Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation with a heat source

Su, Sheng; Dai, Weizhong

doi:10.1016/j.ijheatmasstransfer.2006.03.002

Cited by 16 publications

(4 citation statements)

References 24 publications

(30 reference statements)

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“…The difference between the solutions of the phase-lagging equation and the damped-wave equation is studied by investigating the solutions of a test problem [65]. As expected, it is found that the damped-wave equation is a good approximation to the phase-lagging equation when the time-lag is small [66].…”

Section: Temperature Formulationmentioning

confidence: 59%

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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Section: Temperature Formulationmentioning

confidence: 59%

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

2015

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“…What is clear here is the fact that predefined boundary conditions, including the ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library presented in [138,139] the corresponding solution of the classical (no phase-lag) heat equation.…”

Section: U(x) T(t) == Q"(x)p(t -T)mentioning

confidence: 99%

“…On the other hand, what was solution of the PLE according to the first theorem. Now, it is seen that in[138,139] the and, if it is set p(O)~:>., the theorem is proved. Although the first interval was c considered, it is possible to redo above procedures for all intervals.…”

mentioning

confidence: 91%

“…It applying to the case, when one wants to solve all the equations in the model of superfluidity simultaneously and work with the non-linear momentum terms. Separable not be good methods for the beginning and are also far technical than simple difference numerical methods byDai and Su [135,136,138,139] also seem to depend on an initial discretion of variables like in the heat equation with no lag. With respect to the4.2.1-Difference SchemeThe work here begins with the dimensional form of PLHE without source term.…”

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confidence: 99%

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Investigation of superfluidity in ultra-short flows : effect of time-lags in transport phenomena

Tavallali¹

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Since the model presented in this report is the newest model to describe the superfluidity, and predict it at high temperatures, the author has tried to show the validation of the model by converting it into one of the previous well-known models by using mathematical linear approximation procedure. This approach, clearly, paves the way for the model to suggest that, not only is the model could be correct, both physically and mathematically, but also a more rigorous one among all other models. As mentioned earlier, Delay Differential Equations (DDEs) are a consequence of the idea behind the phase-lagged formulations. As a result, the solutions of these equations become vital to the model. The analytic solution for a subclass of Partial Delay Differential Equations (PDDE) has been proposed. The numerous numerical solutions have also been presented in the text. The model presented in this report will have the ability of extension into other fields of physics. The model will be useful in areas such as superfluidity, superconductivity, startup flows, ultra-short phenomena (such as ultra-short laser pulses), supertransport of energy, Quantum Mechanics, etc.

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Introduction

Wang¹

2014

Springer Theses

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Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation with a heat source

Cited by 16 publications

References 24 publications

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

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

Investigation of superfluidity in ultra-short flows : effect of time-lags in transport phenomena

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