Stability of a Poiseuille-type flow for a MHD model of an incompressible polymeric fluid

TL;DR

This paper investigates the stability of a Poiseuille-type flow in a magnetohydrodynamic model of incompressible polymeric fluids, extending classical flow stability analysis to nonisothermal, viscoelastic, and magnetic conditions.

Contribution

It provides a formal asymptotic eigenvalue analysis and establishes a necessary condition for the flow's asymptotic stability in a generalized MHD polymeric fluid model.

Findings

Derived asymptotic eigenvalue representations for the linearized problem

Identified a necessary stability condition for the flow

Extended classical flow stability analysis to nonisothermal, viscoelastic, MHD flows

Abstract

We study a generalization of the Pokrovski--Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeric medium to nonisothermal flows in an infinite plane channel under the influence of magnetic field. For the linearized problem (when the basic solution is an analogue of the classical Poiseuille flow for a viscous fluid described by the Navier-Stokes equations) we find a formal asymptotic representation for the eigenvalues under the growth of their modulus. We obtain a necessary condition for the asymptotic stability of a Poiseuille-type shear flow.