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Analytical solution of the transient electro-osmotic flow of a generalized fractional Maxwell fluid in a straight pipe with a circular cross-section. (English) Zbl 1408.76018
Summary: In this study, we examine the transient electro-osmotic flow of a generalized Maxwell fluid with a fractional derivative in a narrow capillary tube. Using 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. We show that the distribution and establishment of the velocity comprises two parts: the steady and unsteady parts. We demonstrate the effects of the relaxation time, fractional derivative parameter, and the Debye-Hückel parameter on the generation of flow in a graphical manner and analyze them numerically. The velocity overshoot and oscillation are observed and discussed.

MSC:
76A05 Non-Newtonian fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
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