This study presents a new exact-analytical solution for convective heat transfer of thermally fully-developed laminar nanofluid flows in a circular tube for the first time. In this problem, the pipe wall is exposed to a constant temperature. The solution is based on the Whittaker function and perturbation technique. In the nanofluid model, it is assumed that nanoparticles and base-fluid behave as a single-phase with average properties. In this study, the effects of Reynolds number, volume fraction of the particles, Peclet number, and particle diameter are investigated on the average heat transfer coefficient, surface mass transfer, and Nusselt number.