The present work deals with magnetoconvection of molten gallium in a cuboid rotating about a vertical axis passing through its center. The governing equations are derived in a non-inertial frame of reference considering both centrifugal and Coriolis forces. A vertical magnetic field is applied through the center opposite to the direction of gravity. The cuboid is heated from below and cooled at top, while the remaining walls of the cuboid are thermally insulated. The modified Marker and Cell method is adopted for the numerical solution of the governing equations. The gradient dependent consistent hybrid upwinding scheme of second order is adopted for the discretization of the convective terms in the momentum equations. The operator splitting algorithm is used for the numerical treatment of the energy equation. The effects of cavity rotation and applied magnetic field on heat and momentum transport processes have been investigated. The uniform thorough mixing of fluids by rotation and regularization of flow by magnetic field are observed. The governing flow field and temperature distribution are shown graphically to elucidate the intricate physics of the phenomenon. (C) 2014 Elsevier Ltd. All rights reserved.