Passage of an electric current through a long conducting rod

Passage of an electric current through a long conducting rod of radius r j and thermal conductivity k results ri uniform volumetric heating at a rate of q. The conducting rod is wrapped in an electrically non-conducting cladding material of outer radius ro and thermal conductivity kc, and convection cooling is provided by an adjoining fluid.

Conducting rod, q, k, T, h Čladding, ke

For steady-state conditions, write appropriate forms of the heat equations for the rod and cladding. Express appropriate boundary conditions for the solution of these equations.