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Energies 2020, 13, 6163 5 of 18 Videal = −∆gf (6) 2F Activation overpotential acting on cathode and anode is obtained from the following equations: RTI+IRT I ηact = cell ln 0 + cell sinh−1 4αcF I0 αaF αc =a0Tcell+b0 I0 = a1 e−b1 Tcell 2kehθh2 (7) (8) (9) where R is the universal gas constant, Tcell is the operating temperature, αc is the cathode charge transfer coefficient, F is the faraday constant, I is the current density, keh is the hydrogen electro-oxidation rate constant, θh2 is the hydrogen surface coverage, I0 is the exchange current density, λair is the cathode stoichiometry ratio, and αa is the anode charge transfer coefficient, and it is assumed to be the same as the cathode charge transfer coefficient. Ohmic overpotential and concentration overpotential acting on the cathode is given by: ηohmic = RohmicI (10) Rohmic = a2Tcell + b2 (11) ηconc = Rconc I (12) λair − 1 Rconc = a3Tcell + b3 (13) Linear regression was used for the cathode charge transfer coefficient, ohmic resistance (Rohmic), and concentration resistance (Rconc), and the exchange current density was expressed as an exponential function type. The values of the regressions used are shown in Table 1. Table 1. Numerical value for regressions used in the High Temperature Proton Exchange Membrane Fuel Cell (HT-PEMFC) model. Parameters Charge transfer constant, a0 Charge transfer constant, b0 Limiting current constant, a1 Limiting current constant, b1 Ohmic loss constant, a2 Ohmic loss constant, b2 Diffusion limitation constant, a3 Diffusion limitation constant, b3 It was assumed that all cell unit performances of the HT-PEMFC were the same, and the electric power (WFC) and thermal power (QFC) of HT-PEMFC were calculated in proportion to the number of cells (Ncell) and single cell active area (Acell) as in Equations (14) and (15). Moreover, the power efficiency (ηFC) of HT-PEMFC can be obtained as in Equation (16) based on the lower heating value (LHV) of hydrogen. Table 2 shows the parameters used in the HT-PEMFC model Values Unit 2.761 × 10−3 [K−1] −0.9453 - 3.3 × 103 [A] −0.04368 - −1.667 × 10−4 −8.203 × 10−4 [Ω/K] 0.2289 [Ω] [Ω/K] 0.4306 [Ω] WFC = NcellVcellIAcell (14) LHV QFC = Ncell 2F − Vcell IAcell (15) ηFC = WFC (16) Ncell LHV IAcell 2FPDF Image | Combined Power Generation System Based on HT-PEMFC and ORC
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