Convective flow patterns in rectangular boxes of finite extent under an external magnetic field

Stationary convective instability in rectangular boxes of finite extent, under the action of an external magnetic field is considered within the framework of linearized theory. In the case where the magnetic field is vertical, by changing the scale accordingly, the situation is shown to be similar to a complete lack of magnetic field. When the magnetic field is horizontally applied, the isotropic property of the governing operator is broken. Calculations performed for various situations show transitions from transversal to longitudinal rolls and suppression of dislocations when the horizontal magnetic field is increased.