Exact solution of the dual-phase-lag heat conduction model for a one-dimensional system excited with a periodic heat source

The one-dimensional thermal wave transport in a semi-infinite medium is studied under the framework of the dual-phase lag model of heat conduction in its exact form considering a modulated thermal excitation for Dirichlet and Neumann boundary conditions. By requiring that the thermal waves have physical meaning, it is shown that their validity is restricted to an interval of permitted modulation frequencies, which depend only on the difference of the time delays corresponding to the medium where the thermal waves propagate. The behavior of characteristic propagation properties of the thermal waves, such as the wavelength, penetration depth, phases and group velocities are discussed. In addition, formulas to determine the difference of the time delays as well as other thermal properties of a semi-infinite layer are obtained.