Innovative coupled fluid–structure interaction model for carbon nano-tubes conveying fluid by considering the size effects of nano-flow and nano-structure

In this article, we reappraise the well-known equation of motion for a pipe conveying viscous fluid. We utilize prominent principles of fluid mechanics such as Navier–Stokes’ equation as well as several benchmark references in the field of fluid–structure interaction (FSI) to reveal that the viscosity of the fluid flow should not appear explicitly in the equation of motion of pipe conveying fluid. Based on this result, we could develop an innovative model for one dimensional coupled vibrations of carbon nano-tubes (CNTs) conveying fluid using slip velocity of the fluid flow on the CNT walls as well as utilizing size-dependent continuum theories to consider the size effects of nano-flow and nano-structure. Therefore, this innovative coupled FSI equation suggests that CNTs conveying nano-flow remain stable for higher velocities. In the other words, the critical average velocity of the fluid flow at which the divergence instability occurs, should be greater in comparison with the critical velocity predicted by the models used plug flow and classical continuum theories.