“Integer” and “fractional” solutions of Fourierʹs problem of a ring heated by moving δ-source of energy

The new exact solutions of the classical Fourierʹs problem of heat conduction in a thin ring with a moving periodical δ-source of energy are obtained. Such kind of solutions of heat conduction equation is not yet studied in the literature. It is shown that they are typical for the heating of rotating hollow bodies and can be used for quantitative description of heat transfer through the moving caterpillar track. Under some conditions the “integer” solution of heat conduction equation can be approximated with a high accuracy by means of a strict succession of positive whole numbers.