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The goal of this work is to provide a preliminary evaluation of a new high-potential concept for liquid cooling: an electrically conductive fluid can flow through channels, while magnetic fields promote flow-wall impinging, causing an effect analogous to channel ribs (turbulence promoters), but in principle the effect is controllable. In order to evaluate the magneto-hydrodynamic effect, DNS has been used to investigate the influence of non-uniform magnetic fields on liquid metal flowing through a two-dimensional channel. The dimensionless numbers governing this flow field are the Reynolds (Re) and the Stuart (St) numbers. The latter provides the relative weight of the Lorentz forces with respect to the inertial forces. A liquid-lithium flow in laminar regime has been simulated both in absence of the magnetic field (Re = 2000, St = 0) and for increasing values of the Stuart number (Re = 2000, St equal to 750, 1000 and 2000), with the aim of putting into evidence the effects of magnetic forces on the magnitude of convective heat transfer. For a channel with a hydraulic diameter of 2 cm, such Stuart number range corresponds to magnetic field intensities varying between 1 and 2T, which are technically feasible by using either electromagnets or permanent magnets. Simulation results show that the local Nusselt number can be up to 2.8 times higher than that evaluated in the non-magnetic case.