In the current analysis, an attempt is made to develop a nonlinear size-dependent fluid-structure interaction model for the chaotic motion of nanofluid-conveying nanotubes subject to an external excitation. The material properties of the nanotube are assumed to be viscoelastic. Size effects in both solid and fluid nanoscale parts are taken into consideration. In addition, the effects of both centripetal and Coriolis accelerations are incorporated in the model. Using Hamilton's principle, the nonlocal strain gradient elasticity and the Beskok-Karniadaki theory, the nonlinear size-dependent governing equation is derived. For developing a precise solution approach, Galerkin's procedure and a direct-time-integration method are eventually used. Different parameters of the nanosystem are taken into consideration to study the size-dependent chaotic motion of the viscoelastic nanotube conveying nanofluid subject to a harmonic excitation.