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系統識別號 U0026-0107201312202600
論文名稱(中文) 混合有限差分/殘差修正法於脈衝雷射加工熱傳分析
論文名稱(英文) Application of Finite Difference/ Residual Correction Method to Pulse Laser Heating Process
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 101
學期 2
出版年 102
研究生(中文) 劉英涵
研究生(英文) Ying-Han Liu
學號 n16014182
學位類別 碩士
語文別 中文
論文頁數 80頁
口試委員 指導教授-陳朝光
口試委員-賴新一
口試委員-周煥銘
中文關鍵字 最大值原理  有限差分法  殘差修正法  脈衝雷射加工 
英文關鍵字 maximum principle  finite difference method  residual correction method  pulse laser heating 
學科別分類
中文摘要 本研究以微分方程式最大值原理為主要觀念,建構理論,來求解微分方程式之較大、較小近似解,及數值解的誤差範圍,而用於探討的問題為脈衝雷射應用於皮膚的熱傳現象,在熱對流的邊界下,利用有限差分法來離散暫態熱傳方程式,再搭配殘差修正法,可求得相對於物體溫度場分佈之正確解的近似上下限。
有限差分法為早期便開始使用的數值方法,其具有運算簡單,使用於低階的方程式又具有良好的準確性,而應用殘差修正法的特點為可有效解決傳統數值方法上常無謂地增加格點數或近似函數數目之缺點,可節省計算時間與運算空間,此理論還具備誤差分析之特性,可避免不必要反覆式地數值精度測試,整體來說,殘差修正法為便利且效率高又具有良好精度的數值方法,預期將成為極具學術價值與實用性之數值研究方法。
探討脈衝雷射應用於皮膚治療之表面及內部熱傳分佈的情形,首先以一維模型分析,藉由調整脈衝雷射強度及參數討論治療時的狀態,再以二維圓柱模型進一步模擬,期望能更接近真實治療之情況,以供臨床參考。
英文摘要 The maximum principle of the differential equation is used as the main concept to form the complete structure in this study. Based on this, the upper and lower approximate solutions of the exact solution and their error range can be obtained. This study focused on the heating process of a pulse laser. Under boundary conditions of convection, the transient heat transfer equation is discretized by using the finite difference method. Then, the approximate solution of the workpiece temperature field distribution can be obtained by residual correction. The upper and lower approximate solutions is achieved and the error range can be analyzed.
Finite difference method is used in the early period. It is simple to operate and has good accuracy in low-order equations. A good point for residual correction method is analyzing the error according to the mean value of the upper and lower approximate solutions. It can effectively deal with the defects resulting from increasing the numbers of grids or approximate functions when using traditional numerical methods. This methodology can reduce the computing time, save the memory, and promote the numerical accuracy outstandingly. Predictably, it will achieve high academic value and practicability in numerical research in the future.
In this dissertation, an application of tissue treatment by using pulse laser is simulated and the heat transfer distributions of the surface and interior are demonstrated. At first, using one dimensional equation to simulate. Then using tow dimensional equation in order to close to the real situation. Let heat transfer distributions can be used in treatment by adjusting parameters of pulse laser intensity. Therefore, the proposed heat transfer distribution can be used as a prior simulation of clinical treatment.
論文目次 摘要 I
ABSTRACT II
誌謝 IV
目錄 V
表目錄 VIII
圖目錄 IX
符號表 X
第一章 緒論 1
1.1 研究動機及其背景 1
1.1.1 殘差修正法 1
1.1.2 雷射加工 3
1.1.3 皮膚組織 9
1.2 文獻回顧 11
1.2.1 殘差修正法 11
1.2.2 脈衝雷射加工 13
1.3 本文架構 15
第二章 最大值原理及其單調性 16
2.1 前言 16
2.2 一維最大值原理及其單調性 17
2.2.1 一維最大值原理之基礎理論 17
2.2.2 邊界值問題之單調性 18
2.2.3 初始值問題之單調性 21
2.2.4 非線性問題之單調性 24
2.3 偏微分方程最大值原理及其單調性 25
2.3.1 橢圓型方程最大值原理 26
2.3.2 橢圓型偏微分方程式之單調性 26
第三章 使用有限差分法於殘差修正法步驟 30
3.1 有限差分法 30
3.2 微分方程最大值原理與有限差分法之關聯 33
3.3 殘差修正法 37
3.4 殘差修正法之解題步驟 40
第四章 實例分析 43
4.1 前言 43
4.2 一維暫態熱傳問題 44
4.3 二維暫態熱傳問題 59
第五章 結論與建議 73
5.1 結論 73
5.2 建議及展望 75
參考文獻 76
自述. 80
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