Dual-phase-lag heat conduction in the composites by introducing a new application of DQM
- 15 Downloads
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
Heat source, J
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.
- 1.Wang L, Zhou X, Wei X (2007) Heat ceonduction: mathematical models and analytical solutions. Springer Science & Business MediaGoogle Scholar
- 12.Vernotte P (1961) Some possible complications in the phenomena of thermal conduction. Comptes Rendus 252:2190–2191Google Scholar
- 22.Wang L, Zhou X (2000) Dual-phase-lagging heat conductionGoogle Scholar
- 24.Basirat H, Ghazanfarian J, Forooghi P (2006) Implementation of dual-phase-lag model at different knudsen numbers within slab heat transfer. In: Proceedings of the International Conference on Modeling and Simulation (MS06), Konia, Turkey, vol 895Google Scholar
- 33.Polyanin AD, Zaitsev VF (2016) Handbook of nonlinear partial differential equations. Chapman and Hall/CRCGoogle Scholar