Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution

被引:1
|
作者
Andrianov, Igor, V [1 ]
Awrejcewicz, Jan [2 ]
Starushenko, Galina A. [3 ]
Kvitka, Sergiy A. [3 ]
机构
[1] Rhein Westfal TH Aachen, Chair & Inst Gen Mech, Aachen, Germany
[2] Lodz Univ Technol, Dept Automat Biomech & Mechatron, 15 Stefanowskiego Str, PL-90924 Lodz, Poland
[3] Natl Acad State Management President Ukraine, Dnipropetrovsk Reg Inst State Management, Dnipro, Ukraine
来源
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2022年 / 102卷 / 11期
关键词
EFFECTIVE THERMAL-CONDUCTIVITY; TRANSPORT-PROPERTIES; ASYMPTOTIC MODELS; HOMOGENIZATION;
D O I
10.1002/zamm.202200216
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Paper is devoted to the effective stationary heat conductivity for the fibre composite materials. We are aimed on getting on analytical expression for effective thermal conductivity coefficient. Asymptotic homogenization approach, based on the multiple scale perturbation method, is used. This allows to reduce the original boundary value problem in multiply connected domain to the sequence of boundary value problems in simply connected domains. These problems include: the local problem for the periodically repeated cell and homogenized problem with effective coefficient. It is shown that for densely packed and high contrast fibre composites, the cell problem can be solved analytically. For this aim, lubrication approach (asymptotics of thin layer) has been employed. We also generalise obtained solution to the case of medium-sized inclusions in the framework of the Pade approximants.
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页数:13
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