## 1 Introduction  
Due to the environmental issues posed by fossil energy sources, reducing the effects of these sources is one of the main priorities in energy planning today. In this context, in addition to striving for maximum energy savings, the most important concern is to replace these energy sources with renewable energies [1]. Consequently, the use of these resources such as fuel cell, wave [2,3], wind [4], solar, and hydrothermal energies attained substantial attention [5; 6; 7]. Fuel cells, especially PEM fuel cells with high power density, high efficiency, and short startup time are recognized as one of the most encouraging technologies for achieving these goals that can be employed in various applications [8; 9; 10]. Numerous research has been done recently for optimization of the PEM fuel cells performance considering various parameters that can be effective on its proficiency [11; 12; 13; 14; 15]. The operating temperature in determining the type of PEM fuel cells is an important parameter. In addition to operating temperature, the main difference between normal PEM fuel cell and high temperature is the membrane of the fuel cell. The normal polymer membrane is a Nafion(r) type that is made from perfluoro-carbon-sulfonic acid ionomer. The fuel entering the cell should be saturated with steam so that the membrane does not dry because the transfer mechanism uses the water as a proton carrier from the membrane. The function of the fuel cell at the desired temperature can lead to a blockage problem, which causes the membrane to flood and reduce the ionization of the membrane. Therefore, research was directed into the development of a new membrane so that it can function well above 100 \({}^{\circ}\)C and have a high conductivity in low moisture [16]. Improved membranes should have low material costs and high durability. Acid-based polymer membranes have been developed to achieve high proton conductivity, and one of the most favorite acid-base polymer membranes is polybenzimidazole (PBI) doped with phosphoric acid to increase the protonic conductivity. Phosphoric acid has more stability than other acids. In the context of the development of HT-PEMFCs, [PERSON] et al. performed extensive studies and evaluated the results of one, two, and three-dimensional simulations in this area [16]. Studies have shown that most research has been done to examine the materials and processes for improving fuel cell performance, including optimizing and simplifying fuel cell components and simulation of fuel cell systems to diminish their cost and enhance the efficiency, stability and durability compared to combustion engines; these should be considered in the studies. [PERSON] et al. [17] reviewed the research on various HT-PEMFCs and parameters affecting their performance. Based on their investigations, it is possible to find suitable solutions for increasing the stability and durability of the fuel cell and create proper conditions for better fuel cell performance. For this purpose, firstly, the components and performance of low-temperature fuel cell have been explored, and the need to go towards the design and development of high-temperature fuel cell components has been expressed in order to be able to achieve key factors in optimum fuel cell performance. Also, the effect of various parameters on the performance of PEMFC such as different working temperatures, working pressures, and combinations of these parameters was evaluated experimentally by [PERSON] et al. [18]. Voltage-current diagrams obtained from experimental results have shown the effect of these variables on fuel cell performance. Graphs have revealed that fuel cell performance has improved with increasing fuel cell pressure and temperature due to increased fuel reaction rate. Furthermore, the simulation of a three-dimensional fuel cell model was implemented, and the results were compared with experimental work, which showed an acceptable match between experimental and numerical data.