A Method for Obtaining Analytical Solutions to Boundary Value Problems by Defining Additional Boundary Conditions and Additional Sought-For Functions

Abstract

A method of obtaining analytical solutions to thermal conduction problems is considered. It is based on a separation of thermal conduction into two stages of its time evolution using additional boundary conditions and additional sought-for functions in the heat balance integral method. Solving the partial differential equations is thus reduced to the integration of two ordinary differential equations for some additional sought-for functions. The first stage is characterized by fast convergence of an analytical solution to the exact one. For the second stage, an exact analytical solution is obtained. The additional boundary conditions for both stages are such that their fulfillment by the sought-for solution is equivalent to the fulfillment of the original equation at the boundary points and at the temperature perturbation front. It is shown that if the equation is valid at the boundary points, it is also valid inside the domain.