current and temperature dependent conductivity (sigma(T,j) )

Dear all,

I am trying to model a conducting wire, where the conductivity depends both on the actual temperature and the actual current density. The temperature dependence is no problem. But I don´t know how to add the j dependecny.

I am using the electric current and heat tansfer modules. Is it only possible to solve linear equations?
Sigma(T,j) would be non-linear, as j also depends on the temperature.


Thanks for any help or comments