  We study the influence of fringing magnetic fields on turbulent thermal
convection in a horizontally extended rectangular domain. The magnetic field is
created in the gap between two semi-infinite planar magnetic poles, with the
convection layer located near the edge of the gap. We employ direct numerical
simulations in this setup for fixed Rayleigh and small Prandtl numbers, but
vary the fringe-width by controlling the gap between the magnetic poles and the
convection cell. The magnetic field generated by the magnets is strong enough
to cease the flow in high magnetic flux region of the convection cell. We
observe that as the local vertical magnetic field strength increases, the large
scale structures become thinner and align themselves perpendicular to the
longitudinal sidewalls. We determine the local Nusselt and Reynolds numbers as
functions of the local Hartmann number (based on the vertical component of the
magnetic field) and estimate the global heat and momentum transport. We show
that the global heat transport decreases with increasing fringe-width for
strong magnetic fields but increases with increasing fringe-width for weak
magnetic fields. In the regions of large vertical magnetic fields, the
convective motion becomes confined to the vicinity of the sidewalls. The
amplitudes of these wall modes show a non-monotonic dependence on the
fringe-width.
