Laminar how heat transfer in a vertical circular duct is investigated by taking into account both viscous dissipation and the effect of buoyancy. The temperature on the duct wall is considered as uniform and the velocity field is assumed to be parallel. A perturbation method is employed to solve the momentum balance equation and the energy balance equation. The radius of convergence of the perturbation series is evaluated by means of Domb Sykes plots. A comparison with the velocity and temperature profiles in the case of laminar forced convection with viscous dissipation is performed in order to point out the effect of buoyancy. The case of convective boundary conditions is also discussed.