In the present paper, mixed convection of TiO₂-water and CuO-water nanofluids in a laminar flow within a vertical rectangular duct is investigated numerically. The two-phase Euler-Lagrange approach is applied to simulate nanoparticles dispersion in the base fluid. Effects of nanoparticles concentration, aspect ratio, buoyancy and Brownian and Thermophoretic forces in a wide range of Richardson number (Ri) on the hydrodynamics and thermal parameters are presented and discussed. It is observed that at Ri < 1, dispersion of nanoparticles in the base fluid improves heat transfer rate more considerably. Whilst an improvement in convective heat transfer of CuO-water nanofluids is shown to be more than 22% at Ri=0.5, it does not exceed 15% at Ri=5. Moreover, at Ri > 1, particles disperse in the centre region of duct cross section and variation in aspect ratio does not alter the amount of enhancement of heat transfer significantly.