The heat transfer problem in a circular duct with an internal longitudinal fin is investigated under constant wall temperature. Different fin heights are considered. The problem is solved in two stages. In the first stage, the distribution of axial velocity corresponding to the fully developed laminar viscous flow is obtained using comsolmultiphysics. In the second stage, the variable-separation method is implemented to reduce the solution of the energy transfer equation under constant wall temperature to an eigenvalue problem. Finally, the temperature distribution is obtained in the analytical form as a series expansion. The influence of fin height on the Nusselt number and the friction factor is discussed.