We propose a numerical framework to solve thermobuoyant flows in enclosures with large temperature differences under the influence of an applied magnetic field. The solution methodology is based on a staggered/nonstaggered finite volume framework which is modified to solve quasiincompressible flows with heat transfer. The present framework solves a single equation for normal momentum at the face wherein a second-order convection scheme and central differencing is adopted for the convective and viscous term, respectively. An implicit solution approach which is first order accurate in time is employed, and the resulting nonlinear system of equations is solved using the Newton–Krylov approach. The momentum field at the cell centroids is reconstructed using an iterative-defect-correction approach. The energy conservation equation is discretized as in a collocated framework, with a first-order upwind scheme for the convective terms and central differencing for viscous terms, in conjunction with implicit Euler time stepping. Thus the equation is linearized by considering the velocity field at the latest available time step, and the resulting linear system of equations is solved, using an incomplete LU (ILU) preconditioned GMRES solver. The proposed approach is, however, still pressure based, but the energy equation is employed to derive the divergence constraint to be used for solution of the pressure correction equation. This leads to a nonsolenoidal velocity field with a variable coefficient poisson equation, which is also efficiently solved using an ILU preconditioned GMRES solver. Validation studies for small and large temperature differences under the action of imposed magnetic field are carried out to ascertain the applicability of the approach. Finally, investigations of magnetohydrodynamic thermobuoyant flow in an enclosure with a heat obstacle are conducted with a view to understand the effect of magnetic field and heat transfer. © 2019 by Begell House, Inc.