Passage of an electric current through a long conducting rod of radius r j and thermal conductivity k results r_i 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 k_c, and convection cooling is provided by an adjoining fluid.

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.