Analytical solutions to various problems of thermal conductivity are presented, as a rule, in the form of infinite series and require knowledge of the roots of the characteristic equation, for the determination of which numerical methods are currently used. In this article, the problem of unsteady thermal conductivity of a hollow spherical body and an analytical method for solving a characteristic equation for boundary conditions of the second kind are considered. Simple algebraic expressions for determining the eigenvalues of the characteristic equation are proposed. Earlier in the works of the authors 6, 7, 8, analytical methods for solving characteristic equations for flat bodies (single-layer and multi-layer) under various boundary conditions were considered. This article is a further development of analytical methods for determining the roots of characteristic equations.
Yu. V. Vidin (Wed,) studied this question.