A limit model for thermoelectric equations

Details A limit model for thermoelectric equations A limit model for thermoelectric equations

2010-02-05

arxiv.org/abs/1002.1255v2

Annali dell'Universita di Ferrara vol. 57 n.2 (2011), 229-244

Mathematics

Analysis of PDEs

20 pages

Scientific paper

10.1007/s11565-011-0129-1

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.

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