Fully developed laminar slip and no-slip flow in rough microtubes |
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Authors: | F Talay Akyildiz Dennis A Siginer |
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Institution: | 1.Department of Mathematics,Petroleum Institute,Abu Dhabi,UAE;2.Department of Mechanical Engineering and Department of Mathematics,Petroleum Institute,Abu Dhabi,UAE |
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Abstract: | The effect of surface roughness on developed laminar flow in microtubes is investigated. The tube boundary is defined by \({r=R\left{1+\varepsilon\, {\rm sin}\left( {\lambda \theta }\right)}\right]}\), with R representing the reference radius and \({\varepsilon}\) and λ the roughness parameters. The momentum equation is solved using Fourier–Galerkin–Tau method with slip at the boundary. A novel semi-analytical method is developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow that are not restricted to small values of \({\varepsilon \lambda }\) . The analytical solution collapses onto the perturbation solution ofDuan and Muzychka (J. Fluids Eng., 130:031102, 2008) for small enough values of \({\varepsilon \lambda }\) . |
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