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(+) begins to slide in its plane with a velocity At. 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 alpha = beta = 1, M = 0, the solutions corresponds to the ordinary Oldroyd-B fluids, while theta = 0 and lambda = 0 describe the Maxwell fluid and the generalized second grade fluid, as limiting cases of present results, respectively. (C) 2011 Elsevier Ltd. All rights reserved.