Wave propagation analysis of magnetic nanotubes conveying nanoflow

According to the nonlocal strain gradient theory, wave propagation in magnetic nanotubes conveying magnetic nanoflow under longitudinal magnetic field is inspected. The nonlocal strain gradient Timoshenko beam model is coupled with magnetic nanoflow considering slip boundary condition to model fluid structure interaction. By applying Hamilton's principle, the size-dependent governing equations of motion have been obtained. Calculation of the wave frequency as well as phase velocity has been carried out based on the harmonic solution. The influences of strain gradient length scale, nonlocal parameter, Knudsen number, longitudinal magnetic field and magnetic nanoflow on nanotubes' wave propagation behavior have been examined. According to analytical results, the magnetic intensity related to the longitudinal magnetic field contributes significantly to increasing nanotubes' wave frequency as well as phase velocity. Besides, the magnetic nanotubes conveying magnetic nanoflow predict the highest phase velocity and wave frequency. Also, the wave frequency decrease when the nonlocal parameter increases or the strain gradient length scale decreases. Moreover, an increase in fluid velocity reduces the wave frequency and phase velocity.