The effects of non-uniform flow velocity on vibrations of single-walled carbon nanotube conveying fluid

The vibrational behavior of a viscous nanoflow-conveying single-walled carbon nanotube (SWCNT) was investigated. The nonuniformity of the flow velocity distribution caused by the viscosity of fluid and the small-size effects on the flow field was considered. Euler-Bernoulli beam model was used to investigate flow-induced vibration of the nanotube, while the non-uniformity of the flow velocity and the small-size effects of the flow field were formulated through Knudsen number (Kn), as a discriminant parameter. For laminar flow in a circular nanotube, the momentum correction factor was developed as a function of Kn. For Kn = 0 (continuum flow), the momentum correction factor was found to be 1.33, which decreases by the increase in Kn may even reach near 1 for the transition flow regime. We observed that for passage of viscous flow through a nanotube with the non-uniform flow velocity, the critical continuum flow velocity for divergence decreased considerably as opposed to those for the uniform flow velocity, while by increasing Kn, the difference between the uniform and non-uniform flow models may be reduced. In the solution part, the differential transformation method (DTM) was used to solve the governing differential equations of motion.