In this paper we couple a numerical method aimed at simulation of flow and heat transfer of nanofluids with stochastic modelling of input and material parameters. A fast Boundary- Domain Integral Method has been developed to solve the governing equations and set up the deterministic flow and heat transfer solver. Furthermore, the Stochastic Collocation Method is used in combination with the deterministic flow simulation code in order to propagate the uncertainty from input to output parameters. The developed algorithm is used to simulate natural convection of a nanofluid in a closed cavity. By simulation of a very large number of cases and by applying the stochastic analysis, we were able to identify the relative impact of different input parameters. The results reveal that the uncertainty of input parameters results in more stronger influence in the convection dominated flow regimes.