Dual-phase-lag heat conduction in the composites by introducing a new application of DQM

  • A. PourasgharEmail author
  • Z. Chen


The first application of the differential quadrature method (DQM) in solving the nonlinear dual-phase-lag (DPL) heat conduction equation is demonstrated here. To show the effect of DPL parameters, the temperature response of the medium was obtained from Fourier’s low, hyperbolic heat conduction and hyperbolic type DPL heat conduction model were compared. Furthermore, the transient temperature and resultant heat flux distributions have been found for various types of dynamic thermal loading. We show whether thermal waves exist or not in hyperbolic type DPL heat conduction by considering the time lag parameter in the microstructural interactions of fast transient heat conduction. Also, overshooting which is one of the hyperbolic heat conduction is investigated here. The numerical solution at each time level depends on the solutions at its previous levels. This means the temperature and heat flux obtained at the time nth are the initial conditions for the time (n + 1)th. After demonstrating the convergence and accuracy of the method, the effects of different parameters on the temperature and heat flux distribution of the medium are studied.



Specific heat, J/(kg.K)


Temperature gradient’s time lag, s


Heat flux’s time lag, s


Number of sampling points along spatial domain


Number of sampling points along temporal domain


Thermal conductivity, W/(m.K)


Time duration of a thermal shock, s


Thermal diffusivity, m2/s


Heat flux, W/m2


Temperature, K


Spatial domain


Temporal domain


Heat source, J


Density, kg/m3



The authors are grateful to the financial support to the current work provided by the Natural Science and Engineering Research Council (NSERC) of Canada.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of AlbertaEdmontonCanada

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