This paper presents an analysis of the role of orientation on the rheology of discotic nematic liquid crystals. The shear rheological properties exhibited by flow-aligning discotic mesophases are calculated by using a complete generalized nonlinear second-order tensor Landau-de Gennes model that takes into account short-range order elasticity, long-range elasticity, and viscous effects. A unified expression for the extra stress tensor is given. The second-order tensor Landau-de Gennes model was reduced to the uniaxial Leslie-Ericksen to obtain limiting rheological material functions valid at low and high shear rates. Analytical results are able to predict the material functions computed by the full Landau-de Gennes model for nonhomogeneous flow-aligning discotic nematic liquid crystals, Experimentally reported changes in the sign of the first normal stress differences with shear rate are captured by, the model. A new Carreau-Yasuda liquid crystal model has been used to characterize the shear rheology, for characteristic boundary conditions, and a viscosity power law exponent of 0.5 and a normal stress coefficient power law exponent of 0.44 have been obtained.