A transient two-dimensional two-phase hydrodynamic computer model is proposed to describe liquid-solids slurry flows. The carrier fluid-phase is treated as Newtonian while the solids-fluid mixture is treated as non-Newtonian, displaying shear-thinning. Computed results are compared with nonintrusive NMR time-of-flight velocity measurements. Good agreement was obtained between NMR experimental data and model predictions.