On thermal solitons with wave heat transfer in restricted areas

This paper simulates wave heat transfer based on an analysis of the dynamics of an isolated heat wave (thermal soliton). An isolated thermal wave arises under the action of a thermal impulse that acts for a short time and moves along a cold region. Unlike a continuous thermal process in a nonequilibrium state, when the moving front of a traveling heat wave occurs in a semi-infinite body, a thermal soliton has two fronts, anterior and posterior. There is a temperature distribution noted between them over the spatial variable. First-order gaps in the temperature distribution are observed on these fronts with decreasing amplitude due to the dissipation of thermal energy. Reaching the opposite boundary, the soliton is not reflected in the same way as a mechanical wave. At first, the vicinity of the opposite boundary heats up to a certain level, and the soliton then moves along cold space in the opposite direction with decreasing amplitude. The results of an analytical solution of the wave heat transfer problem on the basis of the hyperbolic-type heat conduction equation with allowance for relaxation phenomena are presented.