A stable and convergent three-level finite difference scheme for solving a dual-phase-lagging heat transport equation in spherical coordinates

Dai, Weizhong; Shen, Liran; Nassar, Raja; Zhu, Teng

doi:10.1016/j.ijheatmasstransfer.2003.10.013

Cited by 28 publications

(8 citation statements)

References 22 publications

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“…Hence, a stable and convergent three-level finite difference scheme has been used which was introduced for the first time by Dai et al [28] for 1-D spherical coordinates. This method has been extended for 2-D case in Cartesian coordinates and Eq.…”

Section: Methodsmentioning

confidence: 99%

Investigation of dual-phase-lag heat conduction model in a nanoscale metal-oxide-semiconductor field-effect transistor

Ghazanfarian

Shomali

2012

International Journal of Heat and Mass Transfer

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Section: Methodsmentioning

confidence: 99%

Investigation of dual-phase-lag heat conduction model in a nanoscale metal-oxide-semiconductor field-effect transistor

Ghazanfarian

Shomali

2012

International Journal of Heat and Mass Transfer

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“…Higher-order compact finite difference schemes for solving one-dimensional Fourier heat conduction equation with Dirichlet and Neumann boundary conditions [148], a three-level [149][150][151] and a compact [152] fully implicit finite difference scheme for solving the DPL heat equation, are developed in Cartesian and spherical coordinates. The discrete Fourier stability analysis for the first-order accurate method [152] and the discrete energy method for high-order accurate schemes [149][150][151] are performed, and it is concluded that the proposed numerical methods are unconditionally stable and convergent with respect to the initial values.…”

Section: Finite Difference Methodsmentioning

confidence: 99%

“…The discrete Fourier stability analysis for the first-order accurate method [152] and the discrete energy method for high-order accurate schemes [149][150][151] are performed, and it is concluded that the proposed numerical methods are unconditionally stable and convergent with respect to the initial values. It is also shown for some selective numerical examples that the numerical results efficiently converge to the exact solutions [150].…”

Section: Finite Difference Methodsmentioning

confidence: 99%

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

2015

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The classical model of the Fourier's law is known as the most common constitutive relation for thermal transport in various engineering materials. Although the Fourier's law has been widely used in a variety of engineering application areas, there are many exceptional applications in which the Fourier's law is questionable. This paper gathers together such applications. Accordingly, the paper is divided into two parts. The first part reviews the papers pertaining to the fundamental theory of the phase-lagging models and the analytical and numerical solution approaches. The second part wrap ups the various applications of the phase-lagging models including the biological materials, ultra-high-speed laser heating, the problems involving moving media, micro/nanoscale heat transfer, multi-layered materials, the theory of thermoelasticity, heat transfer in the material defects, the diffusion problems we call as the non-Fick models, and some other applications. It is predicted that the interest in the field of phase-lagging heat transport has grown incredibly in recent years because they show good agreement with the experiments across a wide range of length and time scales.

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“…4 is a third-order PDE containing mixed derivatives of t * and x * or y * , in order to avoid convergence and stability problems the numerical discretization of this equation needs some special considerations. Hence, a stable and convergent three-level finite difference scheme has been used which was introduced for the first time by Dai et al [21], for the 1D DPL model in spherical coordinates. In this method, a weighted average was used for stability and convergence of the method.…”

Section: Numerical Schemementioning

confidence: 99%

Investigation of 2D Transient Heat Transfer under the Effect of Dual-Phase-Lag Model in a Nanoscale Geometry

Ghazanfarian

Abbassi

2012

Int J Thermophys

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Analytical and numerical solutions of the 2D transient dual-phase-lag (DPL) heat conduction equation are presented in this article. The geometry is that of a simplified metal oxide semiconductor field effect transistor with a heater placed on it. A temperature jump boundary condition is used on all boundaries in order to consider boundary phonon scattering at the micro-and nanoscale. A combination of a Laplace transformation technique and separation of variables is used to solve governing equations analytically, and a three-level finite difference scheme is employed to generate numerical results. The results are illustrated for three Knudsen numbers of 0.1, 1, and 10 at different instants of time. It is seen that the wave characteristic of the DPL model is strengthened by increasing the Knudsen number. It is found that the combination of the DPL model with the proposed mixed-type temperature boundary condition has the potential to accurately predict a 2D temperature distribution not only within the transistor itself but also in the near-boundary region.

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A stable and convergent three-level finite difference scheme for solving a dual-phase-lagging heat transport equation in spherical coordinates

Cited by 28 publications

References 22 publications

Investigation of dual-phase-lag heat conduction model in a nanoscale metal-oxide-semiconductor field-effect transistor

Investigation of dual-phase-lag heat conduction model in a nanoscale metal-oxide-semiconductor field-effect transistor

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

Investigation of 2D Transient Heat Transfer under the Effect of Dual-Phase-Lag Model in a Nanoscale Geometry

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