Abstract
In the paper the different variants of the dual phase lag equation (DPLE) are considered. As one knows, the mathematical form of DPLE results from the generalization of the Fourier law in which two delay times are introduced, namely the relaxation time τqand the thermalization one τT. Depending on the order of development of the left and right hand sides of the generalized Fourier law into the Taylor series one can obtain the different forms of the DPLE. It is also possible to consider the others forms of equation discussed resulting from the introduction of the new variable or variables (substitution). In the paper a thin metal film subjected to a laser pulse is considered (the 1D problem). Theoretical considerations are illustrated by the examples of numerical computations. The discussion of the results obtained is also presented.
Highlights
The macroscopic heat conduction model results from the assumption of instantaneous propagation of the thermal wave in the domain under considerations
Seventy years ago Cattaneo [1] formulated an equation in which the delay time of the heat flux in relation to the temperature gradient was taken into account
The very high heating rates typical for the microscale heat transfer cause that the inclusion of the finite value of thermal wave velocity must be somehow taken into account
Summary
The macroscopic heat conduction model (the Fourier model) results from the assumption of instantaneous propagation of the thermal wave in the domain under considerations. Seventy years ago Cattaneo [1] formulated an equation in which the delay time (relaxation time τq) of the heat flux in relation to the temperature gradient was taken into account. This hyperbolic PDE is known as the Cattaneo-Vernotte equation. The very popular model describing the microscale heat transfer is based on the dual phase lag equation (DPLE) – e.g. At the stage of numerical modeling the 1D problem is considered It results from the thermal aspects of the task discussed
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