Steady-State Solutions to the Equations of Motion of Second-Grade Fluids with General Navier Type Slip Boundary Conditions in Holder Spaces

This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

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Nonlocal vibration and instability analysis of embedded DWCNT conveying fluid under magnetic field with slip conditions consideration

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214533102 ◽

2014 ◽

Vol 229 (2) ◽

pp. 349-363 ◽

Cited By ~ 19

Author(s):

A Ghorbanpour Arani ◽

E Haghparast ◽

Z Khoddami Maraghi ◽

S Amir

Keyword(s):

Magnetic Field ◽

Boundary Conditions ◽

Differential Quadrature Method ◽

Equations Of Motion ◽

Nonlocal Elasticity Theory ◽

Small Scale ◽

Slip Boundary Conditions ◽

Slip Boundary ◽

Mechanical Devices ◽

Conveying Fluid

In this study, vibration of double-walled carbon nanotubes (DWCNTs) conveying fluid placed in uniform magnetic field is carried out based on nonlocal elasticity theory. DWCNT is embedded in Pasternak foundation and is simulated as a Timoshenko beam (TB) model which includes rotary inertia and transverse shear deformation in the formulation. Considering slip boundary conditions and van der Waals (vdW) forces between inner and the outer nanotubes, the governing equations of motion are discretized and differential quadrature method (DQM) is applied to obtain the frequency of DWCNTs for clamped–clamped boundary condition. The detailed parametric study is conducted, focusing on the remarkable effects of small scale, Knudsen number, elastic medium, magnetic field, density, and velocity of conveying fluid on the stability of DWCNT. Results indicate that considering slip boundary conditions has significant effect on stability of DWCNTs. Also, it is found that trend of figures have good agreement with the previous researches. Results of this investigation could be applied for optimum design of nano/micro mechanical devices for controlling stability of DWCNTs conveying fluid under magnetic fields.

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