Magnetizing force modeled and numerically solved for natural convection of air in a cubic enclosure: effect of the direction of the magnetic field

Magnetizing force is modeled by considering magnetic susceptibility as a function of temperature and is included in a momentum balance equation as an external force term in addition to the buoyant force term. Under ideal gas behavior, the magnetizing force term can be represented by a new and simple non-dimensional parameter group γ, which represents the ratio of magnetizing force to the gravitational force. This magnetizing force acts on material of high magnetic susceptibility, like oxygen gas in a temperature gradient field, and affects the convection in addition to gravity. Sample computation was carried out for air in a cubic box that is heated from one vertical wall and cooled from the opposing wall, and has the other four walls thermally insulated. With an increase in the magnetic strength, the upward and downward natural convection in the gravity field becomes horizontal circulation under a cusp-shaped magnetic field.