The heat diffusion equation was established in 11.4.2, in the absence of any source term due

Question:

The heat diffusion equation was established in § 11.4.2, in the absence of any source term due to a conductive electric current density, i.e. j_q = q_e j_e = 0. Show that for an electric conductor in the presence of a conductive electric current density j_q, the heat equation becomes,where λ is the thermal diffusivity, σ is the electric conductivity, τ is the Thomson coefficient of the electric conductor and c is the specific heat density of the conduction electrons.