Invariant solutions of viscoplasticity equations and solution of the problem of helical motion of a bingham fluid between coaxial cylinders

Abstract

Besides numerical methods of solution, exact solutions are very important for any equation, especially those which describe the motion of real media. They make it possible to reveal the qualitative characteristics of the phenomena studied, to construct asymptotic solutions of specific problems, and in some cases to find the actual solutions. On the basis of methods of group analysis of differential equations we construct two classes of exact solutions and give a mechanical interpretation of them. The second class of exact solutions is used to construct a closed solution of problems of the helical motion of a Bingham fluid between two coaxial cylinders. i. Group Properties of the Equations of Steady-State Isothermal Flow of a Viscoplastic Medium. The systems of equations describing the slow flow of a viscoplastic medium can be written as [i, 2]