*Article* **Thermodynamic Optimization of a High Temperature Proton Exchange Membrane Fuel Cell for Fuel Cell Vehicle Applications**

**Bing Xu, Dongxu Li, Zheshu Ma \*, Meng Zheng and Yanju Li**

College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China; xb18260078388@163.com (B.X.); Ldx961203@163.com (D.L.); mengzai19950929@163.com (M.Z.); njfulyj@163.com (Y.L.)

**\*** Correspondence: mazheshu@njfu.edu.cn; Tel.: +86-137-7665-9269

**Abstract:** In this paper, a finite time thermodynamic model of high temperature proton exchange membrane fuel cell (HT-PEMFC) is established, in which the irreversible losses of polarization and leakage current during the cell operation are considered. The influences of operating temperature, membrane thickness, phosphoric acid doping level, hydrogen and oxygen intake pressure on the maximum output power density *Pmax* and the maximum output efficiency *ηmax* are studied. As the temperature rises, *Pmax* and *ηmax* will increase. The decrease of membrane thickness will increase *Pmax*, but has little influence on the *ηmax*. The increase of phosphoric acid doping level can increase *Pmax*, but it has little effect on the *ηmax*. With the increase of hydrogen and oxygen intake pressure, *Pmax* and *ηmax* will be improved. This article also obtains the optimization relationship between power density and thermodynamic efficiency, and the optimization range interval of HT-PEMFC which will provide guidance for applicable use of HT-PEMFCs.

**Keywords:** HT-PEMFC; irreversibility; finite time thermodynamic optimization; power density; thermodynamic efficiency
