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Application of Elastic Dispersion Relations to Estimate Thermal Properties of Nano-Scale Rods and Tubes of Varying Wall Thickness and Diameter

[+] Author Affiliations
Michael F. Bifano, Pankaj B. Kaul, Vikas Prakash

Case Western Reserve University, Cleveland, OH

Ajit Roy

Wright-Patterson AFB, Dayton, OH

Paper No. IMECE2009-13302, pp. 277-287; 11 pages
  • ASME 2009 International Mechanical Engineering Congress and Exposition
  • Volume 14: Processing and Engineering Applications of Novel Materials
  • Lake Buena Vista, Florida, USA, November 13–19, 2009
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4387-1 | eISBN: 978-0-7918-3863-1
  • Copyright © 2009 by ASME


This paper reports the dependency of specific heat and ballistic thermal conductance on geometry and size in freestanding isotropic non-metallic crystalline nanowires and nanotubes having varying wall thicknesses and outer diameters. The analysis is performed using real dispersion relations found by numerically solving the Pochhammer-Chree frequency equation of a tube. The frequency equation is derived from the 3D cylindrical elastic wave model with stress free boundary conditions on both the inner and outer wall surfaces. Dimensional dependencies are distinctly noticeable and vary with specimen geometry and temperature. Trends in dimensional transition points are seen by varying the ratio of inner to outer nanotube radius (γ) for a 5 nm fixed outer diameter. With increasing γ, heat capacity and ballistic thermal conductance is shown to collapse onto that of a solid nanowire. Additionally, thermal properties of thick-walled nanotubes (γ = 0.5) having diameters of 5 nm, 10 nm, 15 nm, and 20 nm, are also investigated in this study. Increasing the diameter of a nanotube with a fixed γ is shown to have a similar mechanistic effect as fixing the outer diameter and thinning the tube wall.

Copyright © 2009 by ASME



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