Exact solutions for MHD flow of generalized Oldroyd-B fluid due to an infinite accelerating plate

This paper presents a research for the magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid due to an infinite accelerating plate. The motion of the fluid is produced by the infinite plate, which at time t=0+t=0+ begins to slide in its plane with a velocity AtAt. The fractional calculus approach is introduced to establish the constitutive relationship of the Oldroyd-B fluid. The solutions are established by means of Fourier sine and Laplace transforms in terms of the G and R functions written as a direct sum of the Newtonian solution and the corresponding non-Newtonian solutions. When α=β=1α=β=1, M=0M=0, the solutions corresponds to the ordinary Oldroyd-B fluids, while θ=0θ=0 and λ=0λ=0 describe the Maxwell fluid and the generalized second grade fluid, as limiting cases of present results, respectively.