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The second-order two-scale computation for integrated heat transfer problem with conduction, convection and radiation in periodic porous materials
1. | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710129, China |
2. | LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China, China |
References:
[1] |
S. T. Liu and Y. C. Zhang, Multi-scale analysis method for thermal conductivity of composite material with radiation, Multidiscipline Modeling in Mat. and Str., 2 (2006), 327-344. |
[2] |
G. Allaire and K. El Ganaoui, Homogenization of a conductive and radiative heat transfer problem, Multiscale Model.Sim., 7 (2008), 1148-1170.
doi: 10.1137/080714737. |
[3] |
N. S. Bakhvalov, Averaging of the heat transfer process in periodic media with radiative, Differ. Uraun., 17 (1981), 1765-1773. |
[4] |
T. Tiihonen, Stefan-Boltzmann radiation on non-convex surfaces, Math. Method. Appl. Sci., 20 (1997), 47-57.
doi: 10.1002/(SICI)1099-1476(19970110)20:1<47::AID-MMA847>3.0.CO;2-B. |
[5] |
N. Qatanani, Analysis of the heat equation with non-local radiation terms in a non-convex diffuse and grey surfaces, Eur. J. Sci. Res., 15 (2006), 245-254. |
[6] |
K. Daryabeigi, Analysis and testing of high temperature fibrous insulation for reusable launch vehicles, 37th AIAA Aerospace Sciences Meeting and Exhibit, January 11-14, (1999), Reno, NV.
doi: 10.2514/6.1999-1044. |
[7] |
L. J. Gibson and M. F. Ashby, Cellular Solids:Structure and Properties, second edition, Cambridge University Press, 1997. |
[8] |
K. El Ganaoui, Homogénéisation de Modéles de Transferts Thermiques et Radiatifs: Application au Coeur des Réacteurs A Caloporteur Gaz, Ph.D thesis, Ecole Polytechnique, 2006. |
[9] |
K. Terada, M. Kurumatani, T. Ushida and N. Kikuchi, A method of two-scale thermo-mechanical analysis for porous solids with micro-scale heat transfer, Comp. Mech., 46 (2010), 269-285.
doi: 10.1007/s00466-009-0400-9. |
[10] |
F. Su, J. Z. Cui and Z. Xu, A two-order and two-scale computation method for nonselfadjoint elliptic problems with rapidly oscillatory coefficients, Appl. Math. Mech-Engl., 30 (2009), 1579-1588.
doi: 10.1007/s10483-009-1209-z. |
[11] |
A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structure, North-Holland, Amsterdam, 1978. |
[12] |
O. A. Oleinik, A. S. Shamaev and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992. |
[13] |
L. Q. Cao, J. Z. Cui and D. C. Zhu, Multiscale asymptotic analysis and numerical simulation for the second order Helmholtz equation with oscillating coefficients over general convex domains, SIAM J.Numer.Anal., 40 (2002), 543-577.
doi: 10.1137/S0036142900376110. |
[14] |
Z. Q. Yang, J. Z. Cui, Y. F. Nie and Q. Ma, The second-order two-scale method for heat transfer performances of periodic porous materials with interior surface radiation, CMES: Comp. Model. Eng., 88 (2012), 419-442. |
[15] |
J. Z. Cui, T. M. Shin and Y. L. Wang, Two-scale analysis method for bodies with small periodic configurations, Struct. Eng. Mech., 7 (1999), 601-614.
doi: 10.12989/sem.1999.7.6.601. |
[16] |
A. A. Amosov, Semidiscrete and asymptotic approximations for the nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields, J. Math. Sci., 176 (2011), 361-408.
doi: 10.1007/s10958-011-0399-2. |
[17] |
A. A. Amosov, Nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields, J. Math. Sci., 169 (2010), 1-45.
doi: 10.1007/s10958-010-0037-4. |
[18] |
J. L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications II, Springer-Verlag, Berlin, 1972. |
[19] |
G. Allaire and Z. Habibi, Homogenization of a conductive, convective and radiative heat transfer problem in a heterogeneous domain, SIAM J. Math. Anal., 45 (2013), 1136-1178.
doi: 10.1137/110849821. |
[20] |
L. Q. Cao and J. Z. Cui, The two-scale asymptotic analysis for elastic structures of composites materials with only including entirely basic configuration, Acta Math. Appl. Sin., 22 (1999), 38-46 (in Chinese). |
[21] |
W. Allegretta, L. Q. Cao and Y. P. Lin, Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients, Discret Contin. Dyn. S., 20 (2008), 543-576. |
[22] |
L. Q. Cao, Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains, Numer. Math., 103 (2006), 11-45.
doi: 10.1007/s00211-005-0668-4. |
show all references
References:
[1] |
S. T. Liu and Y. C. Zhang, Multi-scale analysis method for thermal conductivity of composite material with radiation, Multidiscipline Modeling in Mat. and Str., 2 (2006), 327-344. |
[2] |
G. Allaire and K. El Ganaoui, Homogenization of a conductive and radiative heat transfer problem, Multiscale Model.Sim., 7 (2008), 1148-1170.
doi: 10.1137/080714737. |
[3] |
N. S. Bakhvalov, Averaging of the heat transfer process in periodic media with radiative, Differ. Uraun., 17 (1981), 1765-1773. |
[4] |
T. Tiihonen, Stefan-Boltzmann radiation on non-convex surfaces, Math. Method. Appl. Sci., 20 (1997), 47-57.
doi: 10.1002/(SICI)1099-1476(19970110)20:1<47::AID-MMA847>3.0.CO;2-B. |
[5] |
N. Qatanani, Analysis of the heat equation with non-local radiation terms in a non-convex diffuse and grey surfaces, Eur. J. Sci. Res., 15 (2006), 245-254. |
[6] |
K. Daryabeigi, Analysis and testing of high temperature fibrous insulation for reusable launch vehicles, 37th AIAA Aerospace Sciences Meeting and Exhibit, January 11-14, (1999), Reno, NV.
doi: 10.2514/6.1999-1044. |
[7] |
L. J. Gibson and M. F. Ashby, Cellular Solids:Structure and Properties, second edition, Cambridge University Press, 1997. |
[8] |
K. El Ganaoui, Homogénéisation de Modéles de Transferts Thermiques et Radiatifs: Application au Coeur des Réacteurs A Caloporteur Gaz, Ph.D thesis, Ecole Polytechnique, 2006. |
[9] |
K. Terada, M. Kurumatani, T. Ushida and N. Kikuchi, A method of two-scale thermo-mechanical analysis for porous solids with micro-scale heat transfer, Comp. Mech., 46 (2010), 269-285.
doi: 10.1007/s00466-009-0400-9. |
[10] |
F. Su, J. Z. Cui and Z. Xu, A two-order and two-scale computation method for nonselfadjoint elliptic problems with rapidly oscillatory coefficients, Appl. Math. Mech-Engl., 30 (2009), 1579-1588.
doi: 10.1007/s10483-009-1209-z. |
[11] |
A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structure, North-Holland, Amsterdam, 1978. |
[12] |
O. A. Oleinik, A. S. Shamaev and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992. |
[13] |
L. Q. Cao, J. Z. Cui and D. C. Zhu, Multiscale asymptotic analysis and numerical simulation for the second order Helmholtz equation with oscillating coefficients over general convex domains, SIAM J.Numer.Anal., 40 (2002), 543-577.
doi: 10.1137/S0036142900376110. |
[14] |
Z. Q. Yang, J. Z. Cui, Y. F. Nie and Q. Ma, The second-order two-scale method for heat transfer performances of periodic porous materials with interior surface radiation, CMES: Comp. Model. Eng., 88 (2012), 419-442. |
[15] |
J. Z. Cui, T. M. Shin and Y. L. Wang, Two-scale analysis method for bodies with small periodic configurations, Struct. Eng. Mech., 7 (1999), 601-614.
doi: 10.12989/sem.1999.7.6.601. |
[16] |
A. A. Amosov, Semidiscrete and asymptotic approximations for the nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields, J. Math. Sci., 176 (2011), 361-408.
doi: 10.1007/s10958-011-0399-2. |
[17] |
A. A. Amosov, Nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields, J. Math. Sci., 169 (2010), 1-45.
doi: 10.1007/s10958-010-0037-4. |
[18] |
J. L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications II, Springer-Verlag, Berlin, 1972. |
[19] |
G. Allaire and Z. Habibi, Homogenization of a conductive, convective and radiative heat transfer problem in a heterogeneous domain, SIAM J. Math. Anal., 45 (2013), 1136-1178.
doi: 10.1137/110849821. |
[20] |
L. Q. Cao and J. Z. Cui, The two-scale asymptotic analysis for elastic structures of composites materials with only including entirely basic configuration, Acta Math. Appl. Sin., 22 (1999), 38-46 (in Chinese). |
[21] |
W. Allegretta, L. Q. Cao and Y. P. Lin, Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients, Discret Contin. Dyn. S., 20 (2008), 543-576. |
[22] |
L. Q. Cao, Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains, Numer. Math., 103 (2006), 11-45.
doi: 10.1007/s00211-005-0668-4. |
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