Present work aims at the assessment of the flow and heat transfer in forced, free and mixed convection of laminar developing flow of nanofluid inside a vertical tube. Governing equations are solved through a numerical procedure using finite volume method. The adopted model (Buongiorno model) assumes that the nanofluid is a mixture of a base fluid and nanoparticles, with the relative motion caused by Brownian motion and thermophoretic diffusion. The effects of Reynolds number (50?Re?1600), relative strength of Brownian motion to thermophoresis (0.025?N BT ?3.2), Grashof number (0?Gr?3200), and nanoparticles volume fraction (0? ?10%) on the Nusselt number, nondimensional pressure drop, performance evaluation criteria (PEC) and distribution of nanoparticles are investigated. Numerical results are validated against published experimental and numerical data. Good qualitative and quantitative agreement was found between present work and available data in the litraure. The simulations results indicated that the distribution of nanoparticles remained almost uniform except in a region near the hot wall where nanoparticles volume fraction were reduced as a result of thermophoresis. In low nanoparticles volume fraction (4% and less), the difference between Nusselt number and nondimensional pressure drop calculated based on two phase model and the one calculated based on single phase model was less than 1% can be neglected. However, in 10% of nanoparticles volume fraction, the same difference can raise to 5% (in the investigated range in present work). The difference between two phase model and single phase model in Nusselt number and nondimensional pressure drop vanishes as N BT increases because nanoparticles distribution is almost uniform in high values of N BT . In addition, it was found that in forced convection there is an optimal nanoparticles volume fraction of the nanoparticles at each Reynolds number which the maximum performance evaluation criteria (PEC) can be obtained. Optimum nanoparticles volume fraction was about 1% to 2% for all Reynolds numbers. After this optimum point PEC decreased by increasing nanoparticles volume fraction and can get the value less than unity. Maximum achieved PEC in present work was 1.04 and obtained at lowest Reynolds number (Re=50). PEC decreased by increasing Reynolds number at all nanoparticles volume fraction. Also, nanoparticles volume fraction distribution in tube cross section and Sherwood number along the tube length is presented. In free convection, nanoparticles volume fraction impact on Nusselt number was decreased in higher Grashof number. In Gr=10 increasing nanoparticles volume fraction up to 4% leads to 15% increase of Nusselt number. However, in high Grashof numbers, Nusselt number was almost independent of nanoparticles volume fraction. In Gr=300 inceasing nanoparticles volume fraction first increased Nusselt number about 1% and in 4% of nanoparticles volume fraction, Nusselt number was decreaced by about 1%. Keywords: Nanofluid, Convection heat transfer, Numerical simulation, Brownian motion, Thermophresis