We present a linear stability analysis of two-dimensional magnetoconvection considering the effects of spatial confinement (characterised by the aspect ratio) and magnetic field (characterised by the Hartmann number Ha₈=ₗ, ₘ, ₙ with subscript representing its direction). It is found that when the magnetic field is perpendicular to the convection domain (y -direction), it does not affect the onset of convection due to zero Lorentz force. With a magnetic field in the z (vertical) or x (horizontal) directions, the onset of convection is delayed, resulting in a larger critical Rayleigh number Rac for the onset of convection. We outline phase diagrams showing the dominating factors determining Rac. When 0. 83Haᵦ^-0. 5 for vertical and 0. 66Haₓ^-1. 01 for horizontal magnetic field, Rac is mainly determined by the geometrical confinement with Rac=502 ^-4. 0. When 2^1/6 ^1/3Haᵦ^-1/3 for vertical and 5 for the horizontal magnetic field, Rac is mainly determined by the magnetic field with Rac= ²Ha². In the intermediate regime, both the magnetic field and spatial confinement determine Rac, and a horizontal magnetic field is found to suppress convection more than a vertical magnetic field. In addition, under a horizontal magnetic field, there exists a subregime characterised by Rac = 9. 9\, ^-2. 0 Haₓ², which is explained by a theoretical model. The magnetic field also modifies the length scale. For a vertical magnetic field, decreases with increasing Haᵦ, following
Tao et al. (Mon,) studied this question.
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