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# Statistical Multiscale Analysis of Transient Conduction and Radiation Heat Transfer Problem in Random Inhomogeneous Porous Materials

Yiqiang Li1, Liang Ma2, Zhiqiang Yang3, Xiaofei Guan4, Yufeng Nie1, Zihao Yang1, 2

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China.
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China.
School of Astronautics, Harbin Institute of Technology, Harbin 150001, China.
School of Mathematics Sciences, Tongji University, Shanghai 200092, China.

* Corresponding author: Zihao Yang. Email: .

Computer Modeling in Engineering & Sciences 2018, 115(1), 1-24. https://doi.org/10.3970/cmes.2018.115.001

## Abstract

This paper is devoted to the homogenization and statistical multiscale analysis of a transient heat conduction problem in random porous materials with a nonlinear radiation boundary condition. A novel statistical multiscale analysis method based on the two-scale asymptotic expansion is proposed. In the statistical multiscale formulations, a unified linear homogenization procedure is established and the second-order correctors are introduced for modeling the nonlinear radiative heat transfer in random perforations, which are our main contributions. Besides, a numerical algorithm based on the statistical multiscale method is given in details. Numerical results prove the accuracy and efficiency of our method for multiscale simulation of transient nonlinear conduction and radiation heat transfer problem in random porous materials.

## Keywords

APA Style
Li, Y., Ma, L., Yang, Z., Guan, X., Nie, Y. et al. (2018). Statistical multiscale analysis of transient conduction and radiation heat transfer problem in random inhomogeneous porous materials. Computer Modeling in Engineering & Sciences, 115(1), 1-24. https://doi.org/10.3970/cmes.2018.115.001
Vancouver Style
Li Y, Ma L, Yang Z, Guan X, Nie Y, Yang Z. Statistical multiscale analysis of transient conduction and radiation heat transfer problem in random inhomogeneous porous materials. Comput Model Eng Sci. 2018;115(1):1-24 https://doi.org/10.3970/cmes.2018.115.001
IEEE Style
Y. Li, L. Ma, Z. Yang, X. Guan, Y. Nie, and Z. Yang "Statistical Multiscale Analysis of Transient Conduction and Radiation Heat Transfer Problem in Random Inhomogeneous Porous Materials," Comput. Model. Eng. Sci., vol. 115, no. 1, pp. 1-24. 2018. https://doi.org/10.3970/cmes.2018.115.001

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