ISSN 打印: 1064-2285
ISSN 在线: 2162-6561

# 传热学

DOI: 10.1615/HeatTransRes.2018015988
pages 275-285

## VARIATIONAL EQUATION OF NON-FOURIER HEAT CONDUCTION

Xiaomin Zhang
Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, P.R.China
Song Peng
Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, P.R.China
Long Zhang
Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, P.R.China; Department of Theoretical and Applied Mechanics, Chongqing University of Science and Technology, Chongqing, 401331, P.R.China
Zimin Yan
Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, P.R.China
Yuan Liang
School of Foreign Language, Chongqing University of Science and Technology, Chongqing, 401331, P.R.China
Bo Yan
Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, P.R.China

### ABSTRACT

The variational equation containing the finite relaxation time was deduced by promoting Biot's variational equation for non-Fourier heat conduction in the finite relaxation model as well as for non-Fourier media in the Cattaneo−Vernotte (CV) model. In addition, the form in the generalized coordinates and the expression with the potential function corresponding to the variational equation were obtained. The employed variational equation and the heat-affected zone in the semi-infinite space under the influence of a step thermal pulse were investigated. A comparison of the relationships of heat distribution and time between the Fourier and non-Fourier models indicates that the propagation velocity is underestimated in the Fourier law under the condition of ultrashort duration. The relationships between the heat-affected zone and the relaxation time, relaxation zone, and duration were discussed as well as the expression of the bounded temperature gradient was obtained.

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