  We developed a unified mesoscopic transport model for graphene nanoribbons,
which combines the non-equilibrium Green's function (NEGF) formalism with the
real-space {\pi}-orbital model. Based on this model, we probe the spatial
distributions of electrons under a magnetic field, in order to obtain insights
into the various signature Hall effects in disordered armchair graphene
nanoribbons (AGNR). In the presence of a uniform perpendicular magnetic field
(B\perp-field), a perfect AGNR shows three distinct spatial current profiles at
equilibrium, depending on its width. Under non-equilibrium conditions (i.e. in
the presence of an applied bias), the net electron flow is restricted to the
edges and occurs in opposite directions depending on whether the Fermi level
lies within the valence or conduction band. For electrons at energy level below
the conduction window, the B\perp-field gives rise to local electron flux
circulation, although the global flux is zero. Our study also reveals the
suppression of electron backscattering as a result of the edge transport which
is induced by the B\perp-field. This phenomenon can potentially mitigate the
undesired effects of disorders, such as the bulk and edge vacancies, on the
transport properties of AGNR. Lastly, we show that the effect of B\perp-field
on electronic transport is less significant in the multimode compared to the
single mode electron transport.
