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Transient Heat Conduction in a Functionally Graded Cylindrical Panel Based on the Dual Phase Lag Theory

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Abstract

The transient heat conduction in a functionally graded cylindrical panel is investigated based on the dual phase lag (DPL) theory in this article. Except for the phase lags which are assumed to be constant, all the other material properties of the panel are assumed to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations based on the DPL theory in the cylindrical coordinate system are written in a general form which are then used for the analyses of four different geometries: (1) a hollow cylinder of an infinite length; (2) a hollow cylinder of a finite length; (3) a cylindrical panel of an infinite length; and (4) a cylindrical panel of a finite length. Using the Laplace transform, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expressions for the radial thermal wave speed are obtained for the four different geometries. The numerical results are displayed to reveal the effect of different approximations of the DPL theory on the temperature distribution for various non-homogeneity indices. The results are verified with those reported in the literature.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    A. H. Akbarzadeh & Z. T. Chen

Authors
  1. A. H. Akbarzadeh
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  2. Z. T. Chen
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Correspondence to Z. T. Chen.

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Akbarzadeh, A.H., Chen, Z.T. Transient Heat Conduction in a Functionally Graded Cylindrical Panel Based on the Dual Phase Lag Theory. Int J Thermophys 33, 1100–1125 (2012). https://doi.org/10.1007/s10765-012-1204-2

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  • DOI: https://doi.org/10.1007/s10765-012-1204-2

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