3.4 Modeling Current Transport and the Potential Field

Solving for three-dimensional electrical conduction is directly analogous to the calculation of heat transfer. The potential field throughout the conductive regions is calculated based on the conservation of charge.

where

and $\sigma$ is the electrical conductivity and $\phi$ is the electrical potential. Therefore, the governing equation for the electric field is the Laplace equation:

The electric field potential calculation combines the following attributes:

• Ohmic losses in all the conducting materials, including the electrolyte, electrodes, and current collectors.

• Contact resistance at the appropriate interfaces.

• Ohmic heating through conduction materials as the result of ohmic losses, and the current density throughout the domain.