Characteristics of Temperature Field due to Pulsed Heat Input Calculated by Non-Fourier Heat Conduction Hypothesis

Yu, Ning; Imatani, Shōji; Inoue, Tatsuo

doi:10.1299/jsmea.47.574

Cited by 12 publications

(4 citation statements)

References 10 publications

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“…The modified Fourier constitutive equation is expressed as , where is the heat flux, and k is the coefficient of thermal conductivity. The thermal relaxation time is usually recognized to be a small parameter (Yu et al 2004), where ρ is the density, c p is the specific heat and v is the heat propagation velocity. The situation for τ→ 0 leads to instantaneous diffusion at infinite propagation speed, which coincides with the classical thermal diffusion theory.…”

Section: Quasi‐reversibility Methodsmentioning

confidence: 99%

Quasi-reversibility method for data assimilation in models of mantle dynamics

Ismail‐Zadeh

Korotkii

Schubert

et al. 2007

Geophysical Journal International

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S U M M A R YRapid progress in imaging deep Earth structures using seismic tomography and in studies of physical and chemical properties of mantle rocks facilitates research in assimilation of data related to mantle dynamics. In this paper, we present a new numerical approach for data assimilation, which allows for incorporating observations (at present) and unknown initial conditions (in the past) for mantle temperature and flow into a 3-D dynamic model in order to determine the initial conditions. The dynamic model is described by the backward heat, motion and continuity equations. The use of the quasi-reversibility (QRV) method implies the introduction into the backward heat equation of the additional term involving the product of a small regularization parameter and a higher order temperature derivative. The data assimilation in this case is based on a search of the best fit between the forecast model state and the observations by minimizing the regularization parameter. We apply the QRV data assimilation method to restore the evolution of (i) mantle plumes (a synthetic case study) and (ii) the lithospheric slab imaged by teleseismic body-wave tomography in the southeastern Carpathians. For both models the present temperature and mantle flow are assimilated to the geological past, and the prominent features of mantle structures are recovered. We then model the evolution of the mantle structures forward in time starting from the restored state to the present state and estimate the accuracy of the model predictions. The results of the QRV data assimilation are compared to that obtained by the variational (VAR) and backward advection data assimilation. Although the accuracy of the QRV data assimilation is lower than that of the VAR data assimilation, the QRV method does not require any additional smoothing of the input data or filtering of temperature noise as the VAR method does. Based on the results and the comparison of the methods, we consider the QRV method to be a highly promising approach to assimilation of data related to mantle dynamics.

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Section: Quasi‐reversibility Methodsmentioning

confidence: 99%

Quasi-reversibility method for data assimilation in models of mantle dynamics

Ismail‐Zadeh

Korotkii

Schubert

et al. 2007

Geophysical Journal International

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“…Yu [45] based on Single Phase Lagging model, and adopted finite element method combined with Newmark-β method to research on two-dimensional planar heated by local pulsed heat flux. First introducing dimensionless parameters derived the dimensionless expression of hyperbolic equation.…”

Section: Finite Element Methods (Fem)mentioning

confidence: 99%

Current Research Progress in Non-Classical Fourier Heat Conduction

Wang

2013

AMM

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Classical Fourier law can accurately describe most heat conduction problems. But for ultrafast heat conduction process and micro/nanoscale heat conduction problems, non-classical Fourier (non-Fourier) effect may become dominated. The paper gives a review on the current progress on non-Fourier heat conduction in engineering. It includes basic concept, physical models, thermal relaxation effect, and related experiments. Also introduced are the solution methods of non-Fourier heat conduction equations, including closed-form solution, finite difference method, finite element method, molecular dynamics simulation, variational method, and other hybrid methods. Some challenging issues are discussed at the conclusion of the paper.

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“…In order to describe the mechanical behavior in the same domain, the adiabatic end of the rod is assumed as constrained boundary. A little more practical example, which was only concern on the heat conduction problem, has been investigated in the previous report in a twodimensional domain under the non-Fourier (18) . The same objective domain is condensed into the rod which is long enough compared with its width.…”

Section: Problem Statementsmentioning

confidence: 99%

Hyperbolic Thermoelastic Analysis due to Pulsed Heat Input by Numerical Simulation

Imatani

Inoue

2006

JSME Int. J., Ser. A

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Thermo-mechanical behavior in a rod subjected to a pulsed heat input was investigated by numerical simulation using the hyperbolic thermo-elasticity theory derived from the thermal dynamics in the present paper. Unlike the classical thermo-elastic theory with the parabolic energy equation and the hyperbolic motion equation, temperature response and thermal stress due to the temperature change exhibit significant wavy characteristics in the hyperbolic thermo-elasticity theory which is based on the non-Fourier heat conduction. The whole region of the rod is split into the heat disturbed region and the heat undisturbed region by the thermal wave front which is determined by the propagating velocity of the heat wave. The heat wave and elastic wave travel in the body at a finite velocity and reflect at the end of the rod. Thermal shock due to the discontinuous jump in thermal condition, and the reflection of thermal stress at the end terminate of the rod are significant during the heating process.

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Characteristics of Temperature Field due to Pulsed Heat Input Calculated by Non-Fourier Heat Conduction Hypothesis

Cited by 12 publications

References 10 publications

Quasi-reversibility method for data assimilation in models of mantle dynamics

Quasi-reversibility method for data assimilation in models of mantle dynamics

Current Research Progress in Non-Classical Fourier Heat Conduction

Hyperbolic Thermoelastic Analysis due to Pulsed Heat Input by Numerical Simulation

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