Analytical and numerical solutions for the flow in microtube with three-dimensional corrugated surface, part 1: steady flow

The influences of three-dimensional corrugated wall on the fully-developed steady no-slip flows in microtube are studied by analytical and numerical methods in this article. Detailed analytical solutions for the space-averaged equations and the numerical method for the solutions of the disturbance equations are given. An iterative arithm of coupled equations with respect to space-averaged velocities and disturbance velocities is suggested. The study shows that a three-dimensional subsidiary stress layer exists in the near-wall region. The relative roughness, wavenumber and Reynolds number are three important parameters influencing the subsidiary stresses and the space-averaged pressure drop. The space-averaged pressure drop subject to an invariable flow rate mainly depends on the position of datum surface. When the datum surface is taken at the balance position of wall function, the value of pressure drop is determined by the dynamic characteristics of the flow.