具指数衰减函数边界的一维热传导问题的解及其应用  

The solution to one-dimensional heat conduction problem bounded by the exponential decay condition and its application

作　　者：韦婷[1] 陶月赞[1] 任红蕾 吴丹 WEI Ting;TAO Yuezan;REN Honglei;WU Dan(College of Civil Engineering,Hefei University of Technology,230009 Hefei,China;Department of Architectural Engineering,Hefei University,230601 Hefei,China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009 [2]合肥学院城市建设与交通学院,合肥230601

出　　处：《应用力学学报》2022年第6期1135-1139,1202,共6页Chinese Journal of Applied Mechanics

基　　金：清华大学水沙科学与水利水电工程国家重点实验室2020年度开放基金资助项目(No.sklhse-2020-D-06)。

摘　　要：边界条件为指数衰减函数的一维热传导问题,Laplace正变换后泛定方程的通解与边界条件象函数的乘积组合求逆困难,问题难以求解。应用Laplace变换性质,将边界条件用算符运行于变换过程中,建立一维热传导问题通用的理论解;再将特定问题的边界条件代入通用理论解,获得相应的解。根据边界条件为指数衰减函数时的解,讨论其与经典问题解的转换关系,并结合实例,利用测点温度变化曲线的拐点求算模型参数。文中提出的求解方法,边界条件不参与繁杂的变换过程,解法便捷。For the one-dimensional heat conduction problem bounded by the exponential decay condition,it is hard to find the inversion of the product of the general solution of the universal equation and the image function of the boundary condition after Laplace transform,thus increasing the difficulty in solving the problem.The general theoretical solution of one-dimensional heat conduction problem is established by using properties of Laplace transform and operating the boundary condition during the transformation process with operators.For specific problems,the boundary conditions are substituted into the general theoretical solution to obtain the corresponding solutions.According to the solution when the boundary condition is exponential decay function,the transformation relationship between the solution and that of classical problem is discussed,and the corresponding parameter for the model is calculated by using the inflection point of the temperature measurement variation curve.The proposed solving method is convenient because the boundary conditions do not participate in the complicated transformation process.

关 键 词：指数衰减 LAPLACE变换 通用理论解 卷积 拐点法 

分 类 号：O175.2[理学—数学] O302[理学—基础数学]