Exact Solution of a Constraint Optimization Problem for the Thermoelectric Figure of Merit

Materials (Basel). 2012 Mar 21;5(3):528-539. doi: 10.3390/ma5030528.


In the classical theory of thermoelectricity, the performance integrals for a fully self-compatible material depend on the dimensionless figure of merit zT. Usually these integrals are evaluated for constraints z = const. and zT = const., respectively. In this paper we discuss the question from a mathematical point of view whether there is an optimal temperature characteristics of the figure of merit. We solve this isoperimetric variational problem for the best envelope of a family of curves z(T)T.

Keywords: device optimization; figure of merit; functionally graded material; thermoelectricity.