Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change

Zhao, Wei; Wu, Jiu Hui; Chen, Zhe

doi:10.1007/s00419-013-0814-x

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…Hence, the second term of H a ðn; gÞ and the function b a mi varnish, and the key equations (20) and (37) become the same as in literature [38]. In addition, if the thermal load is assumed to be steady, which means the function M a ðsÞ becomes the constant m a .…”

Section: The Elasticity Fieldmentioning

confidence: 93%

“…(20) can be obtained by an appropriate collocation in n. Once U a ðnÞ is determined, the functions A a ðsÞ and B a ðsÞ can be evaluated to result in the temperature field in Laplace transform domain.…”

Section: The Temperature Fieldmentioning

confidence: 99%

“…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. In addition, Babaei and Chen [21] studied the hyperbolic temperature fields of a functionally graded hollow sphere and cylinder.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Elasticity Fieldmentioning

confidence: 93%

Section: The Temperature Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…A possible extension in future works would be the consideration of moving heat sources, which is essential in many engineering applications [22,23]. When a pulsed electrical source or laser is used to induce thermal shock, the non-Fourier heat equation [24,25], which include additional term containing the relaxation time, should be considered.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

An enhanced nodal gradient finite element for non-linear heat transfer analysis

2019

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The present work is devoted to the analysis of non-linear heat transfer problems using the recent development of consective-interpolation procedure. Approximation of temperature is enhanced by taking into account both the nodal values and their averaged nodal gradients, which results in an improved finite element model. The novel formulation possesses many desirable properties including higher accuracy and higher-order continuity, without any change of the total number of degrees of freedom. The non-linear heat transfer problems equation is linearized and iteratively solved by the Newton-Raphson scheme. To show the accuracy and efficiency of the proposed method, several numerical examples are hence considered and analyzed.

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“…The non-Fourier heat conduction in a finite slab with insulated boundaries was numerically investigated by Rahbari et al [13]. An analytical non-Fourier study was conducted by Zhao et al [14] on a solid sphere under arbitrary surface thermal disturbances. The non-Fourier heat conduction and thermal radiation problem in a concentric spherical shell was studied by Mishra and Sahai [15].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

Noroozi¹,

Saedodin²,

Ganji³

2016

Archive of Mechanical Engineering

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The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

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Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change

Cited by 8 publications

References 22 publications

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

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

An enhanced nodal gradient finite element for non-linear heat transfer analysis

Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

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