Nonspherical particles dispersed in a fluid have a tendency to align because of particle fluid interactions. At high particle concentrations and in the absence of fluid dynamic couples, spontaneous self-alignment can occur due to excluded volume constraints on rotary Brownian motion. This phenomenon prevents a return-to-isotropy from an anisotropic state. In this communication, the low-order moments of the rotary Smoluchowski (S) equation for a rigid rod suspension are used to explore the effect of the Peclet number on the shear viscosity of a suspension. A closure model for the fourth-order orientation tetradic uses an algebraic fully symmetric quadratic (FSQ) mapping of the second-order orientation moment into the fourth-order orientation moment. The algebraic mapping preserves the 6-fold symmetry and the 6-fold contraction properties of the exact fourth-order Orientation moment. The theory predicts that, if the orientation director is in the tumbling regime, shear thickening may occur and, if the orientation director is in the wagging regime, shear thinning may occur.