一种求解复合圆筒壁非稳态导热问题的新方法

A new approximate solution for multiple-layer cylindrical walls of unsteady-state heat conduction

为了求解复合材料内的温度分布,根据导热基本规律,建立了复合圆筒壁导热问题的数学模型。采用Laplace变换和Stehfest数值反演技术对拉氏变换进行多次迭代反演,求得温度分布的近似解。设计了复合圆筒壁温度测试实验装置。复合圆筒壁的非稳态测温装置的测试结果与利用高温四参数测试仪对注汽井的现场测试结果吻合良好,说明该解法的计算结果精度高,适用于不同的初边值条件或含内热源的导热问题,可应用于具体工程问题的分析计算。

The mathematical model was established for multiple-layer cylindrical walls in order to determine the temperature profile according to the fundamental law of heat conduction. The iteration of the Laplace transformation and the Stehfest numerical inversion method were used for Laplace transformation. The temperature profile was obtained. The multiple-layer cylinder apparatus was designed. The measurement results in laboratory and oil field show that the method has high precision. The solution method is also used under different initial and boundary conditions with different heat source systems.