A Numerical Scheme for Non-Fourier Heat Conduction, Part Ii: Two-Dimensional Problem Formulation and Verification

Lam, Tung T.; Yeung, Wing K.

doi:10.1080/10407790190053770

Cited by 19 publications

(6 citation statements)

References 5 publications

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“…(11) subject to Eqs. (8) and (9). Thus, we characterize the constants C pjkr ; b b ij , and q q of non-homogeneous material by where C pjkr ; b ij ; and q are constants (they are the values of C pjkr ; b b ij , and q q in a homogeneous matter), and m is a rational number.…”

Section: Displacement Fieldmentioning

confidence: 99%

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Thermoelastic Stresses in a Rotating Non-Homogeneous Anisotropic Body

Fahmy

2008

Numerical Heat Transfer, Part A: Applications

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The present article concerns the investigation of the transient thermoelastic stresses in a rotating non-homogeneous micro-engineering anisotropic solid. The system of fundamental equations is solved by means of a boundary element method (BEM) and the numerical calculations are carried out for temperature, displacements and stresses. The results indicate that the effects of inhomogeneity and isotropy are very pronounced.

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Section: Displacement Fieldmentioning

confidence: 99%

“…Ho et al [8] proposed lattice Boltzmann scheme for hyperbolic heat conduction equation. Also, Lam and Yeung [9] proposed numerical scheme for non-fourier heat conduction.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic Stresses in a Rotating Non-Homogeneous Anisotropic Body

Fahmy

2008

Numerical Heat Transfer, Part A: Applications

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“…Moosaie has solved the non-Fourier heat conduction in finite mediums under arbitrary periodic surface disturbance [24] and also for the case of insulated boundaries and arbitrary initial conditions [25]. There exist also other proposed schemes for numerical simulation of hyperbolic conduction [26][27][28][29][30][31][32]. This literature survey demonstrates that all research work done for hyperbolic heat conduction in a finite medium during the past years concerns the periodic disturbances except for Moosaie's work [24].…”

Section: Introductionmentioning

confidence: 96%

Non-Fourier heat conduction in a finite medium subjected to arbitrary non-periodic surface disturbance

Moosaie

2008

International Communications in Heat and Mass Transfer

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The non-Fourier heat conduction equation is solved for a finite medium under arbitrarily chosen surface disturbances by utilizing the principle of superposition along with the Fourier integral representation of arbitrary non-periodic functions. The obtained solution is such that for a given non-periodic disturbance, we just have to introduce the Fourier integral coefficients of that function to the presented general solution and perform some definite integrations, analytically if possible, but in general numerically which is a straightforward computational task.

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“…However, the accurate solution for film material and two-dimensional medias are sometimes not easily obtained [19,20]. The finite difference method appears to be firstly used to analyze this problem by Yeung et al [21,22]. They introduced a simple and concise finite difference algorithm developed by applying the Godunov scheme on the characteristic equation.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Modelling of Non-Fourier Heat Behavior Using the Wavelet Finite Element Method

et al. 2019

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Non-Fourier heat behavior is an important issue for film material. The phenomenon is usually observed in some laser induced thermal responses. In this paper, the non-Fourier heat conduction problems with temperature and thermal flux relaxations are investigated based on the wavelet finite element method and solved by the central difference scheme for one- and two-dimensional media. The Cattaneo–Vernotte model and the Dual-Phase-Lagging model are used for finite element formulation, and a new wavelet finite element solving formulation is proposed to address the memory requirement problem. Compared with the current methodologies for the Cattaneo–Vernotte model and the Dual-Phase-Lagging model, the present model is a direct one which describe the thermal behavior by one equation about temperature. Compared with the wavelet method proposed by Xiang et al., the developed method can be used for arbitrary shapes. In order to address the efficient computation problems for the Dual-Phase-Lagging model, a novel iteration updating methodology is also proposed. The proposed iteration algorithms on time avoids the use the global stiffness matrix, which allows the efficient calculation for title issue. Numerical calculations have been conducted in the manner of comparisons with the classical finite element method and spectral finite element method. The comparisons from accuracy, efficiency, flexibility, and applicability validate the developed method to be an effective and alternative tool for material thermal analysis.

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A Numerical Scheme for Non-Fourier Heat Conduction, Part Ii: Two-Dimensional Problem Formulation and Verification

Cited by 19 publications

References 5 publications

Thermoelastic Stresses in a Rotating Non-Homogeneous Anisotropic Body

Thermoelastic Stresses in a Rotating Non-Homogeneous Anisotropic Body

Non-Fourier heat conduction in a finite medium subjected to arbitrary non-periodic surface disturbance

Analysis and Modelling of Non-Fourier Heat Behavior Using the Wavelet Finite Element Method

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