Linear Stability Analysis of Thermal Convection in an Infinitely Long Vertical Rectangular Enclosure in the Presence of a Uniform Horizontal Magnetic Field

Stability of thermal convection in an infinitely long vertical channel in the presence of a uniform horizontal magnetic field applied in the direction parallel to the hot and cold walls was numerically studied. First, in order to confirm accuracy of the present numerical code, the one-dimensional computations without the effect of magnetic field were computed and they agreed with a previous study quantitatively for various values of the Prandtl number. Then, linear stability analysis for the thermal convection flow in a square horizontal cross section under the magnetic field was carried out for the case of Pr = 0.025. The thermal convection flow was once destabilized at certain low Hartmann numbers, and it was stabilized at high Hartmann numbers. 1. Introduction Nuclear fusion energy has received considerable attention as one of the environment-friendly in modern society. Heading towards implementation of the use of nuclear fusion energy, experimental facility called ITER (International Thermonuclear Experimental Reactor) is currently under construction in France. ITER has a toroidal shape like a donut, in which the high-temperature plasma enough to induce nuclear fusion reaction is controlled by both operation of magnetic field generated by the superconducting coils disposed around the plasma and the imposed electric current in the plasma [1]. Blankets located close to the plasma side play an important role for cooling, shielding neutrons, and fuel production. Fusion reactor blanket can be classified into the solid blanket using a solid compound of lithium as fuel production material, or liquid blanket using liquid lithium. Above all, liquid blanket has the advantage of being of relatively simple structure [2], but, on the other hand, it has a serious problem called the MHD pressure loss [3]. The MHD pressure loss obstructs convection of liquid metal as a coolant and it depends on the direction of the magnetic field and the electric conductivity of the wall. To elucidate that problem, researches on thermal convection under the electromagnetic force have been actively conducted not only for the application of fusion reactor blankets but also for crystal growth such as the horizontal Bridgman method. The effect of the direction of uniform magnetic field on the natural convection in a cubic enclosure heated from a vertical wall and cooled from an opposing vertical wall was numerically studied by Ozoe and Okada [5]. They showed that the horizontal magnetic field parallel to the hot and cold walls ( -directional magnetic field) has much less influence on