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

•Dual phase lag, Cattaneo-Vernotte and Fourier heat conduction models are compared.•Modal analysis provides realistic values for lag times of DPL and CV models.•Approximate series solutions converge in terms of an energy norm which is stronger than the maximum norm.•Heat pulse progresses slower into specimen for DPL and CV models than for Fourier model.•Vibrational analysis provides insight into series solutions of DPL and CV models. 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.