Second-order two-scale computations for conductive–radiative heat transfer problem in periodic porous materials

doi:10.1088/1674-1056/23/3/030203

Abstract In this paper, a kind of second-order two-scale (SOTS) computation is developed for conductive–radiative heat transfer problem in periodic porous materials. First of all, by the asymptotic expansion of the temperature field, the cell problem, homogenization problem, and second-order correctors are obtained successively. Then, the corresponding finite element algorithms are proposed. Finally, some numerical results are presented and compared with theoretical results. The numerical results of the proposed algorithm conform with those of the FE algorithm well, demonstrating the accuracy of the present method and its potential applications in thermal engineering of porous materials.

Keywords: second-order two-scale (SOTS) computations periodic porous materials conductive–radiative heat transfer

Received: 16 May 2013
Revised: 07 August 2013
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	44.40.+a	(Thermal radiation)
	02.60.-x	(Numerical approximation and analysis)
	02.60.Cb	(Numerical simulation; solution of equations)

Fund: Project supported by the National Basic Research Program of China (Grant No. 2010CB832702) and the National Natural Science Foundation of China (Grant No. 90916027).

Corresponding Authors: Yang Zhi-Qiang
E-mail: yangzhiqiang@mail.nwpu.edu.cn

Cite this article:

Yang Zhi-Qiang (杨志强), Cui Jun-Zhi (崔俊芝), Li Bo-Wen (李博文) Second-order two-scale computations for conductive–radiative heat transfer problem in periodic porous materials 2014 Chin. Phys. B 23 030203

[1]	Liu S T and Zhang Y C 2006 Multidiscipline Modeling in Mat. and Str. 2 327
[2]	Tiihonen T 1997 Math. Method. Appl. Sci. 20 47
[3]	Bakhvalov N S 1981 Differ. Uraun. 17 1765
[4]	Daryabeigi K 1999 37th AIAA Aerospace Sciences Meeting and Exhibit, January 11–14, 1999, Reno, NV
[5]	Gibson L J and Ashby M F 1997 Cellular Solids: Structure and Properties (2nd Edn.) (Cambridge: Cambridge University Press)
[6]	EI Ganaoui K 2006 Homogénéisation de modèles de transferts thermiques et radiatifs: Application au coeur des réacteurs À caloporteur gaz (PhD Thesis) (Ecole Polytechnique)
[7]	Terada K, Kurumatani M, Ushida T and Kikuchi N 2010 Comp. Mech. 46 269
[8]	Mezedur M, Kaviany M and Moore W 2004 AIChE J. 48 15
[9]	Jen T C and Yan T Z 2005 Int. J. Heat Mass Tran. 48 3995
[10]	Xu R N and Jiang P X 2008 Int. J. Heat Fluid FL. 29 1447
[11]	Allaire G and EI Ganaoui K 2009 Multiscale Model. Sim. 7 1148
[12]	Allaire G and Habibi Z 2013 SIAM J. Math. Anal. 45 1136
[13]	Yang Z Q, Cui J Z, Nie Y F and Ma Q 2012 CMES: Comp. Model. Eng. 88 419
[14]	Bensoussan A, Lions J L and Papanicolaou G 1978 Asymptotic Analysis for Periodic Structure (Amsterdam: North-Holland)
[15]	Oleinik O A, Shamaev A S and Yosifian G A 1992 Mathematical Problems in Elasticity and Homogenization (Amsterdam: North-Holland)
[16]	Cui J Z and Yu X G 2006 Acta Mech. Sin. 22 581
[17]	Feng Y P, Cui J Z and Deng M X 2009 Acta Phys. Sin. 58 S327 (in Chinese)
[18]	Han F, Cui J Z and Yu Y 2009 Acta Phys. Sin. 58 S1 (in Chinese)
[19]	He W M, Qiao H and Chen W Q 2013 Compos. Part B-Eng. 45 742
[20]	He W M, Qiao H and Chen W Q 2013 Eur J Mech ASolid 40 123
[21]	Luo J L and Cao L Q 2004 J. Engrg. Thermophys. 29 1711 (in Chinese)
[22]	ShaoY F, Yang X, Zhao X and Wang S Q 2012 Chin. Phys. B 21 083101
[23]	Yu X X and Wang C Y 2013 Chin. Phys. B 21 027101
[24]	Amosov A A 2011 J. Math. Sci. 176 361

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Second-order two-scale computations for conductive–radiative heat transfer problem in periodic porous materials

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