Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid

In this paper, the systems of carbon nanotubes (CNTs) conveying fluid are considered by the combination of Lie symmetry analysis and the dynamical system method. All of the geometric vector fields of the three systems are obtained, then the symmetry reductions and exact solutions to the systems are investigated by the dynamical system and the power series method. Especially, the convergence of the power series solution to the nonlinear system is shown under the condition which is easily satisfied generally.