Checking the Conservation of Current, Energy, and Mass

The non-isothermal energy conservation equation is:where $T_{IN}$ and $T_{OUT}$ are the temperatures at the inlet and outlet respectively. $\dot{m}$ is the mass flux and $Y_i$ is the mass fraction of species $i$ . The enthalpy of formation, ${\hat{H}}_i$ of species $i$ , that is associated with the mass that is consumed by the reaction, is converted to internal electrochemical heat ( $Q_E$ ), internal Ohmic heat ( $Q_O$ ), and external electric power ( $P$ ):combining Eqn. (5283) and Eqn. (5284), gives:The electrical power that is available to the external circuit is calculated by the anode-cathode potential difference, $U$ , and the total current that is available to the external circuit, $I$ :Simcenter STAR-CCM+ calculates the ohmic heating by accounting for electric potential losses throughout every electrically or ionically conductive substrate:where $\sigma$ is the electrical conductivity and $\nabla \varphi$ is the electric potential gradient.

Simcenter STAR-CCM+ calculates the electrochemical heat that is released from a reaction, $i$, using: where $\eta$ is the overpotential and $\frac{\partial E_{eq}^{ox}}{\partial T}{|}_P$ is the equilibrium potential temperature derivative.