Abstract In this paper, we have presented an innovative model for coupled vibrations of nanotubes conveying fluid by considering the small-size effects on the flow field. By this model, we have demonstrated that ignoring the small-size effects on flow field in a nano-scale fluid–structure interaction (FSI) problem may generate erroneous results. The nanotube has been modeled by Euler–Bernoulli plug-flow beam kinematic theory, and we have formulated the small-size effects on bulk viscosity and slip boundary conditions of nanoflow through Knudsen number ( Kn), as a discriminant parameter. The divergence instability phenomenon has been observed, incorporating various flow regimes for liquids and gases. We have observed that including the effect of nanoflow viscosity, is not so influential on vibration of nanotubes conveying fluid, as compared with the results of vibration of nanotubes conveying an inviscid fluid; however, incorporating the nanoflow slip-boundary conditions hypothesis changes the results drastically, as compared to continuum flow models.