Heat transfer in an axially rotating pipe subjected to turbulent internal flow is strongly suppressed by tube rotation. For increasing rotational speeds of the pipe wall, the flow starts to laminarize and eventually the axial velocity profile of the hydrodynamically fully developed flow approaches the one of a laminar pipe flow. The solution for the heat transfer of a fluid with a hydrodynamically fully developed velocity profile in an axially rotating pipe subjected to external convection leads to a Sturm-Liouville eigenvalue problem. Asymptotic expressions are shown for the eigenvalues and constants based on a matched asymptotic expansion approach. These values are compared with numerical calculations and good agreement is found. (c) 2014 Elsevier Ltd. All rights reserved.