Convective instabilities in thermoviscoelastic micropolar fluids.

Abstract

The infinitesimal instabilities in plane horizontal layer of viscoelastic micropolar fluid under uniform heating are investigated. The micropolar fluid is a fluid each particle of which has a six degrees of freedoms of rigid body. This model possesses a couple stresses and rotational interaction of particles. Hydrodynamics of micropolar fluids has significant applications to a variety of different fields of physics and engineering (magnetohydrodynamics, tribology etc.). Like a model of liquid crystals of nematic or smectic type, the constitutive equations of viscoelastic fluids have property of orientation elasticity. The governing equations of viscoelastic micropolar fluid of differential type are considered. The temperature e_ects are described by using Oberbeck-Boussinesq approximation. The linearized initial boundary problem is deduced and its solutions are obtained. The neutral lines are presented. The material characteristics influence on the critical values of Rayleigh or Grashof numbers is investigated. It is shown that taking into account of the orientation elasticity property of viscoelastic fluid leads to the increasing of critical Rayleigh or Grashof numbers