Wave propagation analysis of carbon nano-tube conveying fluid including slip boundary condition and strain/inertial gradient theory

This article addresses wave propagation in carbon nano-tube (CNT) conveying fluid. CNT structure is modeled by using size-dependent strain/inertia gradient theory of continuum mechanics, CNT wall-fluid flow interaction by slip boundary condition and Knudsen number (Kn). Complex-valued wave dispersion relations and corresponding characteristic equations are derived. Fluid viscosity, gyroscopic inertial force, flow velocity, wave number, wave frequency, and decaying ratio are among parameters that their variations are discussed and some remarkable results are drawn. It was observed Kn could impress complex wave frequencies at both lower and higher ranges of wave numbers, while small-size had impression at higher range.

► Gyroscopic term could effect on upstream and downstream wave frequencies.
► Without gyroscopic term, increase in Kn makes decrease in up/downstream frequency.
► Higher Kn causes increase in decaying ratio and wave number in which decaying is 0.
► The effect of small-size on decaying ratio might be only visible for viscous fluid.
► Small-size appears in higher wave number that up/downstream frequency is the same.