Recent measurements of the synchrotron emission of the external galaxy M51 give indirect
implication for the cosmic-ray electron (CRE) transport in the interstellar medium. In its face-
on geometry, a radial resolved measurement of the star formation rate and the magnetic field
strength is possible. Additionally, the diffusion coefficient can be inferred and seems to be energy
independent. By modelling the CRE transport considering all relevant energy loss processes,
we aim to distinguish the contribution of diffusive and advective transport. Therefore, we use
the publicly available transport code CRPropa3.2 to solve the 3D transport equation. With our
best fit model, the data can be described well. For the best fit, the wind speed followed from the
observation of the star formation rate must be decreased by a factor 5. We find that the inner galaxy
is dominated by advection and the outer is composed by both spatial diffusion and advection. In
general leads this approach of modelling face-on galaxies insights of the only indirect observable
advection profile.