A newly developed method of solute diffusivity measurement in liquid metals and semi-conductors is presented. It is based on the assumption that the strong scattering observed in previous ground-based measurements is a consequence of uncontrolled convection during the experiments, which is usually not accounted for. The idea is to impose a temperature gradient along a shear-cell, in order to create a well organised buoyancy driven flow and to damp it thanks to a vertical uniform magnetic field. The main features of the transport in such configuration is presented through orders of magnitude analysis, accounting for the presence of time dependent solute buoyancy driven convection. To successive phases are present: at the beginning of the experiment, a B(-2)t(-1/2) law is derived, B and t being respectively the intensity of the magnetic field and the elapse of time since the beginning of diffusion; at latter time, a steady state is reached and the transport is governed by a B-4 law. Experimental results provide an illustration of the two phases.