The use of fixed-shape open channels in industrial processes is common in the mineral processing industry. With lack of fundamental understanding about the mechanisms involved in how a turbulent flow of a non-Newtonian carrier fluid transports suspension particles, direct numerical simulation may come into the research as a validation tool. Direct numerical simulation (DNS) of the turbulent flow of non-Newtonian fluids in an open channel is modeled using a spectral element-Fourier method. The simulation of a yield-pseudoplastic fluid using the Herschel-Bulkley model agrees qualitatively with experimental results from field measurements of mineral tailing slurries. The simulation results over-predict the flow velocity by approximately 40% for the cases considered, however, the source of the discrepancy is difficult to ascertain. The effect of variation in yield stress, flow behavior index, and assumed flow depth are investigated and used to assess the sensitivity of the flow to these physical parameters. This methodology is seen to be useful in designing and optimizing the transport of slurries in open channels.