Development of approximate analytical method for modeling transient thermal processes using S-functions

Abstract

A new methodology for mathematical modeling of transient thermal processes in structural components is proposed. It is based on the joint application of the structural method, the Bubnov-Galerkin method and S-functions to solving heat conduction problems with unsteady boundary conditions of the third kind. The analytic structures for solving these problems, accurately satisfying unsteady boundary conditions at any given time dependence of the heat transfer coefficient and ambient temperature are constructed. These qualitative features of the analytic structures for solving heat conduction problems have allowed first proposed solution methods to obtain approximate analytical solutions of these problems.

Using the Bubnov-Galerkin method has allowed to reduce solving heat conduction problems with unsteady boundary conditions to solving the system of ordinary differential equations with respect to the unknown time-dependent coefficients of problem solution structures. Herewith, in the given system of ordinary differential equations, known time-dependent coefficients contain the heat transfer coefficients and the ambient temperature in analytical representation at their any given time dependence. This first allows one-dimensional unsteady heat conduction problems (infinite plates, cylinder, hollow sphere) to obtain an approximate analytical solution of unsteady heat conduction problems for those options of time dependence of the heat transfer coefficient and the ambient temperature, for which the operating method is not applicable.