Abstract In this research, thermal analysis in cylinders with varying thickness constructed from functionally graded materials (FGMs) which are under non-uniform heat fluxes in their inner and outer layers is presented. The heterogeneous distribution of properties is a modelled power function along the thickness and the length of the cylinder. Using first-order temperature theory (FTT) and the energy method, the governing equations are extracted. The system of governing differential equations is a system of ordinary differential equations with variable coefficients that is performed by using the analytical method of matched asymptotic expansion of the perturbations technique for solving it. Results relating to temperature distribution, heat flux, and thermal strain for different heat fluxes and heterogeneous constants are discussed. The results show that the heterogeneity has a magnificent effect on the temperature field and thermal strain inside FG cylinders. Moreover, it is observed that the heterogeneity has no effect on the direction of heat flux vector inside the body but any changes in the heterogeneity would change the magnitude of heat flux. The results achieved from the analytical method are compared with those predicted by finite element method (FEM). A good agreement was found between the predicted results of both methods.

中文翻译：

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使用一阶温度理论和微扰技术对受非均匀热流影响的不同厚度 FGM 圆柱体热传导的解析解

摘要 在这项研究中，提出了由功能梯度材料 (FGM) 构成的不同厚度圆柱体的热分析，这些圆柱体的内外层热通量不均匀。属性的异质分布是沿圆柱体厚度和长度的建模幂函数。使用一阶温度理论（FTT）和能量方法，提取控制方程。控制微分方程组是利用微扰技术的匹配渐近展开解析法求解的变系数常微分方程组。讨论了与不同热通量和非均质常数的温度分布、热通量和热应变有关的结果。结果表明，不均匀性对 FG 圆柱体内的温度场和热应变有很大的影响。此外，观察到异质性对体内热通量矢量的方向没有影响，但异质性的任何变化都会改变热通量的大小。将分析方法获得的结果与有限元方法 (FEM) 预测的结果进行比较。在两种方法的预测结果之间发现了良好的一致性。将分析方法获得的结果与有限元方法 (FEM) 预测的结果进行比较。在两种方法的预测结果之间发现了良好的一致性。将分析方法获得的结果与有限元方法 (FEM) 预测的结果进行比较。在两种方法的预测结果之间发现了良好的一致性。