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題名 | 無限長鈦--鈾棒之熱傳特性分析=The Heat Conduction of an Infinite Long Bar with Elliptic Cross Section |
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作者姓名(中文) | 朱心平; | 書刊名 | 黃埔學報 |
卷期 | 64 2013.04[民102.04] |
頁次 | 頁251-263 |
分類號 | 440.12 |
關鍵詞 | 微分轉換法; 有限差分法; Differential transform method; Finite difference method; |
語文 | 中文(Chinese) |
中文摘要 | 本文針對一無限長具橢圓型截面之鈦-鈾雙層棒之熱傳特性做分析。由於此棒在長 度方向假設為無限長,因此本問題可視為一二維熱傳問題。又因為鈦及鈾之熱傳導係數 與比熱均為溫度的函數,因此本問題為一非線性問題。本文以微分轉換法與有限差分法 求解,微分轉換法為一以泰勒級數為基礎之數學方法,可用於求解動態問題。本文所使 用的有限差分項為二階中央差分法所求得,由於本研究所分析之長棒具橢圓形截面,因 此須以不等長格點法求解。本文求解邊界溫度由1000K下降至700K之溫度變化,顯示長 棒截面溫度隨時間變化之情形,並比較以非線性參數與線性化參數求解的結果。 |
英文摘要 | This paper discusses the heat conduction condition of an infinitive long bar with elliptic cross section. The inner layer of the bar is made by uranium and the outer layer is made by titanium. The problem can be solved by a second order partial differential equation. Since the specific heat and the conductivity of uranium and titanium vary with different temperature, the problem is nonlinear. This paper use differential transform method and finite difference method to solve the equation. Since the cross section is elliptic, the unequal grid steps method is applied in the finite difference method. The temperature of the bar is originally at 1000K, then the boundary temperature drops to 700K gradually and keep at 700K. The temperature of a cross section at different times are shown and discussed. The results of linear and nonlinear equations are shown and discussed. |
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