Exact Solution for Hyperbolic Heat Equation and for Guyer–Krumhansl Type Equation

The heat transfer in the mathematical framework of the Guyer–Krumhansl model is studied. Exact analytical one-dimensional solution for Guyer–Krumhansl equation is obtained The operational approach is employed. With its help the propagation of various pulses of heat in the medium is studied with account for phonon and ballistic heat transport. The obtained results are used for modelling heat transfer in ultra-thin films with account for molecular effects in systems with reduced dimensions. We model propagation of ultra short laser heat pulses and propagation of isolated smooth spatial heat waves with account for the Knudsen . The solution for periodic function is obtained. The exact solutions of the above problems are studied in the model of thin films; the maximum principle and the non-negativity of the solutions are discussed in the context of heat conduction.