Variable heat generation (Wiedemann-Franz law) in a heated source

In the present work, we study analytically and numerically the variable heat generation of a source immersed in a laminar channel cooling flow. We assume this internal heat generation is proportional to the local electrical resistivity, represented through the well-known Wiedemann-Franz law. It provides a relationship between the local electrical resistivity and the temperature of the source. Taking into account a finite thermal conductivity of the source's material, the nondimensional temperature profile and maximum longitudinal temperature and average temperature differences have been obtained as functions of the nondimensional parameters α, γ and Pe. α is the heat conduction parameter and represents the competition between the longitudinal heat conduction in the material to the heat convection in the laminar cooling flow. γ is a nondimensional parameter associated with the temperature's dependence on the electrical resistivity. Pe is the characteristic Peclet number of the cooling flow. The numerical and asymptotic results of the above nondimensional variables show a very sensible dependence of the parameters α, γ and Pe. Therefore, this set of nondimensional parameters controls directly the thermal performance of this simplified generating-heat strip model.