We present results on modelling magnetic flux tubes in an unstably stratified medium and the flows around them using 2D axisymmetric magnetohydrodynamic (MHD) simulations. The study is motivated by the formation of magnetic field concentrations at the solar surface in sunspots and magnetic pores and the large-scale flow patterns associated with them. The simulations provide consistent, self-maintained models of concentrated magnetic field in a convective environment, although they are not fully realistic or directly applicable to the solar case. In this paper, we explore under which conditions the associated flows near the surface are converging (towards the spot centre) or diverging (away from the axis) in nature. It is found that, depending on the parameters of the problem, the results can depend on the initial conditions, in particular for zero or low rotation rates and Prandtl numbers smaller than unity. The solutions with a converging flow generally produce more strongly confined magnetic flux tubes.