. 2023 May 19;9(5):e16164. doi: 10.1016/j.heliyon.2023.e16164

Table 1.

Electrochemical equations [37].

Title	Equation
$V_{o h m} = R_{c} + ρ_{c} . L_{c} + ρ_{a} . L_{a} + ρ_{e} . L_{e} + ρ_{int} . L_{int}$	Ohmic voltage drop
$ρ_{c} = {((\frac{42 E 6}{t_{S O F C . o u t}}) * \exp (\frac{- 1200}{t_{S O F C . o u t}}))}^{- 1}$
$ρ_{a} = {((\frac{95 E 6}{t_{S O F C . o u t}}) * \exp (\frac{- 1150}{t_{S O F C . o u t}}))}^{- 1}$
$ρ_{c} = {((\frac{9.3 E 6}{t_{S O F C . o u t}}) * \exp (\frac{- 1100}{t_{S O F C . o u t}}))}^{- 1}$
$V_{a c t} = V_{a c t, a} + V_{a c t, c}$	Activation voltage drop
$V_{a c t, a} = \frac{\overline{R} . (t_{S O F C . o u t})}{F} . \sinh^{- 1} (\frac{j}{2 j_{o a}})$
$V_{a c t, c} = \frac{\overline{R} . (t_{S O F C . o u t})}{F} . \sinh^{- 1} (\frac{j}{2 j_{o c}})$
$V_{C o n c} = V_{C o n c, a} + V_{C o n c, c}$	Concentration voltage drop
$V_{C o n c, a} = \frac{\overline{R} . (t_{S O F C . o u t})}{2 F} (Ln (1 + \frac{P_{H_{2}, 12} . j}{P_{H_{2}, 12} . j_{a s}}) - Ln (1 - \frac{j}{j_{a s}}))$
$V_{C o n c, c} = - (\frac{\overline{R} . (t_{S O F C . o u t})}{2 F}) . Ln (1 - \frac{j}{j_{c s}})$
$j_{a s} = \frac{2 F {. P}_{H_{2}, 12} . D_{a e f f}}{\overline{R} . (t_{S O F C . o u t}) . L_{a}}$
$j_{c s} = \frac{4 F {. P}_{O_{2}, 4} . D_{c e f f}}{(\frac{P_{4} - P_{O_{2}, 4}}{P_{4}}) \overline{R} . (t_{S O F C . o u t}) . L_{c}}$

The last equation of the fuel cell set equations could be the energy conservation and due to the adiabatic nature of the fuel cell, it can be written as Eq. (34).