Thermal relaxation responses of graded materials satisfing power law

XIE Yushan; XU Songlin; YUAN Liangzhu; CHEN Meiduo; WANG Pengfei

doi:10.11883/bzycj-2023-0437

Volume 44 Issue 8

Aug. 2024

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XIE Yushan, XU Songlin, YUAN Liangzhu, CHEN Meiduo, WANG Pengfei. Thermal relaxation responses of graded materials satisfing power law[J]. Explosion And Shock Waves, 2024, 44(8): 081421. doi: 10.11883/bzycj-2023-0437

Citation:

XIE Yushan, XU Songlin, YUAN Liangzhu, CHEN Meiduo, WANG Pengfei. Thermal relaxation responses of graded materials satisfing power law[J]. Explosion And Shock Waves, 2024, 44(8): 081421. doi: 10.11883/bzycj-2023-0437

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Thermal relaxation responses of graded materials satisfing power law

doi: 10.11883/bzycj-2023-0437

CAS Key Laboratory for Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, Anhui, China

Received Date: 2023-12-22
Rev Recd Date: 2024-03-03

Available Online: 2024-03-14

Publish Date: 2024-08-05

Abstract

Abstract

To study the thermal relaxation behavior of graded media that satisfies the power law, a one-dimensional hyperbolic non-Fourier heat conduction equation of the graded material which satisfies the power law was derived from the Cattaneo-Vernotte linear hyperbolic heat transfer equation with the thermal relaxation coefficient and graded exponent induced. The equation was first treated dimensionless. Based on the Laplace transformation, the new heat conduction equation was found to conform to the general form of the Bessel equation called the Lommel equation in the frequency domain, and the Bessel series solution of the temperature field in the frequency domain was obtained. With the asymptotic expansion of the Bessel series, a simplified expression of the temperature field in the frequency domain containing trigonometric function was obtained. The inverse Laplace transformation of the temperature field in the frequency domain was employed to get the first analytical solution of the temperature field in the time domain. Besides the first analytical solution, the new heat conduction equation in the frequency domain was simplified to the Euler equation, and the second kind of analytical solution was obtained by the pole residue method. The second analytical solution exhibits similar fluctuation attenuation and diffusion features, and both the waveform and response time are sensitive to the relaxation time coefficient. However, the second kind of analytical solution differs from the first kind of solution in terms of waveform elements which are highly related to the graded structure. The accuracy of the analytical result is verified by numerical calculation. Taking Mo-ZrC graded composite as an example, the thermal relaxation behavior of graded material that satisfies power law under the first kind of temperature boundary and temperature pulse loading are discussed in detail. The temperature field shows both fluctuation attenuation and conduction characteristics. With the increase of the thermal relaxation coefficient, the response time and temperature wave amplitude increase, the unit waveform develops from a trapezoidal wave to a rectangular wave, and the oscillation approaching the boundary shows an obvious bias.
- response of thermal relaxation,
- Mo-ZrC graded material,
- Bessel series,
- Laplace transform

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References(23)

References

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