this regard, a remarkable number of studies have been accomplished
to disclose the vibrational behavior of such nano-structures
conveying fluid. Tuzun et al. [5], Amabili et al. [6], Yoon et al. [7],
Natsuki et al. [8], Wang et al. [9], Xia et al. [10] and Wang and Qiao
[11] made important contributions in this practical area. In this research,
we would undertake a reevaluation for computational
modeling of carbon nano-tubes conveying viscous fluid with some
fresh insights as well as we try to develop an innovative one
dimensional (1D) coupled fluid–structure interaction (FSI) equation
by considering slip condition on the nano-tube wall. Khosravian
and Rafii Tabar [12] studied the flow of viscous fluid through a
carbon nano-tube and established a new equation of motion of
pipe conveying fluid by considering the viscosity effect. They found
that a nano-tube conveying a viscous fluid was more stable against
vibration-induced buckling than a nano-tube conveying a non-viscous
fluid. Wang and Ni [13] reappraised the computational modeling
of carbon nano-tube conveying viscous fluid represented by
Khosravian and Rafii Tabar [12] and then corrected the FSI equation
and disclosed that the effect of viscosity of fluid flow on the
vibration and instability of CNTs could be ignored. Lee and Chang
[14] analyzed the influences of nonlocal effect, viscosity effect, aspect
ratio, and elastic medium constant on the fundamental frequency
of a single-walled carbon nano-tube (SWCNT) conveying

viscous fluid embedded in an elastic medium. They revealed that

the frequency increased as the values of the viscosity parameter increased.
Soltani et al. [15] developed a transverse vibrational model
for a viscous fluid-conveying SWCNT embedded in biological soft
tissue. Their investigation determined that the structural instability
and the associated critical flow velocity could be affected by
the viscosity of the fluid and the nonlocal parameter. Khoddami
et al. [16] studied electro-thermo nonlinear vibration and instability
of embedded double-walled Boron Nitride nano-tubes
(DWBNNTs) conveying viscous fluid based on nonlocal piezoelasticity
theory. They reported that increasing the small scale parameter
decreased the real and imaginary parts of frequency and
critical fluid velocity. Furthermore, they concluded that the effect
of fluid viscosity on the vibration and instability of DWBNNTs
might be ignored. In many recent studies various size-dependent
continuum theories have been developed for vibration and stability

analysis of CNTs conveying fluid. Lee and Chang [17], Zhen

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0927-0256/$ – see front matter  2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.commatsci.2013.04.047
⇑ Corresponding author. Tel.: +98 311 391 5248; fax: +98 311 391 2628.
E-mail addresses: m.mirramezani@me.iut.ac.ir (M. Mirramezani), hrmirdamadi@
cc.iut.ac.ir (H.R. Mirdamadi), ghayour@cc.iut.ac.ir (M. Ghayour).