Exact Solutions for Heat Conduction in Non-uniform Mediums with General Time-dependent Boundary Conditions

具時間邊界條件之非均勻介質熱傳導問題的解析解

李森墉(Sen-Yung Lee) ； 黃聰文(Tsung-Wen Huang)

《中國機械工程學刊》 34卷6期 (2013/12) Pp. 475-485

摘要

發展一種新的解析解，無需積分變換，求解具時間邊界條件之非均勻介質中暫態熱傳導問題的解析解。經由合適的轉換凾數，具變量係數及時間邊界條件之二階差分方程式可轉換成具有均質邊界條件之差分方程式。若介質的物理性質以多項式形式呈現，則可以得到該系統的解析解。最後，以案例來說明分析方法。特殊情況案例與現有的文獻研究做比較。物性參數對該系統溫度分佈的影響將顯現出來。

並列摘要

A new analytic solution method is developed, without integral transform, to find the exact solutions for the transient heat conduction in non-uniform mediums with general time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. If the physic properties of the medium are in polynomial forms, the exact solution of the system can be developed. Finally, examples are given to illustrate the analysis. Limiting cases are studied and compared with those in the existing literature. The influence of physic parameters on the temperature distribution of the system is revealed.

並列關鍵字

heat conduction ； non-uniform medium ； time-dependent boundary conditions ； analytical solution