Fully developed laminar slip and no-slip flow in rough microtubes

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 ${\varepsilon \lambda }$ .