Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative

This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid. The fractional calculus approach is used to establish the constitutive relationship model of a viscoelastic fluid. Exact analytic solutions for the velocity field and shear stress in terms of Fox H-function are obtained by means of the Laplace transform. The influence of the relaxation and retardation times, the orders of the time fractional derivative and the magnetic body force on the velocity and shear stress are analyzed. It is shown that the ordinary Oldroyd-B fluid, generalized second grade fluid and Maxwell fluid are the limiting cases of the presented results.