Numerical Schemes for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Model in a Double-Layered Nanoscale Thin Film

Ji, Cui-cui; Dai, Weizhong; Sun, Zhi‐zhong

doi:10.1007/s10915-019-01062-6

Cited by 24 publications

(11 citation statements)

References 28 publications

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“…Figure 6 (e) also shows that when α is equal to 0.7, 0.9, and almost 1, oscillations appear in maximum temperature plot which present the negative-bias temperature instability (NBTI) [41,42,43]. This phenomenon identified as the short-memory principle is observed in the works [29,44]. In consequence, taking into account the bulk thermal properties for the film structures, notably underestimates the obtained temperature profiles and the peak temperature rise.…”

Section: Result: Cases (I) and (Ii)mentioning

confidence: 84%

“…In 2018, Ji et al have established a fractional dual phase lag model based on the finite difference numerical method, to investigate the heat conduction in nanoscale devices [28]. Also, they have investigated the non-Fourier heat transport in a thin two-layer film exposed to the ultrashort-pulsed laser heating applying the fractional DPL model [29].…”

Section: Introductionmentioning

confidence: 99%

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A time-fractional dual-phase-lag framework to investigate transistors with TMTC channels (TiS3, In4Se3) and size-dependent properties

Fotovvat¹,

Shomali²

2022

Preprint

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In this study, a time fractional dual-phase-lag model with temperature jump boundary condition as a choice for the Fourier's law replacement in thermal modeling of transistors, is utilized. In more details, the numerical simulation of heat transfer in newly proposed TMTC field effect transistors using fractional DPL equation has been investigated. Moreover, the Caputo fractional derivative is employed to formulate the finite difference scheme for discretization of the fractional DPL model. In order to obtain more precise results for the peak temperature rise, the temperature and heat flux profiles, the sizedependent thermal properties are taken into account. Also, the temperature jump boundary condition has been also applied by means of a mixed-type boundary condition. It is obtained that considering size-dependent thermal characteristics for transistors under study, results in increase of the peak temperature rise up to 250 percent. Furthermore, considering constant bulk thermal properties for the silicon MOSFET, certain oscillations are observed in the time-variation of the peak temperature rise for α= 0.7, 0.9 and 1. This presents the so-called negative bias temperature instability appearing in electronic nano-semiconductor devices. Finally, the hotspot temperature has been researched in transistors containing two-dimensional materials with quasi one-dimensional band structure channels. It is obtained that among the studied FETs, titanium trisulfide with maximum temperature increase

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Section: Result: Cases (I) and (Ii)mentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

A time-fractional dual-phase-lag framework to investigate transistors with TMTC channels (TiS3, In4Se3) and size-dependent properties

Fotovvat¹,

Shomali²

2022

Preprint

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“…Xu and Jiang considered a time fractional DPL model by replacing the two first-order derivatives with respect to time by the Caputo fractional derivatives and the phase lags τ q , τ T by τ α q , τ β T of the DPL relation (1.1), where 0 < α, β < 1, and then investigated the corresponding bioheat transfer equation. Recently, based on the fractional Taylor formula, we have extended the DPL relation to a fractional DPL constitutive relation [11] q(x, t) + (τ q ) α Γ(1 + α)…”

Section: Introductionmentioning

confidence: 99%

Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation

null¹,

Dai²

2023

NMTMA

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Nanoscale heat transfer cannot be described by the classical Fourier law due to the very small dimension, and therefore, analyzing heat transfer in nanoscale is of crucial importance for the design and operation of nano-devices and the optimization of thermal processing of nano-materials. Recently, time-fractional dualphase-lagging (DPL) equations with temperature jump boundary conditions have showed promising for analyzing the heat conduction in nanoscale. This article proposes a numerical algorithm with high spatial accuracy for solving the timefractional dual-phase-lagging nano-heat conduction equation with temperature jump boundary conditions. To this end, we first develop a fourth-order accurate and unconditionally stable compact finite difference scheme for solving this time-fractional DPL model. We then present a fast numerical solver based on the divide-and-conquer strategy for the obtained finite difference scheme in order to reduce the huge computational work and storage. Finally, the algorithm is tested by two examples to verify the accuracy of the scheme and computational speed. And we apply the numerical algorithm for predicting the temperature rise in a nano-scale silicon thin film. Numerical results confirm that the present difference scheme provides min{2−α, 2−β} order accuracy in time and fourth-order accuracy in space, which coincides with the theoretical analysis. Results indicate that the mentioned time-fractional DPL model could be a tool for investigating the thermal analysis in a simple nanoscale semiconductor silicon device by choosing the suitable fractional order of Caputo derivative and the parameters in the model.

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“…In the past decades, many tests show that the fractional partial differential equations (FPDEs) can accurately describe complex physical phenomena such as the memory effect, long-range interaction, and the anomalous diffusion, [1][2][3][4] and extensive investigations have been performed on the corresponding mathematical analysis and numerical methods. [5][6][7][8][9][10][11][12][13] In most of the existing works, the singular power-law kernel is widely used to define fractional derivatives. However, the singularity of the power-law kernel often leads to difficulties in the numerical evaluation of fractional derivatives and thus limits the utilization of FPDEs in real-world applications.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical analysis and efficient finite element approximation for variable‐order time‐fractional reaction–diffusion equation with nonsingular kernel

Liu

Zheng

2021

Math Methods in App Sciences

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The fractional derivative with nonsingular kernel has been widely used to many physical fields which was shown to offer a new insight into the mathematical modeling of natural phenomena. In this paper, we first study the well-posedness and regularity of the multidimensional variable-order time-fractional reaction-diffusion equation with Caputo-Fabrizio fractional derivative and then present and analyze a Galerkin finite element approximation to the proposed model based on the proved smoothing properties of the solutions. To improve the computational efficiency of the variable-order Caputo-Fabrizio derivative, we approximate the kernel of the fractional derivative by the K-term truncation of its Taylor expansion at a fixed fractional order to develop a fast evaluation scheme which significantly reduces the memory requirement from (N) to (K) and the computational complexity from (N 2 ) to (K 2 N) where N refers to the number of time steps. We accordingly develop a fast Galerkin finite element method to the proposed model. Numerical experiments are carried out to substantiate the theoretical findings and to show the performance of the fast method. KEYWORDSfast method, fractional derivatives and integrals, reaction-diffusion equations, variable-order Caputo-Fabrizio fractional derivative, well-posedness and regularity MSC CLASSIFICATION35R11; 26A33

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Numerical Schemes for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Model in a Double-Layered Nanoscale Thin Film

Cited by 24 publications

References 28 publications

A time-fractional dual-phase-lag framework to investigate transistors with TMTC channels (TiS3, In4Se3) and size-dependent properties

A time-fractional dual-phase-lag framework to investigate transistors with TMTC channels (TiS3, In4Se3) and size-dependent properties

Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation

Mathematical analysis and efficient finite element approximation for variable‐order time‐fractional reaction–diffusion equation with nonsingular kernel

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