Combined Method of Separation of Variables. 4. Nonstationary Heat Conduction in Solids with Boundary Conditions of the Second Kind

The combined method of separation of variables applied to the solution of the initial boundary-value problems on the nonstationary heat conduction in solids canonical in shape (plate, cylinder, sphere) with boundary conditions of the second kind is presented. New schemes of calculating the eigenvalues and eigenfunctions of such a problem and the coefficients of expansion of its initial condition in terms of eigenfunctions are proposed and substantiated. The simplicity and, at the same time, the high efficiency of solving this problem by the method developed in a definite approximation are demonstrated.