圆柱体状材料上非Fourier热传导奇异摄动解  

Singular perturbation solution for non-Fourier heat conduction on cylindrical material

作　　者：陈序 包立平[1] 吴立群[2] 蒋亚楠 CHEN Xu;BAO Liping;WU Liqun;JIANG Yanan(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China;School of Mechanical Engineering,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018 [2]杭州电子科技大学机械工程学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第2期90-95,共6页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(51775154)。

摘　　要：运用非Fourier热传导定律在圆柱体状材料上建立温度场模型,该模型在数学上表达为三维奇异摄动双曲方程的初边值问题。首先,通过柱坐标变换,使用奇异摄动方法得到内外解方程;其次,使用分离变量法求解内外解,得到形式渐近解;最后,运用余项估计,得到解的一致有效性。In this paper,the non-Fourier heat conduction law is used to establish a temperature field model on a cylindrical material,that is,the model is an initial-boundary value problem of a three-dimensional singularly perturbed hyperbolic equation.Firstly,carry out the cylindrical coordinate transformation,and use the singular perturbation method to obtain the internal and external solution equations.Secondly,use the method of separating variables to solve the internal and external solutions,and the formal progressive solution is obtained.Finally,use the remainder estimation,the uniform validity of the solution is obtained.

关 键 词：分离变量法 热传导方程 奇异摄动 温度场 有界域 

分 类 号：O175.2[理学—数学]