Effects of the vessel bottom wall on a particle rising in an electrically conducting fluid under a strong vertical magnetic field

The drag of a particle rising along a vertical magnetic field in an electrically conducting fluid is studied when the vessel bottom wall exists. A dynamically similar flow using compressed coordinates is obtained when the Hartmann number is much greater than one, the Reynolds number is much smaller than the Hartmann number, and the magnetic Reynolds number is much smaller than one. The drag influenced by the vessel bottom wall is derived from this similar solution. A correction term with respect to the vessel bottom wall is added to Chester's drag in free space. The drag of the particle increases when the distance between the particle and vessel bottom wall decreases. The region of influence of the vessel bottom wall spreads along the magnetic flux lines when the Hartmann number increases. Therefore, the correction term of drag affects a large region in the vessel when the magnetic field is very strong.