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The variation of viscosity with temperature and shear rate plays an important role in the analysis of lubrication of automotive systems. In this paper, a method for predicting the viscosity of non-Newtonian fluids, such as multigrade engine oils, over a wide range of temperatures and shear rates is outlined. This expression determines viscosity parameters for shear thinning fluids in terms of easily measured viscosity values at some reference state. A comparison of predictions with experimental data suggests that viscosity for multigrade engine oils can be predicted to within experimental uncertainty. The proposed method can be used in assessing lubricant viscosity at shear rates greater than 106 s-1, which are beyond the capability of current laboratory instruments. A comparative study with multigrade oils shows that performance at very high shear rates cannot be accurately gauged from high temperature, high shear (HTHS) viscosity measurements.