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Research Papers: Micro/Nanoscale Heat Transfer

Phonon Transport Across Mesoscopic Constrictions

[+] Author and Article Information
Dhruv Singh

School of Mechanical Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907singh36@purdue.edu

Jayathi Y. Murthy1

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907jmurthy@ecn.purdue.edu

Timothy S. Fisher2

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907tsfisher@ecn.purdue.edu

1

Corresponding author.

2

Present address: Air Force Research Laboratory Thermal Sciences and Materials Branch (AFRL/RXBT), Wright-Patterson AFB, OH 45433-7750.

J. Heat Transfer 133(4), 042402 (Jan 11, 2011) (8 pages) doi:10.1115/1.4002842 History: Received December 21, 2009; Revised June 29, 2010; Published January 11, 2011; Online January 11, 2011

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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the geometry being simulated and the corresponding computational mesh. The contact width of the nanowire with the substrates is 2a and D is the wire diameter (top). The contact diameter of a nanoparticle with substrates is 2a and D is the particle diameter (bottom). A 2D axisymmetric model of particle on substrate is simulated.

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Figure 2

Definition of ΔTjump, ΔTwire, and ΔTsub: the solid line shows the computed temperature profile and dash-dotted lines show the fitted temperature profile in each section

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Figure 3

Contours of dimensionless temperature in wire and substrates for (a) Fourier conduction and (b) gray BTE for D∗=0.15 and 2a∗=0.45×10−2

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Figure 4

Temperature distribution along the center line for wire between substrates by Fourier diffusion and gray BTE for D∗=0.15 and 2a/D=0.03, 0.09

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Figure 5

Variation of contact resistance with D∗ for a wire between substrates, 2a/D=0.03

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Figure 6

Variation of contact resistance with D∗ for a sphere between substrates, 2a/D=0.04

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Figure 7

Correction factor γ as a function of 2a∗ for wire, sphere, and point contact

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Figure 8

Variation of constriction resistance with constriction width 2a/D

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Figure 9

Schematic of the geometry and unstructured mesh used in coupled BTE-Fourier slip calculation

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Figure 10

Contours of nondimensional temperature for thermal conduction across nanoparticle of diameter 40 nm (left) and 2.8 μm(right) sandwiched between two substrates with air in the surrounding gap. 2a/D=0.04

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