Molecular dynamics simulations are used to investigate the rheological behavior of confined linear alkane chains under shear flow conditions. The simulated fluids are contained between atomistic, pure titanium walls, coupled to an external bath to maintain the temperature at a constant value. Shear flow conditions are imparted by moving the metal walls in opposite directions, and the corresponding density, velocity, and temperature profiles of the systems are calculated. For the shear rates investigated, all linear alkane chains exhibit a tendency for slip at the walls, evidenced by density profiles divided into two distinct regions and small discontinuities in the velocity and temperature profiles at the wall/fluid interface. Compared to equilibrium, alkane chains show higher mean-square end-to-end distances, characterized by higher components along the shear flow direction.