Thermal stress state of a cylinder whose thin surface layer possesses time dependent thermal properties under heating by volume heat sources (Q2870364)

The authors discuss the structure of solutions to the thermal elasticity problem for a long circular cylinder with a thin surface layer. The layer parameters of the heat transfer and the heat capacity vary in time under heating by volume heat sources of time-variable intensity and at cooling by the external medium. For the cylinder surface temperature, which becomes part of the solution structure, an integro-differential equation with variable coefficients and an integral Volterra-type operator is derived. For the solution of this equation, a spline approximation method is applied. A possibility to choose variable thermal parameters in order to partially counterbalance the action of the time-dependent heat sources is considered.