In the present paper, mixed convection of TiO2-water nanofluid in a laminar flow within a vertical rectangular duct is investigated numerically. A single phase and a two phase method is applied to simulate nanoparticles dispersion in the base fluid. An Euler-Lagrange approach is employed to track particles individually. In this approach, the base fluid is assumed to be a continuous phase while the particles are dispersed through it. The presence of particles in the base fluid is modeled as a source term in the momentum and energy equations. Governing equations is discretized using Control Volume based Finite Element Method (CVFEM). Effects of nanoparticles concentration, particles size, aspect ratio of cross section, asymmetrical boundary condition and buoyancy on the hydrodynamics and thermal parameters are presented and discussed. It is observed that increasing nanoparticles concentration enhances heat transfer rate and this enhancement is more considerable in higher aspect ratios. Also, at smaller values of Richardson number (Ri) where the effect of forced convection is more than natural convection, dispersion of nanoparticles in the base fluid improves heat transfer rate more considerably. Whilst an improvement in convective heat transfer is shown to be more than 6.5% at Ri=0.05, it does not exceed 4% at Ri=0.5.