Phonon transport across constrictions formed by a nanowire or a nanoparticle on a substrate is studied by a numerical solution of the gray Boltzmann transport equation (BTE) resolving the effects of two length scales that govern problems of practical importance. Predictions of total thermal resistance for wire/substrate and particle/substrate combinations are made for the entire range of Knudsen number, with an emphasis on resolving transport in the mesoscopic regime where ballistic-diffusive mechanisms operate and analytical expressions are not available. The relative magnitudes of bulk and constriction resistance are established, and a correlation for overall thermal resistance spanning the range of practical Knudsen numbers is provided.
Issue Section:
Micro/Nanoscale Heat Transfer
Keywords:
ballistic transport,
Boltzmann equation,
diffusion,
Knudsen flow,
mesoscopic systems,
nanoparticles,
nanowires,
phonons,
thermal conductivity,
Boltzmann transport equation,
constriction resistance,
ballistic-diffusive transition,
gas gap conductance,
slip flow and heat transfer,
Knudsen number,
temperature jump
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