M. S. Krakov ¹, I. V. Nikiforov ².

1. Belarussian State Polytechnic Academy, Belarus, 220027, Minsk, 65, F.Skorina Ave.

2. Belarussian State University, Belarus, 220050, Minsk, 4, F. Scorina Ave.

Introduction.

It’s well known that magnetic field influences natural convection in magnetic fluids. The main reason of the influence is additional magnetic force arising in magnetic fluids because of nonuniform magnetic field. In some cases outer uniform magnetic field affects the natural convection too. Geometry of the cavity filled with magnetic fluid and temperature dependence of fluid magnetization has an influence on the magnetic field distribution in the cavity: outer uniform magnetic field becomes uniform. As a result, magnetic field influence on the natural convection.

The present paper studies the natural convection in square cavity filled with magnetic fluid in the presence of outer uniform magnetic field. The governing equations are the Maxwell’s equations for the field, Navies-Stokes equation for fluid motion and energy equation for the temperature. They are numerically by the finite element method.

The square cavity is considered heated from the bottom and sidewalls of the cavity are thermal insulated. The criterions for the problem description are Grasshoff number Gr = gb_rDTl³ / n², magnetic Grasshoff number Gr = m₀M_S²brDT / rn, Nusselt number Nu and other usual criterions. The magnetization saturation M_S, cavity dimension l, temperature difference DT were used as scales.

Nongravity convection.

In the case of Gr = 0 the outer magnetic field only the reason of convective motion in a nonisothermal fluid. As the structure of magnetic field distortions depends on the field orientation relatively of a square cavity, also the pattern of convective motion in the cavity should depend on a direction of a magnetic field. As is known, the intensity of convective heat transfer depends on structure of flow. It means, that the change of orientation of a magnetic field can cause significant change of heat flux through a square cavity.

The computer simulation of convective motion for various orientation of a magnetic field has been done. Some results are represented in a figure 1 – 5 for Gr = 0, Gr_m = 5000, H = 10 and different meanings of an angle a between temperature gradient and magnetic field.

From figures 1-5 could be seen, that the turn of a magnetic field causes quicker turn of systems of two convective vortexes in the opposite direction. As the consequence, intensity of convective heat transfer through the cavity changes drastically with turning of the system of vortexes (Figure 6).

Gravity convection in vertical magnetic field.

In the case of Gr ¹ 0, Gr_m = 0 convective instability has a threshold character. After threshold the convective flow in a cavity has structure of one main cell and two additional small cells in corners. In opposite case Gr = 0, Gr_m ¹ the convective flow in a cavity has structure of two convective cells (figure 1). As two mechanisms of natural convection create different flow structures, the competition is unavoidable. So, the dependence of heat flux (Nusselt number) on the magnetic field (magnetic Grasshof number) is very complicated and is determined by gravity Raylegh number (Ra = GrPr) and, in some cases, even is discovered, as seen from Figure 7).