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Exact Relations Satisfied by the Effective Tensors of Two-Dimensional Two-Phase Thermoelectric Composites
Childs, Sarah Rebekah
Childs, Sarah Rebekah
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Thesis/Dissertation
Date
2020
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Mathematics
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DOI
http://dx.doi.org/10.34944/dspace/311
Abstract
Thermoelectric materials have been used for cooling and heating systems for
over a hundred years. Today practical applications of thermoelectric devices
include cooling car seats, power generation, and
refrigeration. Thermoelectric materials are special for their ability to
convert temperature imbalances into electricity. Their applications can
inform the discourse about the transition to renewable energy
sources---something that our Earth most desperately needs. The goal of this
dissertation is to describe how the effective tensors of two-dimensional
thermoelectric composites made from two isotropic materials depend on
thermoelectric parameters of the constituents. Using the theory of exact
relations and links developed by Grabovsky and his collaborators, we
describe all equations satisfied by the thermoelectric effective tensor of a
composite without the explicit knowledge of its microstructure. In some
special cases, the effective tensor can be determined completely. Even in
the general case, four out of 10 components of the two-dimensional
thermoelectric tensor can be expressed in terms of the remaining 6,
regardless of the microstructure. We started with special cases and worked
our way up to the more general ones.
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