analytical solution, exact solution, diffusion flows, variable internal source, parallelepiped, fast expansions

The authors solve the problem of diffusion in a parallelepiped-shaped body with boundary conditions of the 1st kind and an internal source of substance, depending on the parallelepiped points coordinates with the fast expansions method. The proposed exact solution in general form contains free parameters, which can be used to obtain many new exact solutions with different properties. An example of constructing an exact solution with a variable internal source depending on one coordinate z is shown in the work. An analysis of the features of diffusion flows in a parallelepiped with the indicated internal source is given. It was found that the concentration of a substance in the center of a parallelepiped is equal to the sum of the arithmetic mean of the concentration of a substance at its vertices and the amplitude of the internal source multiplied by the value c^2/Pi^2

Chernyshov Alexander Danilovich

e-mail: chernyshovad@mail.ru, Dr. Sci. Phys. & Math., Professor, Voronezh State University of Engineering Technology, Voronezh.

Goryainov Vitaly Valerievich

e-mail: gorvit77@mail.ru, Ph.D. Phys. & Math., Assoc. Professor, Voronezh State Technical University, Voronezh.

Kuznetsov Sergey Fedorovich

e-mail: sfs134@mail.ru, Ph.D. Phys. & Math., Assoc. Professor, Voronezh State University of Engineering Technology, Voronezh.

Nikiforova Olga Yurievna

e-mail: niki22@mail.ru, Senior Lecturer, Voronezh State University of Engineering Technology, Voronezh.