Butler-Volmer model current-overpotential equation

Charge transport is modeled by Ohm s law (Equation (3.10)) and the charge conservation equation (Equation (3.68)), while the current density distribution at the electrode/electrolyte interface is modeled through the Butler-Volmer equation (Equation (3.102)). It should be noted that, contrarily to Section 3.7, Equation (3.102) is here derived from Equation (3.37) rather than Equation (3.39), because the former allows for a better agreement between experimental and simulated results. Equations (3.40)-(3.42) are used to model, the exchange current density, the activation overpotential, and the ideal potential drop at the electrode/electrolyte interface, respectively. Heat transfer is modeled through Equation (3.6), and the appropriate heat terms for each domain. 

Fig. 9.21 Simulink electrochemical model with R-C model capacitance behavior. The BV Fen block is the quasi-steady Butler-Volmer overpotential equation giving current through the Ret charge transfer resistor as a function of charge transfer overpotential, r).

Additional parameters specified in the numerical model include the electrode exchange current densities and several gap electrical contact resistances. These quantities were determined empirically by comparing FLUENT predictions with stack performance data. The FLUENT model uses the electrode exchange current densities to quantify the magnitude of the activation overpotentials via a Butler-Volmer equation [1], A radiation heat transfer boundary condition was applied around the periphery of the model to simulate the thermal conditions of our experimental stack, situated in a high-temperature electrically heated radiant furnace. The edges ofthe numerical model are treated as a small surface in a large enclosure with an effective emissivity of 1.0, subjected to a radiant temperature of 1 103 K, equal to the gas-inlet temperatures. 

Once the local concentration overpotential is known, the activation overpotential, ria, is obtained by subtracting Tjc from total Tj. The local activation overpotential is the actual driving force of the electrochemical reaction. It is related to the local current density at any point of the reaction zone by an electrochemical rate equation such as the Butler-Volmer equation (Eq. (10a)). Therefore, the rate equation, the Nernst equation (Eq. (37)), and the potential balance in combination couple the electric field with the species diffusion field. In addition, the energy balance applies also at the electrode level. Although this introduces another complication, a model including a temperature profile in the electrode is very useful because heat generation occurs mainly by electrochemical reaction and is localised at the reaction zone, while the... 

A simplified and naive model of activation overpotential versus current density expression from a Butler-Volmer equation can be written as ... 

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