Unsteady Heat Conduction of a Spherical Body with an Internal Cavity under Mixed Boundary Conditions

The article studies the characteristic equation arising in the problem of heating/cooling a hollow sphere under boundary conditions of the first kind using analytical methods. The obtained mathematical formulas make it possible to calculate the eigenvalues \({{\mu }_{n}}\) of this problem and determine the numerical values of the dimensionless temperature. Expressions for the eigenfunctions \({{K}_{n}}\left( \psi \right)\) and coefficients \({{A}_{n}}\) are also given. To improve calculation accuracy, the simple principle of subsequent approximation can be used by passing to the inverse function.