P004.md

P004: Thermoelectric compatibility factor (CF) (G.J. Snyder et al., 2003)

• G.J. Snyder, T.S. Ursell, Thermoelectric efficiency and compatibility, Phys. Rev. Lett. 91 (14830114) (2003). https://doi.org/10.1103/PhysRevLett.91.148301.

• W. Seifert, K. Zabrocki, G.J. Snyder, E. Müller, The compatibility approach in the classical theory of thermoelectricity seen from the perspective of variational calculus, physica status solidi (a) 207 (3) (2010) 760-765. https://doi.org/10.1002/pssa.200925460.

• W. Seifert, V. Pluschke, C. Goupil, K. Zabrocki, E. Müller, G.J. Snyder, Maximum performance in self-compatible thermoelectric elements, J. Mater. Res. 26 (15) (2011) 1933-1939. https://doi.org/10.1557/jmr.2011.139.

$$ $$

$$ +------------------------------------------+ $$

For the thermoelectric generator:

$$ s = \frac{\sqrt{1+ZT}-1}{ST} $$

For the Peltier cooler:

$$ s = \frac{-\sqrt{1+ZT}-1}{ST} $$

$$ +------------------------------------------+ $$

For generators thermally in parallel:

$$ \eta _{np} = \frac{\eta _{p} Q_{p} + \eta _{n} Q_{n}}{Q_{p} + Q_{n}} $$

For two segments thermally in series:

$$ \eta _{1,2} = \frac{P_{1} + P_{2}}{Q_{1}} = 1 - (1-\eta _{1})(1-\eta _{2})$$

$$ +------------------------------------------+ $$

$$ u = \frac{J}{\kappa \nabla T} $$

$$ \Phi = ST+1/u $$

$$ \eta = 1 - \frac{\Phi(T_{c})}{\Phi(T_{h})} $$

$$ COP = \left( \frac{\Phi(T_{h})}{\Phi(T_{c})} - 1 \right) ^{-1} $$

$$ +------------------------------------------+ $$