Equipartition of Joulean Heat in Thermoelectric Generators

Abstract

The present article is devoted to the study of a thermoelectric generator from the perspective of a heat engine. Two important dimensionless parameters are identified to designate negligible Thomson effect; low thermal conductivity and poor electrical resistivity of a good semiconductor or semimetal. For ideal values of these parameters it has been demonstrated that the temperature maximum passes through the longitudinal center of a one-dimensional thermoelectric element while exactly half of the Joulean heat arrives at both hot and cold junction. When half the Joulean heat affects hot end and half the cold side, thermal conductance inventory (heat exchanger) is allocated equally between the high and low temperature side. The final architecture of a cascaded assembly of thermoelectric module exhibits a fractal like but deterministic (constructal) pattern that develops from the largest to the smallest scale with the fundamental construct being a T-shaped region in space. The physicists’ knowledge of equipartitioned Joulean heat and the engineers’ wisdom of equipartitioned heat exchanger allocation are unified with reference to a thermoelectric generator. The chief objective of this contribution is to draw the attention of the colleagues of cross disciplines that Bejan advocated for a possible cross fertilization of the field.