We investigate the joint effect of viscous and Ohmic dissipation on electric current flow through a slit in a barrier dividing a graphene sheet in two. In the case of the no-slip boundary condition, we find that the competition between the viscous and Ohmic types of the charge flow results in the evolution of the current density profile from a concave to convex shape. We provide a detailed analysis of the evolution and identify favorable conditions to observe it in experiment. In contrast, in the case of the no-stress boundary condition, there is no qualitative difference between the current profiles in the Ohmic and viscous limits. The dichotomy between the behavior corresponding to distinct boundary conditions could be tested experimentally.

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• Transport phenomena
• Graphene
• Hydrodynamic models