In this study, a numerical analysis of heat transfer enhancement of Alumina/water nanofluid in a steady-state, single-phase, laminar flow in a circular duct is presented for the case of constant wall heat flux and constant wall temperature boundary conditions. The analysis is performed with a newly suggested model (Corcione) for effective thermal conductivity and viscosity, which show the effects of temperature and nanoparticle diameter. The results for Nusselt number and heat transfer enhancement are presented in graphical and tabular forms, for a given Peelet number, nanoparticle volumetric fraction, and particle diameter in the thermal entrance region. The results are compared with the experimental results available in the literature under the same conditions and a good agreement is found. The two boundary conditions are compared and slightly differing results are discussed. Finally, the effect of the axial conduction and viscous dissipation are investigated. The axial conduction effect is found to be negligible for practical cases while the viscous dissipation effect is found to be significantly important depending, on the boundary conditions and the pipe diameter.