Thermal wave interference as the origin of the overshooting phenomenon in dual-phase-lagging heat conduction

Xu, Mingtian; Guo, Jiangfeng; Wang, Liqiu; Cheng, Lin

doi:10.1016/j.ijthermalsci.2010.12.006

Cited by 58 publications

(22 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, four examples of different physical situations are analyzed in order to illustrate the accuracy and potentialities of the proposed unified method. The obtained results show good agreement with works of [1][2][3][4]. …”

supporting

confidence: 87%

“…The obtained results show good agreement with those depicted by [1] who solved this problem using separation of variables method.…”

supporting

confidence: 86%

“…Also, the Green's function for a finite medium subjected to arbitrary heat source and arbitrary initial and boundary conditions is constructed. To examine the applicability of the present method, calculations are performed on four different previously solved researches [1][2][3][4]. The obtained results show good agreement with these researches.…”

Section: Introductionmentioning

confidence: 52%

“…In this example the overshooting phenomenon was investigated by M. Xu et al [1]. The overshooting phenomenon is studied based on the one-dimensional dualphase-lagg heat conduction model.…”

Section: Examplementioning

confidence: 99%

See 3 more Smart Citations

Green’s Function Solution for the Dual-Phase-Lag Heat Equation

Al-Khairy¹

2012

View full text Add to dashboard Cite

The present work is devoted to define a generalized Green's function solution for the dual-phase-lag model in homogeneous materials in a unified manner .The high-order mixed derivative with respect to space and time which reflect the lagging behavior is treated in special manner in the dual-phase-lag heat equation in order to construct a general solution applicable to wide range of dual-phase-lag heat transfer problems of general initial-boundary conditions using Green's function solution method. Also, the Green's function for a finite medium subjected to arbitrary heat source and arbitrary initial and boundary conditions is constructed. Finally, four examples of different physical situations are analyzed in order to illustrate the accuracy and potentialities of the proposed unified method. The obtained results show good agreement with works of [1][2][3][4].

show abstract

supporting

confidence: 87%

“…The obtained results show good agreement with those depicted by [1] who solved this problem using separation of variables method.…”

supporting

confidence: 86%

Section: Introductionmentioning

confidence: 52%

“…In this example the overshooting phenomenon was investigated by M. Xu et al [1]. The overshooting phenomenon is studied based on the one-dimensional dualphase-lagg heat conduction model.…”

Section: Examplementioning

confidence: 99%

See 2 more Smart Citations

Green’s Function Solution for the Dual-Phase-Lag Heat Equation

Al-Khairy¹

2012

View full text Add to dashboard Cite

show abstract

“…Because of this approximation relationship between them, the SPL model is sometimes considered as an extension or explanation of the CV one [17][18][19][20][21]. In addition, this approximation also has some defects [22].…”

Section: Introductionmentioning

confidence: 99%

On Thermodynamics Problems in the Single-Phase-Lagging Heat Conduction Model

Cao

2016

Entropy

View full text Add to dashboard Cite

Thermodynamics problems for the single-phase-lagging (SPL) model have not been much studied. In this paper, the violation of the second law of thermodynamics by the SPL model is studied from two perspectives, which are the negative entropy production rate and breaking equilibrium spontaneously. The methods for the SPL model to avoid the negative entropy production rate are proposed, which are extended irreversible thermodynamics and the thermal relaxation time. Modifying the entropy production rate positive or zero is not enough to avoid the violation of the second law of thermodynamics for the SPL model, because the SPL model could cause breaking equilibrium spontaneously in some special circumstances. As comparison, it is shown that Fourier's law and the CV model cannot break equilibrium spontaneously by analyzing mathematical energy integral.

show abstract

Fractional derivative heat conduction modeling based on thermal elements combination

Fang

Sun

Zhang

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper proposes a general theoretical framework to establish the timespace fractional derivative models for non-Fourier heat conduction. Similar to viscoelastic modeling in mechanics, some new heat conduction elements are proposed instead of mechanical ones. With different combinations of the thermal elements, the time-space fractional generalizations, such as the Kelvin-Voigt model, the Maxwell model, and the Zener model, are presented.In addition, it is possible to obtain the fractional derivative heat conduction equations from the corresponding transport equations. While incorporating the existing non-Fourier heat conduction models into the proposed theoretical framework, some new time-space fractional derivative models are presented. Finally, the nonlocal models considering the long-range heat fluxes are investigated and confirmed to be consistent with the proposed framework.

show abstract

Thermal wave interference as the origin of the overshooting phenomenon in dual-phase-lagging heat conduction

Cited by 58 publications

References 23 publications

Green’s Function Solution for the Dual-Phase-Lag Heat Equation

Green’s Function Solution for the Dual-Phase-Lag Heat Equation

On Thermodynamics Problems in the Single-Phase-Lagging Heat Conduction Model

Fractional derivative heat conduction modeling based on thermal elements combination

Contact Info

Product

Resources

About