本文藉數值分析的方式來模擬微型質子交換膜燃料電池內燃料之濃度場的分佈及變化情形，並對流道中流場、電流場加以分析。模擬三維微型蛇形流道質子交換膜燃料電池之性能，得出結果並與實驗作比對，以驗證數值模擬之結果，並找出微型質子交換膜燃料電池設計時可能存在之問題。
理論分析中，我們使用Navier-Stokes equation作為流場的統御方程式，並依燃料電池製造材料之多孔性質，對Navier-Stokes equation作修正，再配上成分守恆方程式和電化學相關的方程式來求解燃料電池內之流場、濃度、壓力、電流密度等分佈及變化。數值方法中以有限容積法來作為離散方法，使用SIMPLEC 法來求得燃料電池中流場之各項分佈。
本文中分別採用不同的操作參數來作數值模擬，結果顯示，使用空氣當氧化劑時，陰極側氧氣濃度分佈對電池性能有極大影響，當氧氣分佈不均或不足時，便會造成濃度過電位，而使燃料電池的性能下降；而提高電池操作溫度及進氣壓力時，即可提升電池之性能。

A three dimensional numerical model for a micro proton exchange membrane fuel cell was developed to simulate the concentration distribution of the fuel gas, and analyze the flow field and current field in the fuel cell. Finite control volume scheme with SIMPLEC algorithm was employed in the numerical method.
Various operating conditions on the performance of the fuel cell were studied. It was shown that the concentration of oxygen at the cathode can strongly influence the cell performance. Increase the operating temperature and the pressure of the inlet gas can improve the performance of the fuel cell.

目錄 I
表目錄 III
圖目錄 IV
摘要 VII
Abstract VIII
符號說明 IX
第一章 緒論 1
1.1前言 1
1.2燃料電池的發展簡介 1
1.3文獻回顧 11
1.4研究目的 15
第二章 理論分析 22
2.1數學模型 22
2.2基本假設 22
2.3統御方程式 22
2.4邊界條件 34
第三章 數值方法 36
3.1模型格點測試 36
3.2數值方法 36
3.3解題流程 41
第四章 結果與討論 45
4.1電池操作溫度變化對燃料電池性能之影響 45
4.2與實驗結果比較 47
4.3改變進口氧氣濃度對性能的影響 48
第五章 結論 76
參考文獻 78

1. J. Larminie and A. Dicks, Fuel Cell System Explained, John Wiley, chapter 1-4, pp. 1-107, 2000.
2. 黃鎮江, 燃料電池, 全華科技圖書股份有限公司, 2005.
3. D. M. Bernardi and M. W. Verbrugge, Mathematical Model of a Gas Diffusion Electrode Bonded to a Polymer Electrolyte,AIChE Journal, Vol. 37, No. 8, pp. 1151-1163, 1991.
4. T. E. Springer, T. A. Zawodzinski and S. Gottefeld, Polymer Electrolyte Fuel Cell Model, Journal of The Electrochemical Society, Vol. 138, No. 8, pp. 2334-2341, 1991.
5. T. V. Nguyen and R. E. White, A Water and Heat Management Model for Proton-Exchange-Membrane Fuel Cells, Journal of The Electrochemical Society, Vol. 140, No. 8, pp. 2178-2186, 1993.
6. K. Broka and P. Ekdunge, Modeling the PEM fuel cell cathode, J.Appl. Electrochem, Vol. 27, pp. 281-289, 1997.
7. V. Gurau, H. Liu and S. Kakac, Two-Dimensional Model for Proton Exchange Membrane Fuel cells, AIChE Journal, Vol. 44, No. 11, pp. 2410-2421, 1998.
8. J. S. Yi and T. V. Nguyen, Multicomponent transport in porous electrode of Proton Exchange Membrane Fuel Cells using the interdigitated gas distributors, Journal of The Electrochemical Society, Vol.146, No. 1, pp. 38-45, 1999.
9. D. Singh, D. M. Lu and N. Djilali, A two-dimensional analysis of mass transport in proton exchange membrane fuel cells, International Journal of Engineering Science, Vol. 37, pp. 431-452, 1999.
10. K. Dannenberg, P. Ekdunge and G. Lindbergh, Mathematical model of the PEMFC, J.Appl.Electrochem., Vol. 30, pp. 1377-1387, 2000.
11. S. Um, C. Y. Wang and K. S. Chen, Computation Fluid Dynamics Modeling of Proton Exchange Membrane Fuel Cells, Journal of The Electrochemical Society, Vol. 147, pp. 4485-4493, 2000.
12. S. Dutta, S. Shimpalee and J. W. Van Zee, Numerical prediction of mass-exchange between cathode and anode channels in a PEM fuel cell, International Journal of Heat and Mass Transfer, Vol. 44, pp. 2029-2042, 2001.
13. S. Mazumder and J. V. Cole, Rigorous 3-D Mathematical Modeling of PEM Fuel Cells I.Modeling Predictions without Liquid Water Transport, Journal of The Electrochemical Society, Vol. 150, pp. 1503-1509, 2003.
14. S. Mazumder and J. V. Cole, Rigorous 3-D Mathematical Modeling of PEM Fuel Cells II.Model Predictions with Liquid Water Transport, Journal of The Electrochemical Society, Vol. 150, pp. 1510-1517, 2003.
15. G. Hu, J. Fan, S. Chen, Y. Liu and K. Cen, Three-dimensional numerical analysis of proton exchange membrane fuel cells (PEMFCs) with conventional and interdigitated flow fields, Journal of Power Sources, Vol. 136, pp. 1-9, 2004.
16. S. Um and C. Y. Wang, Three-dimensional analysis of transport and electrochemical reactions in polymer electrolyte fuel cells, Journal of Power Sources, Vol. 125, pp. 40-51, 2004.
17. P. H. Lee, S. S. Han and S. S. Hwang, Three-Dimensional Transport Modeling for Proton Exchange Membrane(PEM) Fuel Cell with Micro Parallel Flow Field, Sensors, Vol. 8, pp. 1475-1487, 2008.
18. S. S. Hsieh , S. H. Yang, J. K. Kuo, C. F. Huang, H. H. Tsai, Study of operational parameters on the performance of micro PEMFCs with different flow fields, Energy Conversion and management, Vol. 47, pp. 1868-1878, 2006.
19. J. P. Van Doormaal and F. D. Raithby, Enhancements of the SIMPLE method for tredicting incompressible fluid flows, Numerical Heat Transfer, Vol. 7, pp. 147-163, 1984.
20. S. V. Patankar, Numerical heat transfer and fluid flow, Hemisphere publishing corpotation, 1978.
21. 涂正輝, 質子交換膜燃料電池之三維流道設計與熱質傳分析, 碩士論文, 國立成功大學機械工程學系, 2003.