The influence of thermal relaxation and thermal damping on transient processes with cyclic boundary conditions

Variants of the differential equation of heat conduction in a solid body, which follow from the Fourier and Cattaneo–Vernotte hypotheses and the Lykov equation, are considered. A boundary value problem describing temperature fields in a body (cylinder) upon cyclic heat exchange with cold and hot media is formulated. An analytical solution to the boundary value problem with a hyperbolic differential equation of heat conduction with allowance for thermal relaxation and temperature damping with cyclic boundary conditions of the third kind is given. The thermal transient processes calculated by the classical heat equation and hyperbolic equation of heat conduction on the axis of the cylinder at different values of factors such as the ratio of the thermal damping time to the thermal relaxation time, the duration of cyclic periods, the Fourier relaxation number, and the Biot number are compared. A conclusion is made that the theory of regenerative air heater should be improved by taking into account thermal relaxation and thermal damping in the nozzle and measurements of the thermal relaxation and thermal damping times of the corresponding materials.