The present analysis deals with the velocity and temperature distribution in steady state, hydrodynamically and thermally fully developed, laminar forced flow for Newtonian fluids in rectangular ducts. The analytical solutions are presented for all the eight modified H2 thermal boundary conditions around the periphery of the duct cross-section. The velocity profile represents the rigorous solution to the Navier-Stokes equation; the temperature profile is obtained resorting to series solutions of trigonometric functions. The temperatures and the Nusselt numbers are predicted as functions of the aspect ratio and compared with the results available in literature. Finally, very simple polynomial representations are given for the Nusselt numbers.