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Z. Naturforsch. 69a, 697 – 704
(2014)
doi:10.5560/ZNA.2014-0066
Exact Solutions of Electro-Osmotic Flow of Generalized Second-Grade Fluid with Fractional Derivative in a Straight Pipe of Circular Cross Section
1 Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, P.R. China
2 Geotechnical and structural engineering research center, Shandong University, Jinan 250061, P.R. China
3 School of Mathematical Sciences, University of Jinan, 106 Jiwei Road, 250022, Jinan, P.R. China
4 Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, P.R. China
5 College of Civil Engineering, Shandong Jiaotong University, Jinan 250357, P.R. China
Received May 28, 2014 / revised August 28, 2014 / published online November 20, 2014
Reprint requests to: S. W.; E-mail:
shaoweiwang@sdu.edu.cn
The transient electro-osmotic flow of generalized second-grade fluid with fractional derivative in a narrow capillary tube is examined. With the help of the integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson–Boltzmann equation and the Navier–Stokes equation. It was shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The effects of retardation time, fractional derivative parameter, and the Debye–Hückel parameter on the generation of flow are shown graphically.
Key words: Analytical Solutions; Fractional Calculus; Laplace Transform; Viscoelastic Fluids; Electro-Osmotic Flow.