摘要
基于微分思想提出了一种针对层合材料传热问题的新解法.将层合材料交界处的温度随时间变化的曲线在微小时间段内近似为直线,用分离变量法求得了在微小时间段内各层包含未知系数的解析解,根据交界处能量连续的条件求得各层解析解中的未知系数,然后循环求得整个时间域内的温度场.最后利用此方法求解了某三层结构的传热问题,将计算结果与有限元法求得的结果进行了比较,讨论了几个参数对温度场的影响,从而进一步验证了方法的正确性.
A new analytical method for solving heat transfer problems of laminate materials was proposed based on the differential theory. The curves of temperature variation at the interface of the laminate material were approximately linear in a small time interval. With the method of separation of variables,the analytical solution containing unknown coefficients of each layer in a small time interval was obtained. According to the continuous condition of energy at the interface,the unknown coefficients of each layer were determined. Then the temperature field in the whole time domain was obtained. Finally,the analytical method was used to solve the heat transfer problem of a 3-layer structure. The analytical results were compared with those of the finite element method,and the influences of several parameters on the temperature field were discussed,with the correctness of the proposed method verified.
作者
李细霞
戴海燕
李长玉
LI Xixia;DAI Haiyan;LI Changyu(Guangzhou College of South China University of Technology, Guangzhou 510800, P.R. China)
出处
《应用数学和力学》
CSCD
北大核心
2018年第6期728-736,共9页
Applied Mathematics and Mechanics
基金
广东省青年创新类人才项目基金(2016KQNCX226)
关键词
层合材料
热传导
分离变量
微分思想
laminate material
heat conduction
separation of variables
differential theory
