Stationary boundary value problem of heat conduction for thin cylindrically isotropic ring plates
Stationary temperature fields in a thin ring plate are studied. Linear distribution of temperature along the \(z\) coordinate is assumed: \(t(r,\varphi,z)=T_1(r,\varphi)+z\delta^{-1}T_2(r, \varphi)\), where \(\delta\) is the plate thickness. 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 (in angular coordinate) and the Hankel (in radial coordinate) transforms. General formulas for the Fourier coefficients of solution are presented.
scientific article; zbMATH DE number 1670317