Wave propagation of magnetic nanofluid-conveying double-walled carbon nanotubes in the presence of longitudinal magnetic field

摘要

In this article, the effect of longitudinal magnetic field on wave propagation of an embedded double-walled carbon nano-tube with conveying fluid is studied using either the Euler-Bernoulli beam or the Timoshenko beam models. Conveying fluid is magnetite (Fe_3O_4) nanofluid, which is a ferrofluid. Ferrofluids are effective in the presence of magnetic field. Based on Eringen's nonlocal theory, energy method, and Hamilton's principle, wave motion equations are derived for both Euler-Bernoulli beam and Timoshenko beam models. The cut-off frequency, upstream, and downstream phase velocities are evaluated using a harmonic solution. A detailed parametric study is conducted to elucidate the influences of the small-scale coefficient, stiffness of the elastic medium, magnetic field, and fluid velocity on the wave propagation of the double-walled carbon nanotube. The results indicate that double-walled carbon nanotube has higher phase velocity in the presence of magnetic field when the wave number is relatively low for both the beam models. In addition, the effect of magnetic field may be ignored for higher wave numbers. Furthermore, during the flow of a ferrofluid through a double-walled carbon nanotube, the magnetic effect of flowing ferrofluid on the wave propagation of double-walled carbon nanotube may be ignored. The present study will hopefully be useful to deliver medicines and other appliances in nanoscale.