Niestacjonarny Przepływ Ciepła w Grubej Rurze Ogrzanej Ruchomym Polem Temperatury - Różnowski, T.; Skalski, K. (Engineering Transactions, 1971)
A solution is given to the nonsteady problem of temperature in a long hollow cylinder suddenly heated by a moving ramp type temperature along its inner and outer boundary. The classical heat equation with constant coefficients subject to the initial and boundary conditions (2.2) is assumed as a point of departure. The solution is obtained in the form of infinite series involving both Bessel functions and error functions. Limiting cases are discussed when (i) the thermal load tends to a step function and (ii) the velocity of the boundary temperature goes to zero.