Second-order slip flow of a generalized Oldroyd-B fluid through porous medium

Yaqing  Liu; Liancun  Zheng

doi:10.3934/dcdss.2016083

Article Contents

2016, Volume 9, Issue 6: 2031-2046. Doi: 10.3934/dcdss.2016083

This issue Previous Article Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure Next Article On the Cauchy problem of the modified Hunter-Saxton equation

Second-order slip flow of a generalized Oldroyd-B fluid through porous medium

Yaqing Liu^1, and
Liancun Zheng^2,

1.
Gengdan Institute of Beijing University of Technology, Beijing 101301
2.
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083

Received: July 31, 2015

Revised: August 31, 2016

Published: November 2016

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Abstract

This work is concerned the flow of a generalized Oldroyd-B fluid in a porous half-space with second-order slip effect. The fractional calculus approach is used to establish the constitutive relationship of the non-Newtonian fluid model. A new motion model is firstly proposed by modifying the boundary condition with second-order slip effect. Exact solutions for velocity and shear stress are obtained in terms of Fox H-function by using the discrete inverse Laplace transform of the sequential fractional derivatives. The similar solutions for the generalized Oldroyd-B fluid with first-order slip or no slip, and the solutions for a generalized Oldroyd-B fluid in nonporous medium, are obtained as the limiting cases of our solutions. Furthermore, the behavior of various parameters on the corresponding flow characteristics is shown graphical through different diagrams.

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Mathematics Subject Classification: Primary: 35R11, 76D05; Secondary: 76F10.

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