Modeling of heat transport and exact analytical solutions in thin films with account for constant non-relativistic motion

Abstract

One-dimensional heat equations beyond Fourier law with account for non-relativistic motion of an observer with respect to the media are considered. Some analytical solutions to these heat transport equations are obtained. The effect of the motion of the observer in the media is studied. Heat transport in thin films is modelled by the system of inhomogeneous differential equations (DE), which involve Guyer–Krumhansl-type and Telegrapher's type equations. Analytical solution to this system is found for the initial Gaussian distribution in the case of Cauchy conditions and for zero initial heat flux. The comparative analysis of the obtained solutions is performed in wide range of Knudsen numbers, Kn⊂[0.1–1]. The effect of the relative media–observer speed on the perceived heat transport is explored.