Non-Fourier heat conduction in a finite medium with insulated boundaries and arbitrary initial conditions

Moosaie, Amin

doi:10.1016/j.icheatmasstransfer.2007.08.001

Cited by 39 publications

(12 citation statements)

References 23 publications

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“…Consequently, setting 2 /γ = 1 in the asymptotic solutions will enable the Fourier solutions to be easily recovered. It has been shown that if 2 /γ > 1, then the temperature is dominated by diffusion; if 2 /γ < 1, then the temperature propagates as a wave [56][57][58].…”

Section: Model Reformulationsmentioning

confidence: 99%

Asymptotic analysis of the Guyer–Krumhansl–Stefan model for nanoscale solidification

Hennessy

Calvo-Schwarzwälder

Myers

2018

Applied Mathematical Modelling

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Nanoscale solidification is becoming increasingly relevant in applications involving ultrafast freezing processes and nanotechnology. However, thermal transport on the nanoscale is driven by infrequent collisions between thermal energy carriers known as phonons and is not well described by Fourier's law. In this paper, the role of non-Fourier heat conduction in nanoscale solidification is studied by coupling the Stefan condition to the Guyer-Krumhansl (GK) equation, which is an extension of Fourier's law, valid on the nanoscale, that includes memory and non-local effects. A systematic asymptotic analysis reveals that the solidification process can be decomposed into multiple time regimes, each characterised by a non-classical mode of thermal transport and unique solidification kinetics. For sufficiently large times, Fourier's law is recovered. The model is able to capture the change in the effective thermal conductivity of the solid during its growth, consistent with experimental observations. The results from this study provide key quantitative insights that can be used to control nanoscale solidification processes. IntroductionAdvances in the field of nanotechnology are improving the efficiency, functionality, and costeffectiveness of modern devices. Nanowire-based solar cells, for instance, offer several advantages over traditional wafer-based and thin-film technologies [1]. Furthermore, the unique physical properties of carbon nanotubes have enabled the fabrication of new electrochemical biosensors [2]. Nanotechnology is also playing an increasing role in biology and medicine [3], where it finds applications in drug and gene delivery [4], protein detection [5], and tissue engineering * Published in Applied Mathematical Modelling, https://doi.

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Section: Model Reformulationsmentioning

confidence: 99%

Asymptotic analysis of the Guyer–Krumhansl–Stefan model for nanoscale solidification

Hennessy

Calvo-Schwarzwälder

Myers

2018

Applied Mathematical Modelling

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“…Then the two dimensional problem in cylinder was solved [14][15][16]. Later, Moosaie [17][18][19] solved one dimensional hyperbolic heat conduction in a finite medium subjected to arbitrary periodic/non-periodic surface disturbance, and a finite medium with insulated boundaries and arbitrary initial conditions. Recently, Zhao and Wu [20] analyzed a solid sphere under sudden surface temperature change, simple harmonic periodic surface temperature change, triangular surface temperature change and pulse surface temperature changes.…”

Section: Introductionmentioning

confidence: 99%

Thermal shock fracture of a cylinder with a penny-shaped crack based on hyperbolic heat conduction

Guo

Wang

2015

International Journal of Heat and Mass Transfer

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“…Solutions to Hyperbolic Heat Conduction Equation (HHCE) can be obtained both analytically and numerically [33][34][35][36][37][38][39][40], although numerical methods seem to be more commonly used [41][42][43][44]. Analytical study gives deeper insight in the problem; operational analytical approach and solutions to HHE were developed in [45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Some Exact Solutions to Non-Fourier Heat Equations with Substantial Derivative

Zhukovsky

Oskolkov

Gubina

2018

Axioms

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Abstract:One-dimensional equations of telegrapher's-type (TE) and Guyer-Krumhansl-type (GK-type) with substantial derivative considered and operational solutions to them are given. The role of the exponential differential operators is discussed. The examples of their action on some initial functions are explored. Proper solutions are constructed in the integral form and some examples are studied with solutions in elementary functions. A system of hyperbolic-type inhomogeneous differential equations (DE), describing non-Fourier heat transfer with substantial derivative thin films, is considered. Exact harmonic solutions to these equations are obtained for the Cauchy and the Dirichlet conditions. The application to the ballistic heat transport in thin films is studied; the ballistic properties are accounted for by the Knudsen number. Two-speed heat propagation process is demonstrated-fast evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow diffusive heat-exchange process. The comparative analysis of the obtained solutions is performed.

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Non-Fourier heat conduction in a finite medium with insulated boundaries and arbitrary initial conditions

Cited by 39 publications

References 23 publications

Asymptotic analysis of the Guyer–Krumhansl–Stefan model for nanoscale solidification

Asymptotic analysis of the Guyer–Krumhansl–Stefan model for nanoscale solidification

Thermal shock fracture of a cylinder with a penny-shaped crack based on hyperbolic heat conduction

Some Exact Solutions to Non-Fourier Heat Equations with Substantial Derivative

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