Flow of a Herschel-Bulkley (H-B) fluid in tubes of non-circular cross-section in investigated analytically. This study complements results presented in  where the equation of motion was solved in tubes of arbitrary cross-section for Bingham type of fluids, and the shapes of plug zones centered on the tube axis and stagnant zones attached to the corners were predicted when the cross-section is triangular and square. In this paper we investigate the effect of the power index in the H-B model on the flow for values greater and lesser than unity, considering thus the shear-thinning and shear-thickening effects, which could not be accounted for with the Bingham model. The equation of motion is solved when the cross-section is an equilateral triangle or a square by means of the shape factor method previously introduced in . Thus, shear-thickening and shear-thinning effects are accounted for and related to the tube geometry in predicting the existence and the extent of undeformed regions in the flow field.
- Fluids Engineering Division
Herschel-Bulkley Viscoplastic Flow in Tubes of Non-Circular Cross-Section
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Letelier, MF, Siginer, DA, Godoy, F, & Rosas, C. "Herschel-Bulkley Viscoplastic Flow in Tubes of Non-Circular Cross-Section." Proceedings of the ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. Volume 1B, Symposia: Fluid Mechanics (Fundamental Issues and Perspectives; Industrial and Environmental Applications); Multiphase Flow and Systems (Multiscale Methods; Noninvasive Measurements; Numerical Methods; Heat Transfer; Performance); Transport Phenomena (Clean Energy; Mixing; Manufacturing and Materials Processing); Turbulent Flows — Issues and Perspectives; Algorithms and Applications for High Performance CFD Computation; Fluid Power; Fluid Dynamics of Wind Energy; Marine Hydrodynamics. Washington, DC, USA. July 10–14, 2016. V01BT34A001. ASME. https://doi.org/10.1115/FEDSM2016-1069
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