Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions
Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions
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DOI：
10.1115/1.4030348
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发表时间：
2015-10-01
影响因子：
--
通讯作者：
Norouzi, M.
中科院分区：
文献类型：
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作者：
Delouei, A. Amiri;Norouzi, M.
本文给出了多层球形纤维增强复合材料层合板非稳态导热问题的精确解析解。介绍了球坐标系下正交各向异性热传导方程。考虑了球形层合板内外的导热、对流和辐射换热的最广义线性边界条件。每层中纤维的角度和复合材料可以改变。采用拉普拉斯变换将解的域从时域变换到频域。在频域中，采用分离变量法，求解与傅里叶-勒让德级数系数有关的方程组。利用亚纯函数技术确定复拉普拉斯逆变换。通过两个算例，考察了该方法求解不同布置方式的多层球面层板工业非定常问题的能力。
The current study presents an exact analytical solution for unsteady conductive heat transfer in multilayer spherical fiber-reinforced composite laminates. The orthotropic heat conduction equation in spherical coordinate is introduced. The most generalized linear boundary conditions consisting of the conduction, convection, and radiation heat transfer is considered both inside and outside of spherical laminate. The fibers' angle and composite material in each lamina can be changed. Laplace transformation is employed to change the domain of the solutions from time into the frequency. In the frequency domain, the separation of variable method is used and the set of equations related to the coefficients of Fourier-Legendre series is solved. Meromorphic function technique is utilized to determine the complex inverse Laplace transformation. Two functional cases are presented to investigate the capability of current solution for solving the industrial unsteady problems in different arrangements of multilayer spherical laminates.