臺灣博碩士論文加值系統

傳統使用橢圓近似周長公式分析所得絕熱橢圓管之熱傳特性結果不夠正確，且隨著橢圓長短軸比值越大時其誤差越大。本文以積分法求出準確之橢圓周長來獲得之二維數值結果與一維PWTR模型和CPWTR模型解作比較。本文發現，絕熱橢圓管的熱傳特性，在以實際管尺寸在真實應用狀態下，當橢圓管長短軸比≦3.5:1時，可應用一維PWTR模型分析，或當橢圓管長短軸比≧3.5:1時，可採用一維9-1 CPWTR模型分析，兩者均能獲得可靠的一維近似解；若在實用絕熱厚度(t/R2＜0.5)的情況下，其熱傳率誤差率則大多在0.5%以內; 即使在包覆相當大絕熱厚度(t/R2=2.0)的情況，其熱傳率誤差率大多在2%以內。此外，本文對於小尺寸絕橢圓管的臨界厚度和中性厚度的熱傳特性，亦進行了深入探討。 本文發現小尺寸絕熱橢圓管之臨界特性，隨著長短軸比值增大而逐漸不同於等效的絕熱圓管，而且隨著無因次尺寸和/或長短軸比的改變而有不同臨界結果。

Conventional unreliable heat transfer results of an insulated oval duct are generated by an inaccurate approximation of an oval perimeter equation. The greater the long-short-axes ratio, the bigger the error becomes. On the other hand, the present results are based on very accurate oval perimeters obtained by an integral method. The one-dimensional results of PWTR and 91-CPWTR models are compared with those of numerical results. It is found that in practical situations, that is, long-short-axes ratio is less or equal to 3.5, satisfactory and reliable solutions can be obtained by the one-dimensional PWTR model. However, when the long-short-axes ratio is greater than 3.5, accurate and reliable solutions can only be achieved by the one-dimensional 9-1CPWTR model, which returns most errors within ±0.5 % for situations of practical duct sizes and insulated thickness (t/R2＜0.5). Even in situations of a extraordinary large insulated thickness (t/R2=2.0), most errors are within ±2 %. Apart from this, the heat transfer characteristics of critical and neutral thickness of a very small insulated oval duct are also investigated in this study. It is found that the critical heat transfer characteristics of a very small insulated oval duct are different from those of an equivalent insulated circular duct. The bigger the long-short-axes ratio is, the greater difference becomes. In here, results are presented along with the change of dimensionless duct size or/and long-short-axes ratio.

摘要-----i
Abstract------ii
誌謝------iv
目錄------v
表目錄------viii
圖目錄------xi
符號說明vxiii
一、 緒論------1
1.1 前言------1
1.2 研究目的------2
二、 理論分析------8
2.1 近似橢圓周長與準確橢圓周長誤差（ES）------8
2.1.1 包覆絕熱棉後近似橢圓周長與準確橢圓周長誤差（EEC） ------10
2.1.2 準確之橢圓內管壁、外管壁與包覆絕熱後的表面面積------12
2.1.3 近似橢圓內管壁、外管壁與包覆絕熱後的表面面積------13
2.1.4 近似橢圓之等效圓管的內管壁、外管壁與包覆絕熱後的表面面積------13
2.2 二維數值熱傳模型------14
2.3 一維平板熱阻(PTR)模型------14
2.3.1 PTR模型之熱傳率(QEP)------15
2.3.2 PTR模型之熱傳誤差率(EEP)------16
2.4 一維平面楔形熱阻(PWTR)模型------16
2.4.1 PWTR模型之熱傳率(QEO)------17
2.4.2 圓管之熱傳率(QEC------19
2.4.3 PWTR模型之熱傳誤差率(EEO)------20
2.4.4 PWTR模型之臨界半徑和臨界厚度------20
2.4.5 PWTR模型之中性半徑和中性厚度------21
2.5 一維組合平板與楔形熱阻(91-CPWTR)模型------22
2.5.1 91-CPWTR模型之熱傳率(Q91)------23
2.5.2 91-CPWTR模型之熱傳誤差率(E91)------24
三、 研究方法------25
3.1 數值解(Qn)的正確性分析------25
3.1.1 模型建立的正確性分析------25
3.1.2 網格數目的正確性分析------26
3.2 問題分析------27
3.2.1 無臨界熱傳現象時 (即R2≧Rcr)------27
3.2.2 有臨界熱傳現象時 (即R2＜Rcr)------27
四、 結果與討論------28
4.1 無臨界熱傳現象------28
4.1.1 PTR模型之熱傳誤差率(EEP)------28
4.1.2 PWTR模型之熱傳誤差率(EEO)------29
4.1.3 91-CPWTR模型之熱傳誤差率(E91)------29
4.1.4 近似橢圓周長所得絕熱橢圓管之熱傳率（Qao）不正確性 ------30
4.1.5. J值對於誤差率之探討------30
4.1.6 絕熱橢圓管一維準確近似解的探討------31
4.2 有臨界熱傳現象------31
4.2.1 臨界半徑和臨界厚度------32
4.2.2 絕熱橢圓管長短軸比對臨界厚度和中性厚度影響------32
4.2.3 (R2 / Rcr)W值對於臨界厚度和中性厚度的探討------35
五、 結論------39
參考文獻------42
附錄A、橢圓不同長短軸比例之溫度曲線------98
作者簡介------105

[1]W.L. Chen, L.C. Fang, A numerical study on the flow over a staggered oval pipe for heat-transfer enhancement, J.CSME, Vol.25, 2004, pp.209-216.
[2]W.L. Chen, K.L. Wong and C.T. Huang, A parameter study on the laminar flow in an alternating horizontal or vertical oval cross-section pipe with computational fluid dynamics, International Journal of Heat and Mass Transfer, Vol. 49, 2006, SCI, pp.287-296.
[3]Y. Chen, M. Fiebig, N.K. Mitra, Conjugate heat transfer of a finned oval tube with a punched longitudinal vortex generator in form of a delta winglet-parametric investigations of the winglet, International Journal of Heat and Mass Transfer, Vol.41, 1998, pp.3961-3978.
[4]Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of a finned oval tube with punched longitudinal vortex generators in-line, International Journal of Heat and Mass Transfer, Vol.41, 1998, pp.4151-4166.
[5]Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of finned oval tubes with staggered punched longitudinal vortex generators, International Journal of Heat and Mass Transfer, Vol.43, 2000, pp.417-435.
[6]J.S. Leu, M.S. Liu, J.S. Liaw, Chi-Chuan, A numerical investigation of louvered fin-and-tube heat exchangers having circular and oval tube configurations, International Journal of Heat and Mass Transfer, Vol. 44, 2001, pp.4235-4243.
[7]S. Tiwari, D. Maurya, G.. Biswas, V. Eswaran, Heat transfer enhancement in cross-flow heat exchangers using oval tubes and multiple delta winglets, International Journal of Heat and Mass Transfer, Vol. 46 (2003), pp.2841-2856.
[8]A. Hasan, K. Siren, Performance investigation of plain circular and oval tube evaporatively cooled heat exchangers, Applied Thermal Engineering, Vol. 24, 2004, pp.777-790.
[9]M.H. Kim, J.S. Shin, C.W. Bullard, Heat Transfer and Pressure Drop Characteristics During R22 Evaporation in an Oval Microfin Tube, Journal of Heat Transfer, Volume 123 Issue 2, April 2001, pp.301-308.
[10]F.J. Schulenberg, Finned elliptical tubes and their application in air-cooled heat exchanger, Transactions of the ASME Vol. 88, 1966, pp.179-190.
[11]T. Ota, H. Nishiyama, Y. Taoka, Heat transfer and flow around an elliptic cylinder, International Journal of Heat and Mass Transfer Vol. 27, October, 1984, pp.1771-1779.
[12]O'Brien, E. James, Sohal, S. Manohar, Wallstedt, C. Philip, Local heat transfer and pressure drop for finned-tube heat exchangers using oval tubes and vortex generators, Journal of Heat Transfer, Vol. 126, 5, October, 2004, pp.826-835.
[13]A. Bejan, Heat transfer, John Wiley & Sons Inc. 1993 pp.42-45.
[14]F.P. Incropera, D.P. Witt, Fundamentals of heat transfer, John Wiley & Sons Inc., 1990, pp.79-91.
[15]J.P. Holman, Heat transfer, Eighth SI Metric Edition, McGraw-Hill Inc., 2001, pp.7-~39 and pp.638-642.
[16]A.F. Mills, Basic heat and mass transfer, University of California at Los Angles, IRWIN 1995, pp.7-28.
[17]Kreith and M.S. Bohn, Principles of heat transfer, fifth edition, Harper International Edition, 1993, pp.21- 41.
[18]W.S. Janna, Engineering heat transfer, PWS Engineering Boston, PWS Publishers, 1986 pp.61-71.
[19]J.H. Lienhard, A heat transfer textbooK, 2nd edition, Prentice- Hall Inc., 1987; pp.62-63.
[20]M.N. OzisiK, Heat transfer, A basic approach, McGraw Hill BooK Company, 1998; pp.59-62.
[21]E.G. Pita, Air conditioning principles and system, 3rd edition, Prentice Hall, 1998, pp.252-256.
[22]W.F. StoecKer. and J.W. Jones, Refrigeration and air conditioning, 2nd edition, McGraw-Hill Inc., 1982, pp.24-35.
[23]R.J. Dossat, Principles of refrigeration, 3rd edition, Prentice Hall, 1991, pp.167-178.
[24]R. Chatenever, Air conditioning and refrigeration for the professional, John Wiley & Sons Inc., 1988, pp.445-448.
[25]D. Khrustalev and A. Faghri, Thermal analyze of a micro heat polyhedron, Journal of Heat Transfer, Vol.116, 1994, pp.189-198.
[26]A.W. Porter, On the lagging of pipes and wires, Phil. Mag. London, 20, 1910, pp.511.
[27]J.D. Lewins, T.T. CocKerill, “On the teapot and its cosy., The International Journal of Mechanical Engineering Education 22, 1993, pp.301-306.
[28]F.S. Lien, W.L. Chen, M.A. Leschziner, A multiblock implementation of a non-orthogonal, collocated finite volume algorithm for complex turbulent flows, Int. J. Numer. Methods Fluids 23 (1996) 567-588.
[29]M.S. Soylemez and M. Unsal, Optimum insulation thicKness for refrigeration applications, Energy Conversion and Management 40 , 1999, pp.13-21.
[30]H.M. Chou, K.L. Wong, Heat transfer characteristics of an insulated regular polyhedron by using a multiple solid wedge thermal resistance model, Energy Conversion & Management, 44 no.4, 2003, pp. 629 -645.
[31]K.L. Wong, H.M. Chou, Y.H. Li, Complete heat transfer solutions of an insulated regular cubic tank with a SSWT model, Energy Conversion & Management, 45, 2004, pp.1705-1724.
[32]K.L. Wong, Hsien T.L., Peter Richards, Her B.S., The reliable simple one-dimensional 64-CPWTR model applied to the two-dimensional heat transfer problem of an insulated rectangular duct in an air conditioning or refrigeration system, International Journal of Refrigeration, 28 April, 2005., pp.1029-1039.
[33]H.B. William, CRC standard mathematical table, Chemical Rubber Pub., Cleveland, 1978, 25th ed., pp.14.
[34]K.L. Wong, J.F. Li, Hsien T.L., L.T. Huang and S.S. Ku, C.H. Huang, The analysis of heat transfer characteristics of an insulated oval duct,，2005海峽兩岸大學校長會議暨科學技術研討會，pp. 590-593,2005/11/26.
[35]蔡豐欽，熱傳遞，高立圖書有限公司，中華民國，86年6月20日，第三版，pp.332.