Developing mixed convective flow in the entrance section of a horizontal straight tube is analyzed with special emphasis on the buoyancy-induced secondary vortices. The flow is subject to a constant wall temperature. Elliptic calculations on a half gross-section grid are performed for various Grashof numbers and two Prandtl numbers. It appears that for air (Pr=0.7) the flow exhibits a two-vortex solution for all Grashof numbers and axial positions investigated, whereas for water (Pr=5.0), secondary flow evolves from a two-vortex solution, via a four-voltex solution toward a six-voltex solution for increasing Grashof numbers and axial distances. Calculations on a full cross-section grid reveal that these solutions are axial distances. Calculations on a full cross-section grid reveal that these solutions are insensitive to white noise perturbations in the "initial" flow field.