Analytical solution for the potential flow through the wall of n-sided hollow cylinders of regular polygonal cross-section

The calculation of the potential flow through the wall of hollow cylinders of regular polygonal cross-section with the inner and the outer boundaries considered to be lines of different but constant potential is a classical problem in the field of non-viscous transport phenomena. The known empirical correlation’s result from numerical and experimental investigations and are thus restricted to limited ranges of variables, while a more universal analytic solution has not yet been published, as far as we know. In this paper we do present such an analytical solution together with asymptotes and a simple approximation, that does not need higher mathematical functions, for easy application.