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研究生： 施聿懷
Shih, Yu-Huai
論文名稱： 具熱邊界及熱源之2-D奈米尺度能量傳輸
Two-dimensional nanoscale energy transport with hot boundary and heat source
指導教授： 吳志陽
Wu, C.-Y.
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2009
畢業學年度： 97
語文別： 中文
論文頁數： 172
中文關鍵詞： 熱邊界 、二維 、聲子 、熱傳 、熱源 、離散方向法
外文關鍵詞： hot boundary, heat source, two-dimensional, discrete ordinates method, heat transfer, phonon
相關次數： 點閱：55  下載：2 
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    • 本研究中，應用離散方向法(DOM)與修正的離散方向(MDOM)法於二維聲子輻射傳輸，考慮兩個不同的加熱方式，邊界加熱和內部熱源。且分別比較在兩種模式中，修正的離散方向法和離散方向法所得的結果。在邊界加熱模式中，可以發現在聲學厚度小的時候，MDOM能改善射線效應的影響，得到較準確的結果，並且MDOM能夠比DOM更準確地預測聲子的傳遞速率。隨著時間的增加或當聲學厚度較厚的時候，會大幅增加MDOM計算所需的時間。當縮小加熱區寬度時，會使得DOM的射線效應問題更加明顯，而MDOM則不受影響。整體來說，MDOM在各個聲學厚度皆適用，但特別適合在聲學厚度小或加熱區寬度小且時間較短的狀況下使用。在內部熱源模式中，當熱源開啟時間較長且聲學厚度較大時，DOM使用 方向格點可以得到不錯的結果，但在聲學厚度較小的時候，MDOM使用S8方向格點仍是較佳的選擇。整體而言，MDOM使用S8方向格點在各個聲學厚度或是不同長度的熱源開啟時間都有不錯的結果，但較適合在聲學厚度小或時間較短的狀況下使用。

    In this study, we apply the modified discrete ordinates method (MDOM) and the discrete ordinates method (DOM) to two-dimensional phonon radiative transport. Two cases, one with a hot boundary and the other with an internal heat source, are considered. The results of the two cases, respectively, obtained by the MDOM and the DOM are compared. In the hot-boundary case, the ray effect caused by the DOM is more obvious for the cases with a smaller width of hot boundary, while the MDOM may remedy ray effects and generate more accurate results in acoustically thin media. Furthermore, the MDOM predicts the velocity of phonon transport more accurately than the DOM does. However, the MDOM takes much more computational time as the simulation time or the acoustically thickness increases. From the results, we have seen that it is suitable to use the MDOM in all range of acoustic thickness, especially in acoustically thin media or the case with a smaller width of hot boundary for shorter simulation time. In the heat-source case, the DOM with approximation returns acceptable results for the situations with longer duration of heat source and a larger acoustical thickness; however, in acoustically thin media, the MDOM with S8 approximation is the better choice. In conclusion, the MDOM with S8 approximation returns satisfying results in all range of acoustic thickness or different duration of heat source; however, it is more suitable to be used in acoustically thin media or shorter simulation time.

    中文摘要................................................................i 英文摘要...............................................................ii 誌謝.......................................................................iv 目錄.......................................................................vi 表目錄...................................................................ix 圖目錄....................................................................x 符號說明...........................................................xviii 第一章 緒論........................................................1 1.1 研究動機、背景與文獻回顧.......................................1 1.2 研究目的與方法簡介.............................................4 1.3 本文架構.......................................................5 第二章 理論分析....................................................6 2.1 物理模型.......................................................6 2.2 統御方程式.....................................................7 2.2.1 波茲曼傳輸方程式....................................8 2.2.2 聲子輻射傳輸方程式..................................9 2.2.3 二維的聲子輻射方程式...............................11 2.3 初始條件和邊界條件...................................13 2.3.1 邊界加熱模式.......................................13 2.3.2 內部熱源模式.......................................15 2.4 改寫為彈道傳輸和擴散傳輸兩部分的聲子輻射傳輸方程式...16 2.5 改寫為彈道傳輸和擴散傳輸兩部分的初始條件和邊界條件...46 2.6 參數與鬆弛時間.......................................48 第三章 數值方法..........................................50 3.1離散方向法............................................51 3.1.1 二維的離散方向法...................................52 3.1.2 初始條件及邊界條件.................................56 3.2 修正的離散方向法.....................................58 3.2.1 應用MDOM求解二維聲子輻射傳輸方程式於邊界加熱模.....59 3.2.2 應用MDOM求解二維聲子輻射傳輸方程式於內部熱源模.....61 3.2.3 初始條件和邊界條件.................................64 3.3 無因次參數...........................................66 第四章 結果與討論........................................69 4.1 邊界加熱模式的結果與討論.............................69 4.1.1 MDOM格點數對結果的影響.............................70 4.1.2 MDOM與1-D DOM的結果比較...........................71 4.1.3 MDOM與DOM在Lh=Ly時的結果比較.......................73 4.1.4 MDOM與DOM在Lh=0.5Ly時的結果比較....................77 4.2 內部熱源模式的結果與討論.............................80 4.2.1 當tg=0.01時，MDOM格點數對結果的影響................81 4.2.2 當tg=0.01時，MDOM與DOM的結果比較...................82 4.2.3 當tg=1.0時，MDOM格點數對結果的影響.................86 4.2.4 當tg=1.0時，MDOM與DOM的結果比較....................88 第五章 結論..............................................92 參考文獻.................................................94

    1. C. Kittle, Introduction to Solid State Physics, 6th ed., Wiley, New York, 1986.
    2. J. M. Ziman, Electrons and Phonons, Oxford University Press, London, 1960.
    3. A. Majumdar, “Microscale heat conduction in dielectric thin films,” ASME Journal of Heat Transfer, Vol. 115, pp. 7-16, 1993.
    4. A. A. Joshi and A. Majumdar, “Transient ballistic and diffusive phonon heat transport in thin films,” Journal of Applied Physics, Vol. 74, pp. 31-39,1993.
    5. C. L. Tien and G. Chen, “Challenges in microscale conductive and radiative heat transfer,” ASME Journal of Heat Transfer, Vol. 116, pp 799-807, 1994.
    6. R. Prasher, “Generalized equation of phonon radiative transport,” Applied Physics Letters, Vol. 83, pp. 48-50, 2003.
    7. G. Chen, “Ballistic-diffusive heat conduction equations,” Physical Review Letters, Vol. 86, pp. 2297-2230, 2001.
    8. D. B. Olfe, “A modification of the differential approximation for radiative transfer,” AIAA Journal, Vol. 5, pp. 638-643, 1967.
    9. C.-Y. Wu, W. H. Sutton and T. J. Love, “Successive improvement of the modified differential approximation in radiative heat transfer,” AIAA Journal of Thermophysics and Heat Transfer, Vol. 1, pp. 296-300,1987.
    10. M. F. Modest, “Modified differential approximation for radiative transfer in general three-dimensional media,” AIAA Journal of Thermophysics and Heat Transfer, Vol. 3, pp. 283-288, 1989.
    11. R. Yang and G. Chen, “Two-dimensional nanoscale heat conduction using ballistic-diffusive equations,” Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposition, Vol. 369, pp 363-366, 2001.
    12. G. Chen, “Ballistic-diffusive equation for transient heat conduction from nano to macroscales,” ASME Journal of Heat Transfer, Vol. 124, pp. 320-328, 2002.
    13. R. Yang, G. Chen, M. Laroche and Y. Taur, “Simulation of nanoscale multi- dimensional transient heat conduction problems using ballistic-diffusive equations and phonon Boltzmann equation,” ASME Journal of Heat Transfer, Vol. 127, pp. 298-306, 2005.
    14. A. Majumdar, ”Monte Carlo study of phonon transport in solid thin films including dispersion and polarization,” ASME Journal of Heat Transfer, Vol. 123, pp. 749-759, 2001.
    15. L. Pilon and K. M. Katika, “Modified method of characteristics for simulating microscale energy transport,” ASME Journal of Heat Transfer, Vol. 126, pp. 735-743, 2004.
    16. J. Y. Murthy and S. R. Mathur, “Computation of sub-micron thermal transport using an unstructured finite volume method,” ASME Journal of Heat Transfer, Vol. 124, pp. 1176-1181, 2002.
    17. S. V. J. Narumanchi, J. Y. Murthy and C. H. Amon , “Simulation of unsteady small heat source effects in sub-micron heat conduction,” ASME Journal of Heat Transfer, Vol. 125, pp 896-903, 2003.
    18. S. Chandrasekhar, Radiative Heat Transfer, Dover Publications, New York, 1960.
    19. G. C. Pomraning, The Equation of Radiation Hydrodynamics, Pergamon, New York, 1973.
    20. M. F. Modest, Radiative Heat Transfer, 2nd ed., Academic press, New York, 2003.
    21. T. R. Anthony, W. F. Fleischer, L. Wei, P. K. Kuo, R. L. Thomas and R. W. Pryor, “Thermal diffusivity of isotopically enriched diamond,” Physical Review B, Vol. 42, pp. 1104-1111, 1990.
    22. B. G. Carlson and K. D. Lathrop, “Transport theory－the method of discrete- ordinates,” In：Computing Methods in Reactor Physics, H.Greenspan, C. N. Kelber, and D. Okrent, Gordon and Breach, New York, pp. 165-266, 1968.

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