## 1 Introduction  
In the traditional numerical investigations on the forced convection problem, the parameters that affect the thermal performance and flow behavior are treated as deterministic values. However, for complicated convection heat transfer problem in the real world, uncertainties exist naturally. To obtain a deeper understanding of the forced convection problem of nanofluids in microchannels, uncertainties are suggested to be considered. In 2000, [PERSON] et al. [1] pointed out that nanofluids had tremendous potential in heat transfer enhancement. Then they investigated the transport and thermal performances of nanofluids and proposed two fitting methods for heat transfer correlations. [PERSON] et al. [2] investigated the laminar convection heat transfer performance of nanofluids in two different types of passages. Comparisons were carried out between Al\({}_{2}\)O\({}_{3}\)-water and Al\({}_{2}\)O\({}_{3}\)-Ethylene Glycol. As concluded in this study, nanofluids could improve thermal performance and this effect was strengthened with the increase in particle concentration. The latter had better thermal performance than the former. [PERSON] et al. [3] experimentally studied the thermal behavior of TiO\({}_{2}\) nanofluids in vertical tubes, covering laminar, turbulence, and transition states. It was pointed out that nanoparticles increased thermal conductivity and the beneficial effect was more significant at a larger particle concentration and a smaller particle size. An experimental system of a circular channel with nanofluids flow was constructed by [PERSON] et al. [4]. They studied the heat transfer performance under isothermal wall temperature conditions. The experimental results were obviously higher than the prediction results by single phase heat transfer correlation. [PERSON] et al. [5] performed numerical investigations on the natural convection heat transfer of various water-based nanofluids in horizontal annular tubes, and TiO\({}_{2}\), Ag, Cu, and Al\({}_{2}\)O\({}_{3}\) nanoparticles were considered. They suggested that the heat transfer was significantly influenced by the Rayleigh number and coefficient of thermal conduction of nanoparticles. [PERSON] et al. [6] experimentally studied the heat transfer and flow behavior of Al\({}_{2}\)O\({}_{3}\)-water nanofluids in rectangular microchannels. Wherein, the diameter of nanoparticles was 170 nm. They found that, under laminar condition, the adoption of 1.8% nanofluids improved the heat transfer coefficient by 32% compared with water, meanwhile, no obvious resistance loss was produced. [PERSON] et al. [7] measured the thermal conductivity and pressure drop of Al\({}_{2}\)O\({}_{3}\)-water nanofluids in uniformly heated tubes. They found that the friction data were in accord with prediction results of the Darcy equation, while the heat transfer enhancement was not in good agreement with the Shah equation. [PERSON] et al. [8; 9] reported an experimental study on turbulence heat transfer of TiO\({}_{2}\)-water nanofluids in a double-tube counterflow heat exchanger. In their study, the solid volume fraction is 0.2-2%. The results showed that the heat transfer could be improved by 6-11% using nanofluids, and a larger friction was also produced. Then they presented correlations of the Nusselt number and the friction factor based on experimental results. [PERSON] et al. [10] established microchannels with ribs and carried out a numerical investigation on laminar (Re = 10-100) heat transfer behavior of Al\({}_{2}\)O\({}_{3}\)-water nanofluids of which the maximum volume fraction was 0.04%. Effects of the ribs height and position, nanoparticle concentration, and Re on thermal-hydraulic performance were discussed. It was shown that the increase of rib height and nanoparticle concentration were beneficial to the heat transfer performance. [PERSON] et al. [11] studied the flow and heat transfer of nanofluids in horizontal passages using direct numerical simulation.