Title: Modelling fluid flow over solid surfaces

Authors: Harry Gingold

Addresses: Department of Mathematics, West Virginia University, P.O. Box 6310, Morgantown, WV, 26506-6310, USA

Abstract: Models of fluid flow over solid surfaces are proposed. The models utilise a varying viscosity that is constant away from a solid surface and that becomes infinite as the solid surface is approached. The varying viscosity introduces an inner boundary layer. Consequently, we are able to explain, qualitatively, the discrepancy between theoretical predictions of the conventional theory of fluid flow with experimental data of flow over a flat plate with distributed roughness. Our model also explains the discrepancy between an increased amount of drag observed in some experiments and a theoretical predicted drag from Newtonian fluids with a constant viscosity. Couette flow over a rough surface is utilised to demonstrate the underlining nature of the modelling. Arguments for the consistency of our models are provided.

Keywords: fluid mechanics; inner boundary layer; solid boundary; solid surfaces; virtual viscosity; modelling; fluid flow; solid surfaces; Couette flow; retarded flow; drag; friction; surface roughness; distributed roughness; rough surfaces; velocity gradients; hybrid Newtonian; non-Newtonian; control.

DOI: 10.1504/IJMIC.2014.060727

International Journal of Modelling, Identification and Control, 2014 Vol.21 No.3, pp.237 - 243

Published online: 07 Jun 2014 *

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