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Comparing the dual phase lag, Cattaneo-Vernotte and Fourier heat conduction models using modal analysis

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  • van der Merwe, A.J.
  • van Rensburg, N.F.J.
  • Sieberhagen, R.H.

Abstract

This paper deals with phase lag (or time-lagged) heat conduction models: the Cattaneo-Vernotte (or thermal wave) model and the dual phase lag model. The main aim is to show that modal analysis of these second order partial differential equations provides a valid and effective approach for analysing and comparing the models. It is known that reliable values for the phase lags of the heat flux and the temperature gradient are not readily available. The modal solutions are used to determine a range of realistic values for these lag times. Furthermore, it is shown that using partial sums of the series solutions for calculating approximate solutions is an efficient procedure. These approximate solutions converge in terms of a so-called energy norm which is stronger than the maximum norm. A model problem where a single heat pulse is applied to a specimen, is used for comparing these models with the Fourier (or parabolic) heat conduction model.

Suggested Citation

  • van der Merwe, A.J. & van Rensburg, N.F.J. & Sieberhagen, R.H., 2021. "Comparing the dual phase lag, Cattaneo-Vernotte and Fourier heat conduction models using modal analysis," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308870
    DOI: 10.1016/j.amc.2020.125934
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    References listed on IDEAS

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    1. Civin, D. & van Rensburg, N.F.J. & van der Merwe, A.J., 2018. "Using energy methods to compare linear vibration models," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 602-613.
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