本研究是對質子交換膜燃料電池建立二維之數學模式並分析電池之暫態性能，以有限元素分析法求解所建立之多重耦合非線性偏微分方程式。其中，燃料電池之方程式包含描述流體在多孔性薄膜的擴散層及觸媒層裡流動的Brinkman equation及兩極與交換膜之間電場反應的Charge equation，並使用在擴散及觸媒層裡因需要混合擴散係數而產生的Stefan-Maxwell組成方程式來表達組成之濃度變化。
本文之研究目的為在啟動與關閉過程裡以不同溫度下預測質子交換膜燃料電池的特性，而流場採用交叉逆向流來分析。並探討燃料電池啟動與關閉過程內之濃度場與速度場分佈，以及在啟動與關閉之瞬間電壓降與濃度、陰極與陽極之電流、與交換膜之間的影響。啟動前，因進入之燃料幾乎為零，而電流也跟著毫無變化；啟動瞬間，濃度瞬間加入；啟動之後，系統已為穩態狀態，因此電流穩定輸出。關閉前，電流為穩定輸出；關閉瞬間，將已存在之濃度歸零；關閉之後，燃料濃度保持在零，而電流也趨近於零。主要的結果為在啟動過程裡，70℃時，所產生的電流為最大，電壓降最小；而100℃電流最小，電壓降為最大；關閉過程裡，70℃時，所產生的電流為最大，電壓降最大；而100℃電流最小，電壓降為最小。

This research is to build two-dimensional mathematical models, and analyze the performance of transient condition of the proton exchange membrane fuel cell. In this model the finite element analytic method was used to solve the coupling multiple nonlinear partial differential equations. Among them, equations of the fuel cell contain Brinkman equation describing fluid between the porosity thin film diffusion and the catalyst layers, and Charge equation for the two-pole and the exchange membrane electric field response. Besides, the Stefan-Maxwell species equation resulted from the mixed diffusion coefficient that the process in the diffusion and catalyst layers needs is used to express specie concentration variations.
The research purpose of this article is to forecast the performance of the proton exchange membrane fuel cell in the start-up and the shut-down process under different temperatures, where the flow field uses alternately the counter flow. The concentration and velocity distributions as well as the instantaneous loss of voltage and the concentration negative pole and positive extremely electric current and influence between exchange membrane are also investigated in fuel cell start-up and shut-down process. Before the start-up, the electric current is not changed due to the none of entering fuel; when started-up instantaneously, the concentration instantaneously joins. After the start-up, the system was already the stable state condition, and then electric current output is stable. Before the shut-down, the electric current output is stable; when shot down instantaneously, the existence of concentration is zero. After shut-down, the fuel concentration maintains at zero, but the electric current is also close to zero. The main result is that the fuel cell operating at 70℃produces the highest electric current and the smallest loss of voltage; however, it operated at 100℃ produced the smallest electric currents and the highest voltage reduction

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