tyovenda Tuleun. "Prediction of Cutting Temperature Distribution in Transient Heat Conduction of Monolayer Coated Tools Based on Non-Fourier Heat Conduction during Machining of H13 Hard Steel." International Journal of Engineering Research & Science 9, no. 8 (2023): 01–10. https://doi.org/10.5281/zenodo.8304147.

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<strong>Abstract&mdash;</strong> A predictive model for transient heat conduction during the machining of hard steel based on non-Fourier heat conduction was developed. A mono layer cutting tool coated with TiN coating of carbide substrate was used with 2&mu;m thickness. The work piece material used was a cylindrical bar of H13 hard steel, 300mm length and 70mm external diameter. The cutting speed range was 35.9-244.4m/min, feed rate of 0.2m/rev and depth of cut of 0.2mm. A developed wireless temperature measurement was employed with the thermocouple sensor embedded in the turning tool. The developed model is simplified and contains hypothetical conditions. An infinitesimal convective heat conduction coefficient makes the boundary to be an adiabatic or thermostatic boundary. During machining, the coated tool and workpiece material&#39;s heat dissipation are neglected. Prediction was done and compared between the Fourier heat conduction model and the non-Fourier heat conduction to reveal the non-Fourier model effect on transient heat conduction. Predictions by the two models are considerably dissimilar with 77.10C difference at 0.1s cutting time. The predicted temperature difference between the two models when the cutting duration is 10 s is 4.90C. The temperature tends to stabilize when the cutting time is sufficient and heat conduction reaches its steady state. From the results, it can be concluded that the transient heat conduction model is more suitable for the intensity transient-state in the process of cutting heat conduction. The prediction error is less than 12%, which is acceptable for industrial applications and proves the efficiency of the developed model.
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10

Vedavarz, Ali, Sunil Kumar, and M. Karim Moallemi. "Significance of Non-Fourier Heat Waves in Conduction." Journal of Heat Transfer 116, no. 1 (1994): 221–24. http://dx.doi.org/10.1115/1.2910859.

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11

Liu, Qixin, Peixue Jiang, and Heng Xiang. "Molecular dynamics simulations of non-Fourier heat conduction." Progress in Natural Science 18, no. 8 (2008): 999–1007. http://dx.doi.org/10.1016/j.pnsc.2008.05.001.

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12

Han, S., and J. Peddieson. "Non-Fourier heat conduction/convection in moving medium." International Journal of Thermal Sciences 130 (August 2018): 128–39. http://dx.doi.org/10.1016/j.ijthermalsci.2018.04.001.

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13

Yang, H. Q. "Non-Fourier effect on heat conduction during welding." International Journal of Heat and Mass Transfer 34, no. 11 (1991): 2921–24. http://dx.doi.org/10.1016/0017-9310(91)90252-a.

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14

Li, Zheng-Yang, Marius Mellmann, Yanzheng Wang, et al. "Non-Fourier heat conduction in 2D thermal metamaterials." Materials Today Communications 38 (March 2024): 107828. http://dx.doi.org/10.1016/j.mtcomm.2023.107828.

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15

Ván, Péter. "Theories and heat pulse experiments of non-Fourier heat conduction." Communications in Applied and Industrial Mathematics 7, no. 2 (2016): 150–66. http://dx.doi.org/10.1515/caim-2016-0011.

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Abstract The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments.
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16

Loh, J. S., I. A. Azid, K. N. Seetharamu, and G. A. Quadir. "Fast transient thermal analysis of Fourier and non-Fourier heat conduction." International Journal of Heat and Mass Transfer 50, no. 21-22 (2007): 4400–4408. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.03.021.

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17

Noroozi, Mohammad Javad, Seyfolah Saedodin, and Davood Domiri Ganji. "Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source." Archive of Mechanical Engineering 63, no. 1 (2016): 129–44. http://dx.doi.org/10.1515/meceng-2016-0007.

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Abstract The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.
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18

LIN, SHUEEI-MUH. "ANALYTICAL SOLUTIONS OF BIO-HEAT CONDUCTION ON SKIN IN FOURIER AND NON-FOURIER MODELS." Journal of Mechanics in Medicine and Biology 13, no. 04 (2013): 1350063. http://dx.doi.org/10.1142/s0219519413500632.

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In general, the transport of thermal energy in living tissue is a complex process. The analysis of the heat conduction of skin tissue is helpful for understanding of the bio-thermo-mechanical behavior of skin tissue. So far, three kinds of conduction law — (1) the Fourier model, (2) the C-V model and (3) dual-phase-lag (DPL) model — are often investigated in bio-thermal transfer process. In this study, the mathematical model of heat conduction of the skin tissue subjected to a general transient heating at the skin surface was established. The analytical solutions of these three conduction models are presented. In addition, the measure of thermal injury of the skin tissue subjected to a harmonic heating was investigated. It was found that the phenomenon of Fourier model is greatly different to those of the C-V and DPL models. Moreover, the effects of the phase lags, the heating frequency, and the heat quantity on the temperature variation and the index of thermal injury were significant. In sum, the analytical method can be used to solve the conduction problem of any one-layer tissue.
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19

Li, Shu-Nan, and Bing-Yang Cao. "Vortex characteristics in Fourier and non-Fourier heat conduction based on heat flux rotation." International Journal of Heat and Mass Transfer 108 (May 2017): 2403–7. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.076.

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20

Antaki, Paul J. "New Interpretation of Non-Fourier Heat Conduction in Processed Meat." Journal of Heat Transfer 127, no. 2 (2005): 189–93. http://dx.doi.org/10.1115/1.1844540.

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This work uses the “dual phase lag” (DPL) model of heat conduction to offer a new interpretation for experimental evidence of non-Fourier conduction in processed meat that was interpreted previously with hyperbolic conduction. Specifically, the DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. In addition, comparing the new interpretation to Fourier-based alternatives suggests that further study of all the interpretations could help advance the understanding of conduction in the processed meat and other biological materials such as human tissue.
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21

YU, Ning, Shoji IMATANI, and Tatsuo INOUE. "Transient Analysis based on Non-Fourier Heat Conduction Law." Proceedings of The Computational Mechanics Conference 2002.15 (2002): 199–200. http://dx.doi.org/10.1299/jsmecmd.2002.15.199.

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22

Gembarovic, J., and J. Gembarovic, Jr. "Non-Fourier Heat Conduction Modeling in a Finite Medium." International Journal of Thermophysics 25, no. 4 (2004): 1261–68. http://dx.doi.org/10.1023/b:ijot.0000038514.11849.c1.

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23

Liu, Kuo-Chi, Han-Taw Chen, and Po-Jen Cheng. "Inverse investigation of non-Fourier heat conduction in tissue." Journal of Thermal Biology 62 (December 2016): 123–28. http://dx.doi.org/10.1016/j.jtherbio.2016.07.002.

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24

Liu, Fang, Qiang Chen, Zhanxiao Kang, Weiguo Pan, Dongxiang Zhang, and Liqiu Wang. "Non-Fourier heat conduction in oil-in-water emulsions." International Journal of Heat and Mass Transfer 135 (June 2019): 323–30. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2019.01.105.

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25

Raveshi, M. R. "Non-Fourier heat conduction in an exponentially graded slab." Journal of Applied Mechanics and Technical Physics 57, no. 2 (2016): 326–36. http://dx.doi.org/10.1134/s0021894416020164.

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26

Wang, B. "Fracture of a Finite Medium with a Circular Internal Crack under Hyperbolic Heat Conduction-Prescribed Crack Face Thermal Flux." Advanced Materials Research 706-708 (June 2013): 1373–78. http://dx.doi.org/10.4028/www.scientific.net/amr.706-708.1373.

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This paper studies the fracture mechanics of a thermoelastic medium with an internal circular crack subjecting to a prescribed thermal flux. The time varying crack tip thermal stress intensity factor is solved. Solution for the infinite medium under steady heat conduction is given in closed form. Comparisons between the non-Fourier results and the classical Fourier results are made. Numerical results show that the non-Fourier heat model predicts considerable high transient thermal stress intensity factor than the Fourier model. This paper, together with our previous paper entitled fracture of a finite medium with a circular internal crack under hyperbolic heat conduction-prescribed crack face temperature, completes the analysis of a finite medium with a circular internal crack under hyperbolic heat conduction.
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27

Wang, B. L., and J. E. Li. "Thermal shock resistance of solids associated with hyperbolic heat conduction theory." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2153 (2013): 20120754. http://dx.doi.org/10.1098/rspa.2012.0754.

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The thermal shock resistance of solids is analysed for a plate subjected to a sudden temperature change under the framework of hyperbolic, non-Fourier heat conduction. The closed form solution for the temperature field and the associated thermal stress are obtained for the plate without cracking. The transient thermal stress intensity factors are obtained through a weight function method. The maximum thermal shock temperature that the plate can sustain without catastrophic failure is obtained according to the two distinct criteria: (i) maximum local tensile stress criterion and (ii) maximum stress intensity factor criterion. The difference between the non-Fourier solutions and the classical Fourier solution is discussed. The traditional Fourier heat conduction considerably overestimates the thermal shock resistance of the solid. This confirms the fact that introduction of the non-Fourier heat conduction model is essential in the evaluation of thermal shock resistance of solids.
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28

Chen, Zeng Tao, Hamid Akbarzadeh, and Hossein Babaei. "Thermopiezoelectric Response of a One-Dimensional Functionally Graded Piezoelectric Medium to a Moving Heat Source - A Review." Applied Mechanics and Materials 151 (January 2012): 396–400. http://dx.doi.org/10.4028/www.scientific.net/amm.151.396.

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The multi-physics of piezoelectric materials under different environmental conditions has been an active research subject for a few decades. Particularly, the thermoelastic behaviour of smart materials and structures is of great importance to their reliability in different applications. Traditionally, the Fourier heat conduction theory was introduced in dealing with the thermoelastic reactions of smart materials and structures. This may lead to reasonable analyses and useful guidelines in design of smart structures, especially when no severe thermal gradient is involved. However, when a severe thermal gradient is indeed involved in the service environment of a smart structure, the analysing results based on the Fourier heat conduction theory is unrealistic and usually rendered useless. Non-Fourier heat conduction theories have been introduced in the thermoelastic analysis of smart materials and structures in recent years and resulted in reasonable results. In this paper, we review the recent results of a thermopiezoelectric problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving heat source using both the Fourier and Non-Fourier heat conduction theories. Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on the results.
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29

Ma, Jing, Yasong Sun, and Sida Li. "Element Differential Method for Non-Fourier Heat Conduction in the Convective-Radiative Fin with Mixed Boundary Conditions." Coatings 12, no. 12 (2022): 1862. http://dx.doi.org/10.3390/coatings12121862.

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Fin is an efficient and straightforward way to enhance heat transfer rate. When the heat source varies dramatically in a very short time, non-Fourier heat conduction should be considered. In the paper, taking advantage of numerical stability and no integral and easy-to-implement features of an element differential method, a numerical model is developed to evaluate the fin efficiency of the convective-radiative fin within non-Fourier heat conduction. In this fin, heat is generated by an internal heat source and dissipated by convection and radiation. Both periodic and adiabatic boundary conditions are considered. The accuracy and efficiency of the element differential method is validated by several numerical examples with analytical solutions. The results indicate that the element differential method has high precision and flexibility to solve non-Fourier heat conduction in convective-radiative fin. Besides, the effects of Vernotte number, dimensionless periodicity, thermal conductivity coefficient, and emissivity coefficient on dimensionless fin tip temperature, instantaneous fin efficiency, and average fin efficiency are comprehensively analyzed.
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30

Wang, B. "Fracture of a Finite Medium with a Circular Internal Crack under Hyperbolic Heat Conduction-Prescribed Crack Face Temperature." Advanced Materials Research 716 (July 2013): 402–8. http://dx.doi.org/10.4028/www.scientific.net/amr.716.402.

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This paper studies the fracture mechanics of a thermoelastic material layer with an internal crack subjecting to a prescribed temperature. The hyperbolic heat conduction theory is used and the transient thermal stress intensity factor is obtained. Comparisons of the results from the non-Fourier model and the Fourier model are made. The results demonstrate that the non-Fourier effect has a strong effect on the transient thermal stress around the crack tip. Thermal stress intensity factor predicted by the hyperbolic heat conduction model is considerably high then that predicted by the classical Fourier.
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31

Talaee, M. R., and V. Sarafrazi. "Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source." Journal of Mechanics 33, no. 1 (2016): 65–75. http://dx.doi.org/10.1017/jmech.2016.42.

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AbstractThis paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.
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32

Yang Hongqin, 杨洪钦, 陈建玲 Chen Jianling, 王瑜华 Wang Yuhua, 谢树森 Xie Shusen, and 李晖 Li Hui. "Fourier and Non-Fourier Heat Conduction Effects in Biological Tissue under Laser Irradiation." Chinese Journal of Lasers 36, no. 10 (2009): 2582–86. http://dx.doi.org/10.3788/cjl20093610.2582.

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33

Bhowmik, Arka, Rohit K. Singla, Ranjan Das, A. Mallick, and R. Repaka. "Inverse modeling of a solar collector involving Fourier and non-Fourier heat conduction." Applied Mathematical Modelling 38, no. 21-22 (2014): 5126–48. http://dx.doi.org/10.1016/j.apm.2014.04.001.

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34

Rahideh, H., P. Malekzadeh, and M. R. Golbahar Haghighi. "Non-Fourier Heat Conduction Analysis with Temperature-Dependent Thermal Conductivity." ISRN Mechanical Engineering 2011 (April 26, 2011): 1–10. http://dx.doi.org/10.5402/2011/321605.

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As a first endeavor, the one- and two-dimensional heat wave propagation in a medium subjected to different boundary conditions and with temperature-dependent thermal conductivity is studied. Both the spatial as well as the temporal domain is discretized using the differential quadrature method (DQM). This results in superior accuracy with fewer degrees of freedom than conventional finite element method (FEM). To verify this advantage through some comparison studies, a finite element solution ise also obtained. After demonstrating the convergence and accuracy of the method, the effects of different parameters on the temperature distribution of the medium are studied.
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35

Chen, Gang. "Non-Fourier phonon heat conduction at the microscale and nanoscale." Nature Reviews Physics 3, no. 8 (2021): 555–69. http://dx.doi.org/10.1038/s42254-021-00334-1.

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36

FAN, Qingmei. "Some non-Fourier heat conduction characters under pulsed inlet conditions." Chinese Science Bulletin 49, no. 3 (2004): 225. http://dx.doi.org/10.1360/03ww0033.

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37

YU, Ning, and Shoji IMATANI. "640 Thermo-elasto-plasticity Behaviour under Non-Fourier Heat Conduction." Proceedings of The Computational Mechanics Conference 2003.16 (2003): 559–60. http://dx.doi.org/10.1299/jsmecmd.2003.16.559.

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38

Espinosa-Paredes, G., and E.-G. Espinosa-Martínez. "Fuel rod model based on Non-Fourier heat conduction equation." Annals of Nuclear Energy 36, no. 5 (2009): 680–93. http://dx.doi.org/10.1016/j.anucene.2009.01.006.

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39

Yao, Wei-An, Hong-Xiao Yao, and Bo Yu. "Radial integration BEM for solving non-Fourier heat conduction problems." Engineering Analysis with Boundary Elements 60 (November 2015): 18–26. http://dx.doi.org/10.1016/j.enganabound.2015.04.002.

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40

Fan, Qingmei, and Wenqiang Lu. "Some non-Fourier heat conduction characters under pulsed inlet conditions." Chinese Science Bulletin 49, no. 3 (2004): 225–30. http://dx.doi.org/10.1007/bf03182802.

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41

Vishwakarma, V., A. K. Das, and P. K. Das. "Analysis of non-Fourier heat conduction using smoothed particle hydrodynamics." Applied Thermal Engineering 31, no. 14-15 (2011): 2963–70. http://dx.doi.org/10.1016/j.applthermaleng.2011.05.027.

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42

Calvo-Schwarzwälder, Marc, Timothy G. Myers, and Matthew G. Hennessy. "The one-dimensional Stefan problem with non-Fourier heat conduction." International Journal of Thermal Sciences 150 (April 2020): 106210. http://dx.doi.org/10.1016/j.ijthermalsci.2019.106210.

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43

Fu, Jiawei, Keqiang Hu, Linfang Qian, and Zengtao Chen. "Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack." Advances in Mathematical Physics 2020 (February 1, 2020): 1–11. http://dx.doi.org/10.1155/2020/8121295.

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The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack.
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44

Zhou, Luming, Zhende Zhu, and Xiangcheng Que. "Simulation of non-Fourier heat conduction in discontinuous heterogeneous materials based on the peridynamic method." Thermal Science, no. 00 (2022): 157. http://dx.doi.org/10.2298/tsci220803157z.

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Discontinuous heterogeneous materials, such as rocks and concrete, exhibit non-Fourier heat conduction. To predict this type of conduction behavior in discontinuous materials, a bond-based peridynamic heat conduction model based on the peridynamic theory was derived by introducing the dual-phase-lag model. The model was verified by the results obtained using other numerical methods. The Weibull distribution function was introduced to describe the heterogeneity in the thermal conductivity. The heat conduction in a plate with two pre-existing cracks under thermal shock was simulated. The effects of phase lag and heterogeneity were discussed. The results showed that the heat transfer rate is mainly controlled by the phase lag ?q of the heat flux. When ?q remains unchanged, the heat transfer rate increases with the increase in the phase lag ?T of the temperature gradient. The influence of cracks on the temperature field is mainly reflected in the area near the crack end. Although the temperature in the local area may be positively correlated with ?T in the short term, the long-term influence of the factor becomes increasingly weaker. The proposed method has a wide application prospect in simulating non-Fourier?s heat conduction in discontinuous heterogeneous materials.
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45

Rana, Sohel, Jeevan Kanesan, Ahmed Wasif Reza, and Harikrishnan Ramiah. "Fast Transient Thermal Analysis of Non-Fourier Heat Conduction Using Tikhonov Well-Conditioned Asymptotic Waveform Evaluation." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/671619.

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Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE) and finite element method (FEM). The non-Fourier heat conduction has been investigated where the maximum likelihood (ML) and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML), another well-conditioned scheme, called mass effect (ME) T-WCAWE, is introduced. TWCAWE with ME (TWCAWE-ME) showed more stable and accurate temperature spectrum in comparison to asymptotic wave evaluation (AWE) and also partial Pade AWE without sacrificing the computational time. However, the TWCAWE-ML remains as the most stable and hence accurate model to analyze the fast transient thermal analysis of non-Fourier heat conduction model.
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46

Noroozi, Mohammad Javad, and Majid Goodarzi. "Nonlinear analysis of a non-Fourier heat conduction problem in a living tissue heated by laser source." International Journal of Biomathematics 10, no. 08 (2017): 1750107. http://dx.doi.org/10.1142/s1793524517501078.

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The effect of laser, as a heat source, on a one-dimensional finite living tissue was studied in this paper. The dual phase lagging (DPL) non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method (ADM). It was concluded that the nonlinear analysis was important in non-Fourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.
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47

Fu, Yu, Li Li, Hongfang Chen, Xuelin Wang, Ling Ling, and Yujin Hu. "Rational design of thermoelastic damping in microresonators with phase-lagging heat conduction law." Applied Mathematics and Mechanics 43, no. 11 (2022): 1675–90. http://dx.doi.org/10.1007/s10483-022-2914-5.

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AbstractThe design of thermoelastic damping (TED) affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging the quality factor of widely-used microresonators operating in extreme situations, including ultra-high excitation frequency and ultra-low working temperature. However, there does not exist a rational method for designing the TED in the framework of non-Fourier heat conduction law. This work, therefore, proposes a design framework to achieve low thermoelastic dissipation of microresonators governed by the phase-lagging heat conduction law. The equation of motion and the heat conduction equation for phase-lagging TED microresonators are derived first, and then the non-Fourier TED design problem is proposed. A topology optimization-based rational design method is used to resolve the design problem. What is more, a two-dimensional (2D) plain-strain-based finite element method (FEM) is developed as a solver for the topology optimization process. Based on the suggested rational design technique, numerical instances with various phase lags are investigated. The results show that the proposed design method can remarkably reduce the dissipation of microresonators by tailoring their substructures.
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48

Luo, Jiajian, Haifeng Jiang, Jun Huang, Hongsheng Wang, and Xuejiao Hu. "Analysis of Non-Fourier Heat Conduction Problem with Suddenly Applied Surface Heat Flux." Journal of Thermophysics and Heat Transfer 34, no. 2 (2020): 287–95. http://dx.doi.org/10.2514/1.t5849.

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49

Barletta, A., and E. Zanchini. "Non-Fourier heat conduction in a plane slab with prescribed boundary heat flux." Heat and Mass Transfer 31, no. 6 (1996): 443–50. http://dx.doi.org/10.1007/s002310050081.

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50

Shirmohammadi, Reza, and Amin Moosaie. "Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux." International Communications in Heat and Mass Transfer 36, no. 8 (2009): 827–33. http://dx.doi.org/10.1016/j.icheatmasstransfer.2009.05.002.

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