Heating Due to Electrochemical Reactions
A heat source variable for a boundary defining an electrode-electrolyte interface (electrode surface) may be derived by considering the net enthalpy flux into the interface
(3-37)
where q is the boundary heat source (W/m2), n and νi are the number of electrons participating in the reaction and the stoichiometric coefficients of the reaction, respectively, and iloc local current density at the electrode surface. Subscript e above denotes the electron, and i the electrolyte phase species.
Considering the overall charge neutrality of the electrode reaction
(3-38)
and rearranging, the above relation equates to
(3-39)
where ΔH is the potential-independent net partial molar enthalpy change, defined as
(3-40)
Defining the thermoneutral voltage of the reaction as
the heat source term can be also be written as
(3-41)
Alternatively, using the relation
where ΔG is the Gibbs free energy of the reaction, and where ΔS is the net entropy change, and defining the equilibrium potential as
(3-42)
the boundary heat source may also be written as
(3-43)
where the overpotential is defined as
(3-44)
and the temperature derivative of the equilibrium potential is defined as
(3-45)
The total heat source due to the electrochemical reactions, qEC, for an electrode surface is the sum of all individual heat sources of the electrode reactions according to
where m is the index of the electrode reaction.
For a homogenized formulation of a porous electrode, the domain heat sources due to electrochemical reactions can be obtained by multiplying by the internal surface area av,m (m2/m3). For a porous electrode, the electrochemical sources are hence summed up according to