Singularly Perturbed Solutions of NonFourier Temperature Field Distribution in Single-Layer Materials

BAO Liping; LI Wenyan; WU Liqun

doi:10.21656/1000-0887.390112

Volume 40 Issue 5

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BAO Liping, LI Wenyan, WU Liqun. Singularly Perturbed Solutions of NonFourier Temperature Field Distribution in Single-Layer Materials[J]. Applied Mathematics and Mechanics, 2019, 40(5): 536-545. doi: 10.21656/1000-0887.390112

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Singularly Perturbed Solutions of NonFourier Temperature Field Distribution in Single-Layer Materials

doi: 10.21656/1000-0887.390112

¹School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P.R.China;²School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, P.R.China

Funds: The National Natural Science Foundation of China（51175134）

Received Date: 2018-04-11
Rev Recd Date: 2018-11-12
Publish Date: 2019-05-01

Abstract

Abstract

A temperature field model for single-layer materials was constructed with the non-Fourier heat conduction law, i.e. a type of singularly perturbed hyperbolic equations with small parameters in an unbounded domain. The asymptotic solution to the problem was obtained with the singularly perturbed expansion method. Firstly, the singular perturbation method was used to obtain the external solution and boundary layer correction terms of the problem. Through estimation of the maximum norms of the internal solution and the external solution, and the maximum norms of the time derivative, and under the theory of linear parabolic equations, the existence and uniqueness of the internal and external solutions were obtained, and the formal asymptotic expansion of the solution was obtained. The L² estimator of the asymptotic solution was given with the remainder estimator. The uniform validity of the asymptotic solution and the distribution of the temperature field in the unbounded domain were got. Through singular perturbation analysis, the relationship between the non-Fourier temperature field and the Fourier temperature field was given, and the specific behaviors of the non-Fourier temperature field were described.
- singular perturbation,
- heat conduction equation,
- unbounded domain,
- uniformly valid estimate

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References

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