Abstract
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.
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© 2012 Springer Berlin Heidelberg
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Zohdi, T.I. (2012). Coupled Effects: Joule-Heating. In: Electromagnetic Properties of Multiphase Dielectrics. Lecture Notes in Applied and Computational Mechanics, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28427-4_6
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DOI: https://doi.org/10.1007/978-3-642-28427-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28426-7
Online ISBN: 978-3-642-28427-4
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