Non-stationary boundary value problem of heat conduction for thin cylindrically isotropic sectoral plate (Q2753492)

A non-stationary temperature field in thin sectoral plate \(0\leq r\leq R\), \(0\leq \varphi\leq \varphi_0<2\pi\), \(-\delta\leq z\leq \delta\) is studied. Linear distribution of temperature along \(z\) 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 at plate boundaries are considered. The problem is solved using the finite Fourier and the Hankel transforms. General formulas for the Fourier coefficients of solution are presented.