Non-stationary boundary value problem of heat conduction for thin cylindrically isotropic ring plates (Q2753480)

A non-stationary temperature field in a thin ring plate is studied. Linear distribution of temperature along the \(z\) coordinate is assumed: \(t(\tau, r, \varphi, z) = T_1(\tau, r, \varphi) + z\delta^{-1} T_2(\tau, r, \varphi)\), thus the problem is reduced to two-dimensional ones for functions \(T_1\) and \(T_2\). Different variants of boundary conditions on the boundaries of the plate are considered. The problem is solved using the finite Fourier (in angular coordinate) and the Hankel (in radial coordinate) transforms. General formulas for the Fourier coefficients of solution are presented.