Maximum power and efficiency of an irreversible thermoelectric generator with a generalized heat transfer law

An advanced model of irreversible thermoelectric generator with a generalized heat transfer law is established based on finite time thermodynamics. The generalized heat transfer law represents a class of heat transfer laws including Newtonian heat transfer law, linear phenomenological heat transfer law, radiative heat transfer law, Dulong-Petit heat transfer law, generalized convective heat transfer law and generalized radiative heat transfer law. The inner effects including Seebeck effect, Fourier effect, Joule effect and Thomson effect, and external heat transfer are taken into account in the model. The EulerLagrange functions at maximum power output and maximum efficiency are established. Applying the model to a practical example in engineering, it is found that the external heat transfer law does affect the characteristics and optimal performance of the thermoelectric device, and the maximum power output and maximum efficiency with Newtonian heat transfer law are the maximum among the several typical heat transfer laws. The results can offer principles for the power and efficiency optimization of practical thermoelectric generators at various external heat transfer conditions.