## 1 Introduction
Subsequently, [PERSON] and [PERSON] presented a one-dimensional mathematical model for predicting the performance of HT-PEMFC with PBI membrane [19]. Their attention was on MEA and evaluated the energy and mass transfer in the gas diffusion layer (GDL) and the electrochemical model. The most significant loss in the PBI fuel cell is the activation over-potential. The second-largest was Ohmic over-potential. The performance of this type of fuel cell has also been improved by increasing the membrane conductivity and enhancing catalyst performance. [PERSON] et al. [20] improved a high-temperature fuel cell with PBI membrane condensed by phosphoric acid in a one-dimensional and steady-state. In this research, the effect of operating pressure and cell temperature on the open circuit potential, and the effect of diffusion coefficients, exchange current density, and water transport across the membrane on the conductivity of the PBI membrane were examined. Their results are consistent with experimental data. [PERSON] et al. [21] studied the morphological properties of HT-PEMFC components by one-dimensional modeling, in steady-state and non-isothermal conditions, so that by achieving an optimal state, the catalyst layer can hold the steam generated from electrochemical reactions brought on by the feed gases. Their simulation was carried out at the temperature of 190 \({}^{\circ}\)C and operating pressure of 2 bars. The results showed that the porosity reduction of the GDL leads to retaining more water in the catalyst layer. Also, they stated that the use of micro-porous layer also helps to keep water generated in the catalyst layer by reducing the pore size and porosity of the layer. It should be noted, however, that the pore size and porosity of the fuel cell components should not be too small to prevent the increasing of over-potential of oxygen concentration. Besides, the porosity reduction of the GDL causes the steam to rise in the catalyst layer. The optimal values of the GDL porosity and the micro- porous layer depend on factors such as cell voltage, operating pressure and relative humidity, which have been investigated and calculated in this paper. [PERSON] et al. [22] simulated two-dimensional HT-PEMFC and investigated the role of transport in the cathode catalyst layer. Their calculations showed that close to the oxygen channel inlet, the cathode catalyst layer works in the regime limited by poor proton transport, while close to the outlet, the cathode catalyst layer operation is specified by poor oxygen transport. [PERSON] et al. [23] examined numerically and experimentally the performance of high-temperature fuel cell. In their numerical simulation, they used a two-dimensional model and observed the effect of PBI loading on the fuel cell. In their research, PBI value in the catalyst layer is considered between 5 to 30 wt%, and cell temperature is considered in the range of 160-200 \({}^{\circ}\)C. [PERSON] et al. [24] numerically surveyed the effect of temperature and mass transfer in an HT-PEMFC. Their models were simulated in two-dimensional and single-phase models, and the effect of the porosity of the GDL and its thickness on the fuel cell performance were evaluated. The results show that increasing the cell temperature and the porosity of the GDL and reducing the thickness of the GDL will improve the performance of high-temperature fuel cells. Using the PEM fuel cell simulation, [PERSON] and [PERSON] [25] studied and optimized the parameters affecting the performance of the fuel cell. Their models have a direct gas flow channel and are simulated three-dimensional, single-phase, and non-isothermal. They studied the effect of temperature, pressure, flow stoichiometry, gas channel width, thickness of the GDL, membrane thickness, porosity of the GDL and thermal conductivity of the GDL on the fuel cell performance. [PERSON] et al. [26] investigated the effect of relative humidity on the performance of single-cell PEM fuel cell at temperature of 120 \({}^{\circ}\)C and pressure of 1 atmosphere.