Joule Heating Due to Charge Transport
To derive the heat source for Joule heating we assume a domain where there are no species sources, nor heat of mixing effects present.
As charged species travel in an electric field, the enthalpy changes according to the gradient in the electric potential
ϕ
(V)
(3-34)
where
z
i
is the species charge.
For a current conductor, the only species carrying charge is the electron, with a negative unit charge. The electron flux is related to the current density
i
s
as
(3-35)
resulting in
(3-36)
where the subscript
s
denotes the electron conducting phase.
For the electrolyte phase, the heat source becomes
(3-37)
For a homogenized porous electrode domain, the Joule heating term for both phases are added together:
(3-38)
