In this article, the effect of longitudinal magnetic field on wave propagation of an embedded double-walled carbon nanotube with conveying fluid is studied using either the Euler-Bernoulli beam or the Timoshenko beam models. Conveying fluid is magnetite (Fe 3 O 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 cutoff 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. Keywords Double-walled carbon nanotube with conveying ferrofluid, magnetic field, wave propagation, cutoff frequency, Timoshenko beam Date

Nonlinear vibration and instability of a boron nitride micro-tube (BNMT) conveying ferrofluid under the combined magnetic and electric fields are investigated. Based on Euler–Bernoulli beam (EBB), piezoelasticity strain gradient theory and Hamilton's principle, high order equations of motion are derived for three boundary conditions namely as clamped–clamped (C–C), simply–simply (S–S) and clamped–simply (C–S). The differential quadrature method (DQM) is applied to discretize the motion equations in order to obtain the nonlinear frequency and critical fluid velocity using a direct iterative method. A detailed parametric study is conducted to elucidate the influences of the various boundary conditions, size diameter and magnetic field on vibrational characteristic of BNMT. Numerical results indicate that the effect of magnetic field appears in higher speed of ferrofluid and increases the critical velocity or enlarges the stability region. The results are in good agreement with the previous researches. The results of this study can be used to manufacture smart micro/nano electromechanical systems in advanced biomechanics applications with magnetic and electric fields as parametric controllers.

In the present study, wave propagation characteristics of double-walled boron nitride nanotubes (DWBNNTs) conveying ferrofluid is investigated. Magnetite (Fe 3 O 4) nanofluid is selected as a conveying fluid which reacted in presence of magnetic field. Shear effects of surrounded medium are taken into account using Pasternak model. Stress and strain-inertia gradient elasticity theories are used due to their capability to interpret size effect. Based on Hamilton's principle and employing Euler-Bernoulli, Timoshenko and Reddy beam models, wave equations of motion in double-walled boron nitride nanotubes are derived and solved by harmonic solution. Regarding the various types of flow regimes in fluid-structure interaction, the upstream and downstream phase velocities of double-walled boron nitride nanotubes conveying ferrofluid are calculated. A detailed parametric study is conducted to clarify the influences of the beam models, size effect theories, magnetic field, surrounding elastic medium and fluid velocity on the wave propagation of double-walled boron nitride nanotubes conveying ferrofluid. The results indicated that in lower wave numbers, the effect of flowing fluid and the difference between the upstream and downstream phase velocities were considerable. The results of this work can be used in design and manufacturing of nanopipes and nanovalves conveying fluid flow to avoid water hammer phenomenon.

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