Flow and transport are studied in transparent model fractures with rough complementary self-affine walls with a relative shear displacement u. The aperture field is shown to display long range correlations perpendicular to u: for flow in that direction, the width and geometry of the front of a dyed shear-thinning polymer solution displacing a transparent one have been studied as a function of the fluid rheology and flow rate. The front width increases linearly with distance indicating a convection of the fluids with a low transverse mixing between the flow paths. The width also increases with the flow rate as the fluid rheology shifts from Newtonian at low shear rates towards a shear-thinning behaviour at higher shear rates. The width also increases with the polymer concentration at high flow rates. These results demonstrate the enhancement of the flow velocity contrasts between different flow channels for shear-thinning fluids. The relative widths at low and high shear rates for different polymer concentrations are well predicted by an analytical model considering the fracture as a set of parallel ducts of constant hydraulic apertures. The overall geometry of the experimental front geometry is also predicted by the theoretical model from the aperture map.