Stationary magnetohydrodynamical flows of non-isothermal polymeric liquid in the flat channel

This paper studies the problem of the magnetohydrodynamical flow of incompressible conductive polymeric liquid inside the flat channel in the magnetic field. There is an electric current flowing on the walls of the channel. The walls themselves have different constant temperature. The magnetohydrodynamical model we use in the paper is based on the modified rheological Pokrovskii–Vinogradov model with additional Maxwell equations. We obtain the boundary value problem for this model and look for specific steady-state solutions which are alike the well-known viscous flows of Poiseuille and Couette. The problem for such solutions is reduced to a boundary value problem for a system of nonlinear ordinary differential equations, which in turn is transformed to the system of integral equation. We solve this system by fixed-point iterations. We examine the solutions for various values of parameters and study the influence of these parameters at the flow regime. The results of the paper show that is possible to control the flow of liquid polymer in a flat channel using an external magnetic field and non-inform heating.