Governing Equations
Heat sources are generated due to the following three irreversible voltage losses in an electrochemical cell:
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Charge transport in the electrolyte
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Charge transport in the solid conductor materials
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Activation overpotentials in the electrode reactions
In addition, reversible heat sources and sinks can appear due to the entropy changes in the electrode reactions.
Joule Heating Due to Charge Transport
The charge transport in the solid conductor material and electrolyte create joule heating source terms according to
For an electrode or electrolyte domain this is the total electrochemical heat source. For porous electrodes sources due to electrochemical reactions, it is added to the joule heating.
Heating Due to Electrochemical Reactions
For an electrochemical reaction process one can write the total heat balance as:
Heat generated = Total reaction enthalpy – Electrical energy leaving the system
Using Faraday’s laws for an electrode reaction, m, at the interface between the electron and ion conducting phase this corresponds to
(3-2)
where ΔHm is the enthalpy change of the reaction, and ΔGm is the Gibbs free energy of the reaction, ΔGm, defined as
where ΔSm is the net entropy change. The equilibrium potential is related to ΔGm in the following way:
In Equation 3-2, ηm,tot is the total overpotential, which is defined as
By the relation
the local heat source due to the electrochemical conversion process becomes
where the overpotential expression represents the irreversible activation losses, and the last term is the reversible heat change due to the net change of entropy in the conversion process.
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
Add a Boundary Heat Source node to a Heat Transfer or Heat Transfer in Porous Media interface to couple to this heat source on a boundary.
For a porous electrode joule heating and electrochemical sources are summed up for a total heat source in the domain according to
Add a Heat Source (described in the COMSOL Multiphysics Reference Manual) node to a Heat Transfer or Heat Transfer in Porous Media interface to couple to the total electrochemical heat source in a domain.