Exact harmonic solution to ballistic type heat propagation in thin films and wires

The system of hyperbolic type differential equations is considered for non-Fourier heat transfer in thin films and wires. Structures of the harmonic solutions for telegrapher equation and for Guyer-Krumhansl equation are identified and compared with each other. The exact harmonic solution is obtained; the influence of the phonon heat transfer is explored. The maximum principle violation is demonstrated. Frequency dependence of the solution for Guyer-Krumhansl equation is shown. The exact analytical solution is derived for the inhomogeneous ballistic-diffusion set of differential equations, governing heat propagation in thin films. The contribution of the ballistic, wave and diffusive heat transfer components as well as the influence of the initial conditions and of the Knudsen number on heat conduction in thin films and wires are investigated. The cases of identical and different from each other Knudsen numbers for ballistic and diffusive components are explored. The examples of exact solutions for the heat transfer in each case are demonstrated.