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首页> 外文期刊>Archives of Mechanics >Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions
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Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions

机译：FGM圆柱壳中轴对称稳态温度场，其温度依赖于热导率和任意线性边界条件

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摘要

AN APPROXIMATE ANALYTICAL SOLUTION to the axisymmetric heat conduction equation for a hollow cylinder made of functionally graded material with temperature-dependent heat conductivity is presented. General linear boundary conditions are considered. The Poincare method for regular perturbation problems is employed to obtain an analytical closed-form approximate solution for the temperature field. The hierarchical asymptotic problems are solved up to the second-order approximation. A numerical example is worked out, i.e., the one-dimensional heat conduction in the radial direction with prescribed temperatures at the boundaries. The approximate temperature profiles are compared with a numerical solution of the full nonlinear problem which provides the reference "exact" solution. A good agreement between the approximate and reference solutions is established. The convergence of the asymptotic series as well as the properties of the temperature field are studied.
机译：提出了一种由功能梯度材料制成的空心圆柱体的轴对称导热方程的近似解析解，其温度依赖于导热率。考虑一般的线性边界条件。针对常规摄动问题的庞加莱方法用于获得温度场的解析闭合形式近似解。逐步解决分层渐近问题，直至达到二阶逼近。算出一个数值例子，即在边界上具有规定温度的情况下，沿径向的一维热传导。将近似温度曲线与完全非线性问题的数值解进行比较，该解可以提供参考“精确”解。在近似解和参考解之间建立了良好的协议。研究了渐近级数的收敛性以及温度场的性质。

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