Effects of a vertical magnetic field on chimney convection in a mushy layer

Abstract

Non-linear compositional convection in cylindrical chimneys within a mushy layer during alloy solidification is investigated under an externally imposed magnetic field in the vertical direction. These chimneys produce freckles in the final form of the solidified materials. Freckles are imperfections that reduce the quality of the solidified materials. The undesirable effects of the chimneys can be reduced by reducing the effects of convection within the chimneys. Asymptotic and scaling examinations on weakly non-axisymmetric convection in the chimneys are carried out. The effects of the externally imposed magnetic field are represented by the Chandrasekhar number Q. It is found that for sufficiently large values of Q, convection and the volume flux in the chimneys decrease with increasing Q. Conditions on Q and other parameters are determined under which the walls of the chimneys can or cannot be in the vertical direction.