Theoretical solution of transient heat conduction problem in one-dimensional double-layer composite medium  

作　　者：周龙 白敏丽 吕继组 崔文政 

机构地区：[1]School of Energy and Power Engineering,Dalian University of Technology [2]School of Mechanical and Power Engineering,He nan Polytechnic University

出　　处：《Journal of Central South University》2010年第6期1403-1408,共6页中南大学学报（英文版）

基　　金：Projects(50576007,50876016) supported by the National Natural Science Foundation of China;Projects(20062180) supported by the National Natural Science Foundation of Liaoning Province,China

摘　　要：To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ（τ is nondimensional time） equals 0.1 near the boundaries of ζ =1 （ζ is nondimensional space coordinate） and ζ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate 4.To make heat conduction equation embody the essence of physical phenomenon under study,dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms.Then,a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method.In order to verify the validity of the model,the results of the above theoretical solution were compared with those of finite element method.The results by the two methods are in a good agreement.The maximum errors by the two methods appear when τ(τ is nondimensional time) equals 0.1 near the boundaries of ξ =1(ξ is nondimensional space coordinate) and ξ =4.As τ increases,the error decreases gradually,and when τ =5 the results of both solutions have almost no change with the variation of coordinate ξ.

关 键 词：composite medium transient heat conduction theoretical solution natural eigenfunction expansion method 

分 类 号：O551.3[理学—热学与物质分子运动论]