The viscous flow in an axisymmetric nozzle was analyzed while accounting for the mesh sizes in both in the free stream and the boundary layer. The Navier-Stokes equations were resolved using the finite volume method in order to determine the supersonic flow parameters at the exit of the converging-diverging nozzle. The numerical technique in the aforementioned method uses the flux vector splitting of Van Leer. An adequate time stepping parameter, along with the Courant, Friedrich, Lewis coefficient and mesh size level, was selected to ensure numerical convergence. The boundary layer thickness significantly affected the viscous flow parameters at the exit of the nozzle. The best solution was obtained using a very fine grid, especially near the wall at which a strong variation of velocity, temperature and shear stress was observed. This study confirmed that the boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value. The nozzles are used at the exit of the shock tube in order to obtain supersonic flows for various tests. They also used in propulsion to obtain the thrust necessary to the displacement of the vehicles.