The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale

Yu, Yajun; Li, Chen-Lin; Xue, Zhangna; Tian, Xiaogeng

doi:10.1016/j.physleta.2015.09.030

Cited by 47 publications

(9 citation statements)

References 60 publications

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“…With (38) instead of λ, we can define effective Fourier and Cattaneo laws. Using these effective laws in combination with (19) with r = 0, we finally obtain in dimensionless form: 3 shows that, although no exact correspondence is observed, for small numbers and large times, the effective Cattaneo and Fourier results are qualitatively not far from our results. The temperature jumps are not represented by these effective models, and for large Kn numbers and small times, even the qualitative comparison does not hold.…”

Section: Methods: Constitutional Equation For Ballistic Heat Transportmentioning

confidence: 58%

“…The solutions are compared with those stemming from the combination of the dimensionless Fourier and Cattaneo laws (1)-(2) with the energy balance (19), with r = 0:…”

Section: Comparison With Fourier and Cattaneo Lawsmentioning

confidence: 99%

“…To account for the ballistic effects, some studies proposed ballistic-diffusive phonon transport via Monte Carlo simulations [15,16]. Other works regarded the ballistic-type of phonon transport as an introduction of a non-local effect, obtaining via the phonon Boltzmann equation the Guyer-Krumhansl equation [17][18][19]. Whilst these works appeared to provide quite correct predictions (and as will be mentioned later, our model will give comparable results), these works either demand a high computing cost [15,16], or they lack the distinction between the diffusive and ballistic components [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…Other works regarded the ballistic-type of phonon transport as an introduction of a non-local effect, obtaining via the phonon Boltzmann equation the Guyer-Krumhansl equation [17][18][19]. Whilst these works appeared to provide quite correct predictions (and as will be mentioned later, our model will give comparable results), these works either demand a high computing cost [15,16], or they lack the distinction between the diffusive and ballistic components [17][18][19]. Although they do not make an explicit distinction between the ballistic and diffusive components, this does not necessarily mean that the model is incorrect (it can indeed predict correctly); such a distinction can provide more information on the behavior of the phonons.…”

Section: Introductionmentioning

confidence: 99%

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Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach

Machrafi

2019

Inventions

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As microelectronic devices are important in many applications, their heat management needs to be improved, in order to prolong their lifetime, and to reduce the risk of damage. In nanomaterials, heat transport shows different behaviors than what can be observed at macroscopic sizes. Studying heat transport through nanofilms is a necessary tool for nanodevice thermal management. This work proposes a thermodynamic model incorporating both ballistic, introduced by non-local effects, and diffusive phonon transport. Extended thermodynamics principles are used in order to develop a constitutive equation for the ballistic behavior of heat conduction at small-length scales. Being an irreversible process, the present two-temperature model contains a one-way transition of ballistic to diffusive phonons as time proceeds. The model is compared to the classical Fourier and Cattaneo laws. These laws were not able to present the non-locality that our model shows, which is present in cases when the length scale of the material is of the same order of magnitude or smaller than the phonon mean free path, i.e., when the Knudsen number K n ≤ O ( 1 ) . Moreover, for small K n numbers, our model predicted behaviors close to that of the classical laws, with a weak temperature jump at both sides of the nanofilm. However, as K n increases, the behavior changes completely, the ballistic component becomes more important, and the temperature jump at both sides of the nanofilms becomes more pronounced. For comparison, a model using Fourier’s and Cattaneo’s laws with an effective thermal conductivity has shown, with reasonable qualitative comparison for small Knudsen numbers and large times.

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Section: Methods: Constitutional Equation For Ballistic Heat Transportmentioning

confidence: 58%

“…The solutions are compared with those stemming from the combination of the dimensionless Fourier and Cattaneo laws (1)-(2) with the energy balance (19), with r = 0:…”

Section: Comparison With Fourier and Cattaneo Lawsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach

Machrafi

2019

Inventions

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“…Yu et al. [14] emphasized the size effect of heat conduction, where abnormal result within thermal wave model is eliminated by introducing spatially size effect. The celebrated size‐dependent heat conductive model was formulated by Guyer and Krumhansl [15] in which they solved the phonon Boltzmann equation by a linear assumption and obtained a transport model (GK model) containing the transient and nonlocal terms.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

Sarkar

2020

Z Angew Math Mech

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This is an attempt to design a dynamic model of nonlocal heat conduction in a nonlocal elastic bounded rod. This model is drafted using the Lord-Shulman theory of generalized thermoelasticity due to the involvement of one relaxation time to the heat conduction equation and the equation of motion. This model is then employed to discuss the thermal behavior of the rod when subjected to a moving heat source. Both ends of the rod are assumed to be rigidly fixed and thermally insulated. Analytical solutions for the distribution of temperature, displacement and thermal stresses are obtained using integral transform in the Laplace transform technique is used to obtain the analytical solutions for the field variables such as temperature, displacement and stress. The inverse Laplace transform based on the Zakian method is used to invert the results in the space-time domain. Specific attention is paid to study the effect of thermal nonlocal parameter and the velocity of the moving heat source on the distribution of the field variables. K E Y W O R D SLaplace transform, LS model, nonlocal heat conduction, thermal nonlocal parameter, Zakian algorithm

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Nonlocal heat conduction in single‐walled carbon nanotubes

et al. 2021

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This paper explores how reinforcing the hyperbolic heat conduction by the nonlocality affects temperature distribution in nanostructures such as nanobeam and single‐walled carbon nanotubes (SWCNTs). The work dissects the nonlocal heat conduction by advocating a thoroughly new application of the differential quadrature method. The nanobeam is modeled like a SWCNT (cylindrical shell), and the boundaries on the inner and outer sides are considered under a temperature jump at the nanoscale. The effects of several parameters on the temperature distribution through the thickness of the nanobeam are highlighted, including time‐dependent boundary conditions, time lag, nonlocal parameter, length, and radius of the hollow beam.

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The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale

Cited by 47 publications

References 60 publications

Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach

Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

Nonlocal heat conduction in single‐walled carbon nanotubes

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