Stokes Flow Through a Tube with Wavy Wall

We propose a study of the flow in a tube with wavy wall adopting Malevich - Mityushev - Adler’s method, and find a correction to Hagen-Poiseuille’s solution. The problem is to be solved by expanding the velocity and pressure fields in Fourier series involving an infinite set of unknown coefficients. The boundary surface is expanded in Taylor’s series. A perturbation expansion in terms of the powers of the small parameter \(\varepsilon \) of the full set of Stokes’ equations yields a cascade of boundary value problems which are solved at each step in closed form. Even in the first order approximation \(O(\varepsilon )\), new results are obtained.