This report details progress made in a Maths in Industry Study Group Project. The key conclusions of the study group were that correctly choosing an appropriate rheological model, and using appropriate data to compute the parameters of that model, is vital in recovering the correct fluid behaviour; and that exact mathematical solutions that exist for simplistic channel shapes can be used to approximate the flow in more complicated geometries. The problems of accurate numerical computation for highly non-Newtonian channel flow, as well as the complications that arise from turbulence, were identified as important areas of further research. References N. J. Alderman and R. Haldenwang, ``A review of Newtonian and non-Newtonian flow in rectangular open channels.'' Hydrotransport 17: The 17th International Conference on the Hydraulic Transport of Solids , The Southern African Institute of Mining and Metallurgy and the BHR Group, 2007. http://hdl.handle.net/11189/5192 J. Burger, R. Haldenwang and N. Alderman, ``Experimental database for non-Newtonian flow in four channel shapes.'' Journal of Hydraulic Research , 48 (2010): 363–370. doi:10.1080/00221686.2010.481849 P. Coussot, ``Steady, laminar, flow of concentrated mud suspensions in open channel.'' Journal of Hydraulic Research , 32 (1994): 535–559. doi:10.1080/00221686.1994.9728354 D. A. Rojas and R. H. A. Janssen, ``Design of open channels for non-Newtonian fluids'', in Proceedings of the 16th International Seminar on Paste and Thickened Tailings , Eds R. J. Jewell, A. B. Fourie, J. Caldwell and J. Pimenta, Australian Centre for Geomechanics, 2013. S. W. McCue, J. R. King and D. S. Riley, ``Extinction behaviour for two-dimensional inward-solidification problems.'' Proceedings of the Royal Society of London A , 459 (2003): 977–999. doi:10.1098/rspa.2002.1059 C. C. Mei and M. Yuhi, ``Slow flow of a Bingham fluid in a shallow channel of finite width.'' Journal of Fluid Mechanics , 431 (2001): 135–159. doi:10.1017/S0022112000003013 H. Schlichting and K. Gersten, Boundary-Layer Theory . Springer-Verlag, Berlin Heidelberg, 2000. doi:10.1007/978-3-662-52919-5 K. X. Whipple, ``Open-channel flow of Bingham fluids: applications in debris-flow research.'' The Journal of Geology , 105 (1997): 243–262. doi:10.1086/515916 R. Chhabra and J. F. Richardson, Non-Newtonian Flow: Fundamentals and Engineering Applications , Butterworth-Heinemann, 1999. P. Coussot, Mudflow rheology and dynamics , Balkema, 1997. F. Holland and R. Bragg, Fluid Flow for Chemical and Process Engineers , Butterworth-Heinemann, 1995. E. Mitsoulis, Flows of viscoplastic materials: models and computations, Rheology reviews , 2007 (2007), pp. 135–178. http://www.bsr.org.uk/rheology-reviews/RheologyReviews/viscoplastic-materials-Mitsoulis.pdf D. Pritchard, B. R. Duffy, and S. K. Wilson, Shallow flows of generalised Newtonian fluids on an inclined plane, Journal of Engineering Mathematics , 94 (2015), pp. 115–133. doi:10.1007/s10665-014-9725-2 J. N. Reddy and D. K. Gartling, The finite element method in heat transfer and fluid dynamics , CRC press, 2010.
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