High-accuracy hull iteration method for uncertainty propagation in fluid-conveying carbon nanotube system under multi-physical fields

Abstract

High-accuracy numerical method is of significance in nano-electromechanical systems. This paper focuses on the influence of nano-system uncertainties on the critical flow velocity of fluid-conveying carbon nanotubes (CNTs) under multi-physical fields. A hull iteration method is proposed to estimate the bounds of the critical flow velocity of fluid-conveying CNT. The nonlinear governing equations for a fluid-conveying CNT embedded in an elastic medium and subjected to thermal and magnetic fields are derived by using the nonlocal Euler–Bernoulli beam theory. Considering the limited available information on the uncertainties, the material and geometrical properties of the CNT are described by using unknown-but-bounded parameters. The iterative scheme is presented in the framework of interval mathematics. After the assessment of the proposed method by comparing Monte Carlo simulation and stochastic analysis method, the detailed parametric investigation is carried out to deeply understand the coupled effects of uncertainties and many parameters such as small scale, Knudsen number, elastic medium and magnetic field parameters, as well as temperature changes. Additionally, the effect of geometric nonlinearity on the critical flow velocity is also examined in detail. The results derived in this paper can provide useful insights on the further application of CNTs as nano-channels to convey fluids.