New integral relationships based on the Tikhonov–Samarsky potential for analytical solutions boundary problems of nonsteady transfer

An improved approach based on the heat potentials described by Tikhonov and Samarsky as reference to boundary problems for equations of parabolic type in non-cylindric areas was developed. For the area with nonuniformly moving boundary the method gives new (the simplest) integral relationships of a new form with respect to the results that was known earlier. They allow to consider many partial cases having a practical interest for numerous applications of the nonsteady transfer process.