Combination between the Inclinations of the Enclosure and the Magnetic Field Orientation on the Oscillatory Natural Convection

Abstract

In this paper, we study the combination between the inclinations of the enclosure and the magnetic field orientation on the oscillatory natural convection. For this, a cylindrical enclosure filled with electrically conducting fluid, has an aspect ratio equal to 2, and subjected to a vertical temperature gradient and different uniform magnetic field orientations were considered. The finite volume method is used to discretize the equations of continuity, momentum and energy. Our computer program based on the SIMPLER Algorithm has a good agreement with available experimental and numerical results. The time-dependent flow and temperature field are presented in oscillatory state, for different cases: inclination of the cylinder, under the effect of magnetic field in different orientations (δ = 0°, 30°, 45° and 90°) and the combination between them. The results are presented at various inclinations of the cylinder (φ = 0°, 30° and 45°), and the Hartmann numbers Ha ≤ 50. The stability diagrams of the dependence between the complicated situations with the value of the critical Grashof number Grcr and corresponding frequency Frcr, are established according to the numerical results of this investigation. The combination between the studied state has a significant effect on the stabilization of the convective flow, and shows that the best stabilization of oscillatory natural convection is obtained at the inclination of the cylinder φ = 30°, and the applied of radial magnetic field (δ = 0°).

Keywords

• Natural convection; Magnetic field; Oscillatory convection; Inclined cylinder.