Convective instabilities in thermoviscoelastic micropolar fluids

Victor A. Eremeyev (1, 2) , Denis A. Sukhov (2)

1 Southern Scientific Center
2 Mechanics and Mathematics Department

Infinitesimal instabilities in plane horizontal layer of visco-elas-tic micropolar fluid under uniform heating are investigated. A micropolar fluid is a fluid whose particles have the six degrees of freedom of a rigid body. This model possesses couple stresses and rotational interaction of particles. Hydrodynamics of micropolar fluids has significant applications to a variety of different fields of physics and engi-nee-ring (magnetohydrodynamics, tribology etc.). Like a model of liquid crystals of nematic or smectic type, the constitutive equations of viscoelastic fluids have the property of orientation elasticity. The governing equations of viscoelastic micropolar fluid of differential type are considered. The temperature effects are described by using the Oberbeck-Boussinesq approximation. The linearized initial boundary problem is de-du-ced and its solutions are obtained. The neutral lines are presented. The material characteristics influence on the critical values of Rayleigh or Grashof numbers is investi-ga-ted. It is shown that taking into account the orientation elasticity property of viscoelastic fluid leads to the increasing of critical Rayleigh or Grashof numbers

Domaines: Mécanique [physics.med-ph]

Victor A. Eremeyev, Denis A. Sukhov. Convective instabilities in thermoviscoelastic micropolar fluids. Matemáticas: Enseñanza Universitaria, 2005, XIII (1), pp.31-42. ⟨hal-00835624⟩