In order to improve the output performance of direct methanol fuel cell, the finite-time thermodynamic model of direct methanol fuel cell is developed in this paper. Then, mathematical expressions for energy efficiency, power density, exergy efficiency and exergy coefficient of performance are derived. In addition, the effects of operating temperature, inlet pres-sure and membrane thickness on the performance of direct methanol fuel cells are considered. The results show that the exergetic performance coefficient not only considers the exergy loss rate to minimize the loss, but also the power density of the direct methanol fuel cell to maximize its power density and improve its efficiency. Therefore, the exergetic perfor-mance coefficient is a better performance criterion than conventional power and efficiency. In addition, increasing the inlet pressure and decreasing the membrane thickness can significantly improve the exergetic performance coefficient and en-ergy efficiency.

In this study, an irreversible thermodynamic model for the high temperature proton exchange membrane fuel cell taking electrochemical and heat losses into account is developed. The power density, exergy destruction index, exergy sustainability index and ecological coefficient of performance is derived. The model was validated against experimental data. The influence of parameters on the irreversible thermodynamic performance of high temperature proton exchange membrane fuel cell are considered. The multi-objective particle swarm optimization algorithm is utilized to optimize the power, ecological coeffi-cient of performance and efficiency. The population distribution of the optimization variables was analyzed using a three-dimensional Pareto frontier analysis, and results show that the maximum power density, maximum efficiency and maximum ecological coefficient of performance being 6340 W/m², 64.5% and 1.723 respectively, which are 43.28%, 3.7% and 17.8% higher than the preoptimized high temperature proton exchange membrane fuel cell. Moreover, the nondominated sorting genetic algorithm II and simulated annealing algorithm have been chosen versus multi-objective particle swarm optimization algorithm for making the optimization comparative analysis.