臺灣博碩士論文加值系統

本文欲探討清玻璃於暫態情況下之熱傳物理現象。吾人以二維暫態包含熱產生量的熱擴散物理模型來描述清玻璃的熱傳現象。首先吾人利用拉斯轉換法，有限差分法，反拉斯轉換法並配合高斯消去法之數值方法求解玻璃在受到不同太陽入射熱通量的條件下的直接解熱傳導問題之溫度場分布情形，再來，吾人利用此模擬出來的溫度值當作正確值代入本文之逆向演算法中，此演算法包含正反拉斯轉換法，有限差分法，高斯消去法，並配合最小平方法修正溫度誤差，反求入射玻璃的太陽入射熱通量，並且把此預測值和文中假設的正確值做比較以為後文實際應用在實驗上的可靠性作驗證。接著吾人設計一套以輻射熱加熱玻璃的實驗系統，並量測玻璃加熱面，冷卻面的暫態溫度以及加熱面側和冷卻面側的環境空氣之暫態溫度，並且以此實驗量測的溫度代入本文之逆向演算法中求解入射玻璃的太陽入射熱通量以及清玻璃的消光係數。以吾人之逆向演算法預測的太陽入射熱通量以及清玻璃的消光係數和實際功率與文獻中的值作比較，結果顯示預測值和實際值相當接近，因此印證了本文逆算法之準確性與可靠性。

In this thesis, we will discuss the heat transfer phenomenon of clear glass under transient condition. We utilize two dimension transient heat diffusion physical model in which the heat generation term is included to describe the heat transfer phenomenon of clear glass. First of all, we apply the numerical method inclusive of Laplace transform and inverse Laplace transform, finite difference method and Gauss elimination method to solve the temperature distribution of the clear glass under varies incident solar heat flux. This is so called direct heat conduction problem. Then, we use the simulated temperature as exact value and fill it into the inverse algorithm in this thesis. The inverse algorithm includes Laplace transform and inverse Laplace transform, finite difference method, Gauss elimination method and corresponds with the least square method to modify the temperature errors then gets the incident solar heat flux. Then, we compare the estimated values with the exact values we supposed to verify the reliability under practical experimental setup. Later, we designate a set of experimental system which heats the glass with radiant heat and measure the heated face and cooling face temperature of glass along with air temperature of both faces. We then fill the measured temperature into inverse algorithm to get the incident solar heat flux and extinction coefficient of clear glass. At last, we compare the estimated values with practical power of heated lamp and references; consequently, the outcome shows that these two values are quite close, therefore we verify the accuracy and reliability of the inverse method in our thesis.

中文摘要……………………………………………………………Ⅰ
英文摘要……………………………………………………………Ⅱ
致謝…………………………………………………………………Ⅲ
目錄…………………………………………………………………Ⅳ
表目錄………………………………………………………………Ⅵ
圖目錄………………………………………………………………Ⅷ
符號說明……………………………………………………………ⅩI
第一章 緒論……………………………………………………… 1
1-1研究背景…………………………………………… 1
1-2 文獻回顧…………………………………………… 3
1-3 研究目的…………………………………………… 7
1-4 研究重點與本文架構……………………………… 8
第二章 直接解熱傳導問題之理論分析與數值模擬…………… 10
2-1 簡介……………………………………………… 10
2-2數學模式的建立…………………………………… 10
2-3 數值分析方法與結果………………………………… 13
第三章 逆向熱傳導問題之理論分析與數值模擬…………… 30
3-1簡介…………….…………………………………… 30
3-2 逆向熱傳導問題之理論分析……………………… 30
3-3溫度量測誤差的影響………………………………… 36
3-4結果與討論……………………………………………… 36
3-4-1案例一……………………………………………… 36
3-4-2案例二……………………………………………… 38
第四章 逆向熱傳導問題之實驗操作與預測值………………… 60
4-1簡介………………………………………………………… 60
4-2 實驗設備…………………………………………… 60
4-3實驗步驟…………………………………………… 61
4-4實驗結果與預測值…………………………………… 62
4-4-1水平玻璃平板之實驗結果與數值分析…………… 62
4-4-1-1求太陽輻射入射熱通量以及消光係數………… 68
4-4-2垂直玻璃平板之實驗結果與數值分析…………… 68
4-4-2-1求太陽輻射入射熱通量以及消光係數………… 74
4-4-3消光係數已知時之太陽入射熱通量………………… 74
4-4-4實驗結果與討論……………………………………… 75
第五章 綜合結論與未來展望……………………………… 98
5-1 直接解熱傳導問題之數值模擬結果……………… 98
5-2 逆向熱傳導問題之數值模擬結果………………… 98
5-3實驗預測結果……………………………………… 99
5-4綜合結論…………………………………………… 100
5-5未來發展方向與建議……………………………… 101



參考文獻…………………………………………………………… 102
自述………………………………………………………………… 106

[1] K.A.R. Ismail, J.R. Henriquez, Modeling and simulation of a simple glass window, Solar Energy Materials ＆ Solar Cells, Vol. 80, pp. 355–374 , 2003.

[2] G. Alvarez, M.J. Palacios and J.J. Flores, A test method to evaluate the thermal performance of window glazings, Appl. Thermal Eng., Vol. 20, pp. 803–812 , 2000.

[3] C A Estrada-Gascat, G Alvarez-Garcia and P K Nairt, Theoretical analysis of the thermal performance of chemically deposited solar control coatings, Appl. Phys, Vol. 26, pp. 1304-1309 , 1993.

[4] G Alvarezy, D N Jim?enezy and C A Estradaz, Thermal performance of solar control coatings: a mathematical model and its experimental verification, Appl. Phys, Vol. 31, pp. 2249-2257 , 1998.

[5] G Alvarezy and C A Estradaz, Transient heat conduction in a glass with chemically deposited SnS-CuxS solar control coating, Renewable Energy, Vol. 6, pp.1023-1027, 1995.

[6] A.M. Osman and J.V. Beck, Investigation of transient heat transfer coefficients in quenching experiments, Journal of Heat Transfer, Vol. 112, pp. 843-848, 1990.

[7] S. Chantasiriwan, Inverse heat conduction problem of determining time-dependent heat transfer coefficient, Int. J. Heat Mass Transfer, Vol. 42, pp. 4275-4285, 2000.

[8] T.J. Martin and G.S. Dulikravich, Inverse determination of steady heat convection coefficient distributions, Transactions of the ASME, J. Heat Transfer, Vol. 120, pp. 328-334, 1998.

[9] P.L. Masson, T. Loulou, and E. Artioukhine, Estimation of a 2-D convection heat transfer coefficient during a test: comparison between two methods and experimental validation. Inverse Problems in Sci. and Eng., Vol. 12, pp. 595-617, 2004.

[10] D.A. Murio, The Mollification Method and the Numerical Solution of Ill-Posed Problems. Wiley, New York, 1993.

[11] P. Duda and J. Taler, Numerical method for the solution of non-linear two-dimensional inverse heat conduction problem using unstructured meshes. Int. Journal for Numerical Methods in Engineering, Vol. 48, pp.881-899, 2000.

[12] H.T. Chen, S.Y. Lin and L.C. Fang, Estimation of surface temperature in two-dimensional inverse heat conduction problems, Int. J. Heat Mass Transfer, Vol. 44, pp. 1455-1463, 2001.

[13] H.T. Chen, S.Y. Lin and L.C. Fang, Estimation of two-sided boundary conditions for two-dimensional inverse heat conduction problems, Int. J. Heat Mass Transfer, Vol. 45, pp. 15-23, 2002.
[14] H.T Chen and X.Y. Wu, Estimation of heat transfer coefficient in two-dimensional heat conduction problems. Numerical Heat Transfer B Vol. 50, pp. 375-394, 2006.

[15] H.T. Chen and X.Y. Wu, Investigation of heat transfer coefficient in two-dimensional transient inverse heat conduction problems using the hybrid inverse scheme. Int. J. Numerical Methods in Engineering, Vol. 73, pp. 107-122, 2008.

[16] 徐韶甫，以逆算法配合實驗數據預測垂直平板之暫態自然對流熱傳系數，國立成功大學機械工程所，碩士論文，2008。

[17]　A. Trombe, A. Suleiman, and Y. Le Maoult, Use of an inverse method to determine natural convection heat transfer coefficients in unsteady state, ASME, Vol. 125, pp. 1017-1026, 2003.

[18]　H.T. Chen and S.K. Lee, Estimation of heat-transfer characteristics on the hot surface of glass pane with down-flowing water film, Build Environ, Vol. 45, pp. 2089-2099, 2010.

[19] H.T. Chen and J.Y. Lin, Hybrid Laplace transform technique for non-linear transient thermal problems, Int. J. Heat Mass Transfer, Vol. 34, pp. 1301-1308, 1991.

[20] H.T. Chen and J.Y. Lin, Numerical analysis for hyperbolic heat conduction, Int. J. Heat Mass Transfer, Vol. 36, pp. 2891-2898, 1993.


[21] H.T. Chen and J.Y. Lin, Analysis of two-dimensional hyperbolic heat conduction problems, Int. J. Heat Mass Transfer, Vol. 37, pp. 153-164, 1994.

[22] H.T. Chen, and S.M. Chang, Application of the hybrid method to inverse heat conduction problems, Int. J. Heat Mass Transfer, Vol. 33, pp. 621-628, 1990.

[23] H.T. Chen, S.Y. Lin and L.C. Fang, Estimation of surface temperature in two-dimensional inverse heat conduction problems, Int. J. Heat Mass Transfer, Vol. 44, pp. 1455-1463, 2001.

[24] H.T. Chen, S.Y. Lin and L.C. Fang, Estimation of two-sided boundary conditions for two-dimensional inverse heat conduction problems, Int. J. Heat Mass Transfer, Vol. 45, pp. 15-23, 2002.

[25] H.T. Chen, X.Y. Wu and Y.S. Hsiao, Estimation of surface condition from the theory of dynamic thermal stresses, Int. J. Thermal Sciences, Vol. 43, pp. 95-104, 2004.

[26] G. Honig, U. Hirdes, A method for the numerical inversion of Laplace transforms, J. Comp. Appl. Math., Vol. 9, pp. 113-132, 1984.

[27] Frank P. Incropera and David P. DeWitt, Fundamentals of Heat and Mass Transfer, 6-th Edition, John Wiley ＆ Sons, New York. ,2008.

[28] http://www.taiwanglass.com/userfiles/clear_01.pdf.