Influence of three-dimensional wall roughness on the laminar flow in microtube

The regular perturbation method is introduced to investigate the influences of three-dimensional wall roughness on the laminar flow in microtube. Rough wall surface is modeled by two-dimensional simple harmonic function whose axial and azimuthal wavenumbers are alterable. Under this rough wall model, a set of coupled leading-order and first-order perturbation equations are obtained and computed iteratively. The numerical results show that flow in microtubes are more complex than those in macrotubes; pressure drops are about 0–65% higher than that of Hagen–Poiseuille flow on condition that the relative roughness increases from 0 to 0.05 and the wavenumbers of wall rough function range between 0 and 30; there exists apparent fluctuations in flow fields. Analysis shows that the effects of roughness on the flow pattern is distinct from those on the friction factor.