本論文針對質子交換膜燃料電池(PEMFC)進行三維、瞬態數學模式建立。其中分別對PEMFC中的氣體通道、氣體擴散層、觸媒層及質子交換薄膜等不同區域推導建構連續方程式、動量方程式、能量方程式和成分方程式，並根據PEMFC上述不同區域之邊界特性，建立其邊界條件。
由於PEMFC在實際操作條件下，內部流場、燃料濃度、及溫度分佈等都會呈現三維的變化，且隨著操作時間的改變，內部濕度、薄膜液態水的含量及流場也會呈現空間的改變。薄膜中液態水因為擴散力及電子遷移力的影響，導致在薄膜上的濕潤程度不均勻，所以能預測並做好水管理的工作，能有效延長薄膜的壽命。此外不同幾何形狀的流道會影響燃料在擴散層中的輸送，若流道形狀能加強氣體在擴散層中的對流能力，將有助於電池效能的提升。

因此，基於上述理由，藉由本論文所建立之三維、瞬態數學模式，做為電腦程式模擬的依據，才能更精準預測PEM燃料電池的性能和行為。本論文即完成電腦輔助PEM燃料電池組系統設計之第一段階段性工作，並整理出修改本實驗室原有內燃引擎三維流場軟體(KIVA)所需修改部分。

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