In this paper, the statistical analysis of the effect of nanoparticles volume fraction on one of the most important thermal characteristics turbulent flow of nanofluid i.e. convection heat transfer coefficient, inside a circular tube with uniform wall heat flux is investigated numerically. Also, water as a base fluid and Al2O3 as suspended particles with a diameter of 36 nm are considered. Heat transfer characteristics are computed using the solution of elliptic equations based on discrete the finite volume method and the second order upwind. The relationship between pressure and velocity using SIMPLEC algorithm is established. In this study, the variation of volume fraction of nanoparticles is assumed in the range of 0 to 6%. The best probability distribution function of the heat transfer parameters are selected using chi square test that various probability distribution such as: Gamma, Normal, Lognormal, Gumbel, and Frechet are evaluated based on numerical analysis of tube flow. After reviewing the results, it was found that with increasing volume fraction of nanoparticles, the convective heat transfer coefficient increases. On the other hand, the convective heat transfer coefficients with regard to variation of volume fraction of nanoparticles follow Gumbel Max probability distribution function.
