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題名 | 具橢圓形截面之無限長棒之熱傳特性分析=The Heat Conduction of an Infinite Long Bar with Elliptic |
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作者姓名(中文) | 朱心平; | 書刊名 | 黃埔學報 |
卷期 | 61 2011.10[民100.10] |
頁次 | 頁193-204 |
分類號 | 440.12 |
關鍵詞 | 橢圓型鈾棒; 微分轉換法; 不等長格點法; Uranium; Differential transform method; Finite difference meth; |
語文 | 中文(Chinese) |
中文摘要 | 本文針對一無限長具橢圓型截面之鈾棒之熱傳特性做分析。由於鈾棒在長度方向假 設為無限長,因此本問題可視為一二維熱傳問題。又因為鈾棒之熱傳導系數與比熱均為 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,由於鈾棒具橢圓形截面,因此須以不等長格點法求解。 本文求解邊界溫度由200K下降至160K之溫度變化,顯示鈾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 uranium bar with elliptic cross section. The problem can be solved by a second order partial differential equation. Since the specific heat and the conductivity of uranium 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 uranium bar is originally at 200K, then the boundary temperature drops to 160K gradually and keep at 160K. 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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