Relaxation model for heat conduction and generation and the 2nd law

This paper presents a phenomenological analysis of the relaxation model for heat conduction and generation from the point of view of its consistency with the second law of thermodynamics. The formulation of the second law based on classical irreversible thermodynamics as well as that based on extended irreversible thermodynamics are considered. It is shown that introduction of the transient capacity of the heat source into the energy conservation equation does not lead to any inconsistency with the second law. An analogy between the heat transport and the motion of a particle in the resistive medium is presented. The analysis shows that an inherent property of Cattaneo's model for heat conduction is that heat may flow spontaneously from cold to hot regions.