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Prediction of the Effective Thermal Diffusivity of Discretely Inhomogeneous Media

[+] Author Affiliations
Daniel W. Mackowski, Mario Ramos

Auburn University, Auburn, AL

Paper No. HT2009-88508, pp. 331-338; 8 pages
doi:10.1115/HT2009-88508
From:
  • ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences
  • Volume 2: Theory and Fundamental Research; Aerospace Heat Transfer; Gas Turbine Heat Transfer; Computational Heat Transfer
  • San Francisco, California, USA, July 19–23, 2009
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 978-0-7918-4357-4 | eISBN: 978-0-7918-3851-8
  • Copyright © 2009 by ASME

abstract

An extended definition of the effective thermal diffusivity is posed via an analogy to acoustic and EM wave propagation in discretely inhomogeneous media. Specifically, the propagation of a periodic, plane thermal wave of frequency ω, through an inhomogeneous medium consisting of spherical particles embedded in a continuous matrix, is theoretically examined. An exact solution for the time–harmonic conduction equation, for the multiple sphere system, is developed by use of the scalar wave harmonic functions and the addition theorem for the harmonics. An effective medium model, which is based on the Quasi–Crystalline approximation (QCA) for acoustic and EM wave propagation, is developed, and a formulation for the frequency–dependent effective thermal diffusivity is derived. In the limit of x = Rω/α0→0, where R is the sphere radius and α0 the matrix thermal diffusivity, it is shown that formulation reduces to that derived from a static model.

Copyright © 2009 by ASME

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