2012 | OriginalPaper | Chapter
Coupled Effects: Joule-Heating
Author : Tarek I. Zohdi
Published in: Electromagnetic Properties of Multiphase Dielectrics
Publisher: Springer Berlin Heidelberg
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Heterogeneous microstructures lead to a distortion of the electrical and current field within the material mixture. This leads to the fields becoming amplified within the material, which can lead to a variety of detrimental effects. An important quantity of interest is the amount of heat generated from an electrical field. The interconversions of various forms of energy (electromagnetic, thermal, etc.) in a system are governed by the first law of thermodynamics (which will be derived in detail shortly),
$\rho \dot{w}-{\bf T}:\nabla \dot{{\bf u}}+\nabla \cdot{\bf q}-H=0,$
(6.1)
where
ρ
is the mass density,
w
is the stored energy per unit mass,
T
is Cauchy stress,
u
is the displacement field,
q
is heat flux, and
H
is the rate of electromagnetic energy absorbed due to Joule-heating (a source term)
$H=a\left(\bf J \cdot \bf E\right),$
(6.2)
where 0 ≤
a
≤ 1 is an absorption constant. This standard form of Joule-heating is derived in the next chapter. Thus, a material designer must seek ways by which to modify a base material in order to deliver a specified overall conductivity (for example, by employing particulate additives), while simultaneously avoiding overheating.