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CHAPTER
ONEMICROSCALE ENERGY TRANSPORT IN SOLIDS
Arunava Majumdar
Department ofMechanical Engineering,
University ofCalifornia,
Berkeley, CA 94720
1-1 INTRODUCTION
Recent trends in science and technology have indicated an increasing emphasis on minia
turization of engineering systems and study ofmicroscale phenomena. Examples of such
systems include modem microelectronic devices, the development ofmicromechanical
devices and systems, and microsensors. Many such devices and systems utilize con
trolled transport of mass, energy, and/or charge. Therefore, t he s tudy of microscale
transport phenomena has become an integral part of not only understanding the per
formance and operation of miniaturized systems, but also designing new devices. Mi
croscale charge transport has been studied extensively for many years, espcially in the
context ofmodem microelectronic devices. Mass transport and chemical reactions alsohave received attention for understanding processes such as chemical vapor desposition
and biological reactions. In contrast, microscale energy transport has received lim
ited attention in the context of miniaturized engineering systems. The second law of
thermodynamics requires that any irreversible transport of mass or charge must involve
entropy generation and thereby some exchange of energy with the surroundings. Energy
transportcontrols the performance of several miniaturized systems and is an important
ingredient in the processing of mate rial s. I t is clear that microscale energy transport is
both fundamental from a scientific viewpoint and important for engineering applications.
Inthis chapter, we will investigate the differentmechanisms of energy
transport in solids.
There exists two different ways to study energy transport in materials: the macro
scopic approach and the microscopic approach. The macroscopic approach uses phe
nomenological models that require no knowledge of the mechanism of energy transport
or the microstructure of solids. It focuses on the overall large-scale effects and requires
only a constitutjve relation or a simple transport law. Such a relation usually contains
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