# American Institute of Mathematical Sciences

December  2016, 9(6): 2031-2046. doi: 10.3934/dcdss.2016083

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

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

Received  August 2015 Revised  September 2016 Published  November 2016

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.
Citation: Yaqing Liu, Liancun Zheng. Second-order slip flow of a generalized Oldroyd-B fluid through porous medium. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2031-2046. doi: 10.3934/dcdss.2016083
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