The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary conditions are then applied to the solution using the point matching technique. The results show that both the Nusselt number and the pressure drop parameter are increasing functions of the Grashof to Reynolds ratio. It is also found that, with the exception of the H2 Nusselt number of the triangular duct, which shows an opposite trend, both the Nusselt number and the pressure drop are decreased by increasing the Knudsen number. Furthermore, the pressure drop of the H2 case is found to be higher than that obtained by assuming an H1 thermal boundary condition.