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.
Highlights
A considerable attention has been devoted to predict the behavior of non-Newtonian fluids in view of its various applications in industries, extrusion of polymer fluids, slurry fuels and many others [25]
Bagley and Torvik [1] showed that fractional calculus models of viscoelastic material were in harmony with the molecular theory and obtained the fractional differential equation of order 1/2
Similar solutions for generalized Oldroyd-B fluid flows without slip boundary, first-order slip effect or not in porous medium can be recovered from our solutions
Summary
A considerable attention has been devoted to predict the behavior of non-Newtonian fluids in view of its various applications in industries, extrusion of polymer fluids, slurry fuels and many others [25]. Oldroyd-B fluid, second-order slip, porous medium, exact solution.
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