進階搜尋


下載電子全文  
系統識別號 U0026-1208201316502300
論文名稱(中文) 混合有限差分/微分轉換於雷射熱源之生物熱傳問題研究
論文名稱(英文) Application of Finite Difference/ Differential Transformation Method on Laser Heating Bioheat Transfer Problems
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) 許哲維
研究生(英文) Che-Wei Hsu
學號 n16001197
學位類別 碩士
語文別 中文
論文頁數 66頁
口試委員 指導教授-陳朝光
口試委員-楊玉姿
口試委員-劉晉嘉
中文關鍵字 微分轉換  脈衝雷射  非傅立葉生物熱傳  鬆弛時間 
英文關鍵字 differential transformation  pulsed laser  non-Fourier bio-heat transfer  relaxation time 
學科別分類
中文摘要 本研究應用微分轉換混合有限差分法分析非傅立葉生物熱傳問題。微分轉換法是以據泰勒展開式為基礎的轉換方法,能將線性及非線性微分方程式轉換為代數方程進行迭代求解,有別於其過去利用積分求解的方式,微分轉換於求解熱傳問題上省去冗長及繁雜的計算,不僅較為簡易且模擬時運算處理的時間也較為短暫。
過去研究認為,傳統傅立葉熱傳定律的熱波具有非常大的傳遞速度,其溫度分佈應為一平滑連續曲線。而在脈衝雷射加熱的情況下,應採用非傅立葉熱傳定律之熱波理論,將傳遞速度視為一有限值,造成熱以類似波的形式傳遞,因此在計算時需要加入鬆弛時間做討論。
本文首先簡介非傅立葉熱傳問題的演進以及脈衝雷射的歷史,接著介紹微分轉換理論定義及演算法則,並且推導非傅立葉熱傳問題的數學模型,最後混合微分轉換及有限差分法進行數值迭代,計算在有一脈衝雷射熱源下之單層組織及雙層組織在不同邊界下的情況。最後得到結論:較小的脈衝寬度與較大的吸收係數能得到愈佳的結果,而H值與格點數目的選擇會改變程式的執行結果。
英文摘要 In this research, the hybrid method which combines differential transformation and finite difference approximation techniques was used to solve non-Fourier bio-heat transfer problems. Differential transformation method is a transfer function based on the Taylor expansion series. It converts linear and non-linear differential equations into a form of algebraic equations by constructing systematic processing program and iterating to find the solutions. Unlike the ordinary integral transform methods, differential transformation is briefer to solve heat conduction problem. It also costs less time in computer simulating.
The study results show that the thermal wave propagation speed is infinite in Fourier conduction law and the temperature distribution is continuous. However, in this pulsed laser heating case, it should apply the non-Fourier transfer conduction law. The propagation speed of thermal wave is finite and has a behavior like wave in thermal wave model of bio-heat transfer. According to this situation, we should take account of the relaxation time to conform the thermal behavior.
The history of pulsed laser and derivation of the non-Fourier bio-heat transfer conduction problems were first displayed. Then, the definitions and properties of the differential transformation method will be introduced briefly. Using the combination method of finite difference and differential transformation to iterate the bio-heat transfer problem in one and double layer with a pulsed laser heating source. In conclusion: smaller bandwidth of pulsed laser and larger absorption coefficient get better results. The choice of H and the number of grid also affect the results.
論文目次 摘要...................................................................................................................I
Abstract............................................................................................................II
誌謝................................................................................................................IV
目錄.................................................................................................................V
表目錄.........................................................................................................VIII
圖目錄............................................................................................................IX
符號說明.......................................................................................................XII
第一章 緒論..................................................................................................1
1-1研究背景與動機...............................................................................1
1-2文獻回顧...........................................................................................3
1-2-1生物熱傳文獻回顧….………...............................................3
1-2-2脈衝雷射文獻回顧................................................................4
1-2-3微分轉換法文獻回顧............................................................6
1-3本文架構............................................................................................7
第二章 微分轉換法....................................................................................10
2-1前言..................................................................................................10
2-2微分轉換的數學原理......................................................................10
2-3微分轉換的運算.............................................................................14
2-4 T譜儲存法......................................................................................16
第三章 生物體雙曲線型熱傳導問題........................................................19
3-1前言..................................................................................................19
3-2雙曲線型熱傳導方程式..................................................................19
3-3雙曲線型熱傳導主控迭代式..........................................................20
3-3-1卡式座標系統......................................................................20
3-3-2圓柱座標系統......................................................................22
3-3-3球座標系統......................................................................23
第四章 雷射熱源之生物熱傳問題............................................................25
4-1脈衝雷射為內部熱源的單層組織熱傳..........................................25
4-1-1熱傳導方程式與邊界條件.................................................25
4-1-2數值模擬結果與討論..........................................................31
4-2脈衝雷射為內部熱源的雙層組織熱傳..........................................42
4-2-1熱傳導方程式與邊界條件..................................................42
4-2-2數值模擬結果與討論..........................................................49
4-3結論..................................................................................................59
第五章 總結與建議....................................................................................60
5-1總結..................................................................................................60
5-2未來展望與建議..............................................................................61
參考文獻.......................................................................................................62
參考文獻 Andrä, W., d’Ambly, C.G., Hergt, R., Hilger, I., Kaiser , W. A., Temperature distribution as function of time around a small spherical heat source of local magnetic hyperthermia, J. Magnetism and Magnetic Materials, vol.194, pp.197-203, 1999.
Brazhnikov, A.M., Karpychev, V.A., Luikova, A.V., One engineering method of calculating heat conduction processes, Inzhenerno Fizicheskij Zhurnal, vol.28, pp.677–680, 1975.
Cattaneo, C., Surune forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanée, C.R. Acad. Sci., vol.247, pp.431-433, 1958.
Chen, C.K., Ho, S.H., Application of differential transformation to eigenvalue problem, Appl. Math. Comput., vol.79, pp.173-188, 1996.
Chiou, J.S., Tzeng, J.R., Application of the Taylor transformation to nonlinear vibration problems, Trans. ASME, J. Vib. Acoust., vol.118, pp.83-87,1996.
Chen, C.K., Ho, S.H., Free vibration analysis of non-uniform Timoshenko beam using differential transform, Applied Mathematical modeling, vol.22, pp.219-234, 1998.
Chen, C. K., Lai, H. Y., Liu, C. C. Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam, Microsyst Technol, vol.15, pp.813-820, 2009.
Goldman, L., Wilson, R., Hornby, P., and Meyser R. Laser radiation of malingnacy in man, Cancer, vol.18, pp.929-933, 1965.
Grundfest, W. S., Litvack, F., Forrester, J. S., Goldenberg. T., Swan, H. J., Morgenstern, L., Fishbein, M., Mcdermid, I. S., Rider, D. M., Pacala,T. J., and Lauden Slager, J. B. Laser ablation of human atherosclerotic plaque without adjacent tissue injury, Journal of the American College of Cardiology, vol.5, pp.929-933, 1985.
Gautheric, M., Thermopathology of breast cancer: measurement and analysis of in vivo temperature and blood flow, Ann. N. Y. Acad. Sci., vol.335, pp.383-415, 1980.
Hu, L., Gupta, A., Gore, J.P., Xu, L.X., Effect of forced convection on the skin thermal expression of breast cancer, ASME J. Heat Transfer, vol.126. pp.204-211, 2004.
Kuo, B. L., Chen, C. K. Application of hybrid method to the solution of the nonlinear Burgers’ equation, ASME, vol.70, pp.926-929, 2003.
Liu, J., Ren, Z., Wang, C., Interpretation of living tissue’s temperature oscillations by thermal wave theory, Chinese Sci. Bull., vol.40, pp.1493-1495, 1995.
Lu, W.Q., Liu, J., Zeng, Y., Simulation of the thermal wave propagation in biological tissues by the dual reciprocity boundary element method, Engineering Analysis with Boundary Elements, vol.22, pp.167-174, 1998.
Liu, J., Chen, X., Xu, L.X., New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating, IEEE transactions on Biomedical Engineering, vol.46, pp.420-428, 1999.
Liu, K.C., Thermal propagation analysis for living tissue with surface heating, International Journal of Thermal Sciences, vol.47, pp.507-513, 2008.
Liu, K.C. and Lin, C.N., Temperature prediction for tumor hyperthermia with the behavior of thermal wave, Numerical Heat Transfer, Part A, Vol. 58, pp.819-833, 2010.
Ni, J.H., Chang, C.C., Yang, Y.T., Chen, C.K., Surface heating problems of thermal propagation in living tissue solved by differential transformation method, Journal of the Chinese society of mechanical engineers, vol.72, pp.37-51, 2011.
Pennes, H.H., Analysis of tissue and arterial temperature in the resting human forearm., J. Appl. Physic. vol.1, pp.93-122, 1948.
Peng, H. S. and Chen, C. L., Application of hybrid differential transformation and finite difference method on the laser heating problem, Numerical Heat transfer A, vol.59, pp.28-42, 2011.
Ready, J. F., Effect due to absorption of laser radiation, J Appl Phys, vol. 36, pp. 462-470, 1963.
Sieniutycz, S., The variational principle of classical type for non-coupled non-stationary irreversible transport processes with convective motion and relaxation., International Journal of Heat and Mass Transfer. vol.20, pp. 1221-1231, 1977.
Shen, W. S., Zhang, J., and Yang, F.Q. Three-dimensional model on thermal response of skin subject to laser heating, Computer Methods in Biomechanics and Biomedical Engineering, vol. 8, No. 2, pp. 115-125, 2005.
Vernotte, P., Les paradoxes de la théorie continue de L’ équation de la chaleur, C.R. Acad. Sci., vol.246, pp.3154-3155, 1958.
Vogl, T.J., Eichler, K., Zangos, S., Mack, M.G., Interstitial laser therapy of liver tumors, Med. Laser Appl. Vol.20, pp.115-118, 2005.
Yu, L.T., Chen, C.K., Application of Taylor transformation to optimize rectangular fins with variable thermal parameters, Appl. Math. Model., vol.22, pp.11-21, 1998.
Yilbas, B.S., Kalyon, M. Repetitive laser pulse heating with a convective boundary condition at the surface, Journal of Physics D: Applied Physics, vol.34, pp.222-231, 2001.
Yuan, P., Numerical analysis of temperature and thermal dose response of biological tissues to thermal non-equilibrium during hyperthermia therapy, Medical Engineering & Physics, vol.30, pp.135-143, 2008.
Özisik, N., Heat Conduction, 2nd edn., New York: Wiley, 1993.
趙家奎,微分轉換及其在電路中的應用,華中理工大學出版社,1986。
劉國基,雙曲線型擴散問題之探討,國立成功大學機械工程學系,博士論文,2002。
林聖棋,脈衝雷射於組織治療之研究,國立中央大學機械工程學系,碩士論文,2003。
朱光明,生物組織傳熱及其若干應用研究應用研究,華中科技大學工程熱物理,博士論文,2004。
葉韋志,微分變換於一維樑柱挫曲與熱傳導問題求解之應用,國立成功大學航空太空工程學系暨研究所,碩士論文,2004。
白桂霖,運用混合微分轉換法求解薄膜受超短脈衝雷射作用之研究,國立虎尾科技大學航空與電子科技研究所,碩士論文,2004.
陳柏佑,混合微分轉換/有限差分法在非線性暫態熱傳問題之研究,國立成功大學機械工程學系,博士論文,2005。
李國鑫,殘差修正法於脈衝雷射加工熱傳分析之應用,國立成功大學航太工程學系,碩士論文,2010。
倪瑞珣,生體表面加熱之熱波傳遞問題研究,國立成功大學機械工程學系,碩士論文,2010。
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2013-08-16起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2013-08-16起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw