Electrochemical Contributions to The Heat Equation
The heat equation solved for by the Heat Transfer interface typically has the following form
(3-28)
where Q is the domain heat source (W/m3).
The electrochemistry interfaces typically solve for the transport and electrochemical reactions of a multicomponent system comprising a number of different species with index i. Adding the additional contributions from the multicomponent system to the heat transfer equation, and assuming no other additional heat sources (Q = 0), results in
(3-29)
where Hi is the partial molar enthalpy (J/mol), Ni is the species flux (mol/m2/s), and ci is the concentration.
By treating the contributions from the electrochemical multicomponent system as a heat source defined as
(3-30)
Equation 3-28 can be made to represent the heat transfer equation of a multicomponent electrochemical system.
Writing the general material balance for each species as
(3-31)
where Ri (mol/m3/s) is the local rate production source, the heat source expression may be simplified to
(3-32)
where the second term may be used to define the reaction enthalpies of non-Faradaic reactions (for Faradaic reactions, see below).
The derivations below follow a simplified approach along the principles lined out in Ref. 1. For deepened discussion on thermal effects in electrochemical cells, the reader is referred to Ref. 1 to Ref. 4.
In the derivations, the partial molar species enthalpies are defined as
(3-33)
where is the potential-independent partial molar enthalpy (J/mol) and ϕ the electrostatic potential (V). Apart from when heat of mixing effects are present, is constant.