In the present article, an effort is made to analyse the coupled global dynamics of nanoscale fluid-conveying tubes. The influences of geometric nonlinearity are captured through the nonlinear Euler–Bernoulli strain relation of beams. Moreover, the size influences related to the nanoscale tube are captured via developing a nonlocal strain gradient model of beams. The Beskok–Karniadakis theory is also used for capturing the size influences related to the nanofluid. In addition to size influences, Coriolis acceleration effects together with the influences of the centrifugal acceleration are taken into account. Hamilton's principle gives two coupled equations of motions, which are discretised utilising Galerkin's technique. A time integration scheme is used for extracting the global dynamic characteristics of the nanotube containing nanofluid flow. The non-dimensional critical speed associated with buckling is also determined. It is found that the nanofluid speed plays a crucial role in the global dynamics in both the subcritical and supercritical regimes.