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

  • Authors:

  • Liancun Zheng;Yaqing Liu;Xinxin Zhang

  • Affiliations:

  • Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China;Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China and Mechanical Engineering School, University of Science and Technology Beijing, Beijin ...;Mechanical Engineering School, University of Science and Technology Beijing, Beijing 100083, China

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2011

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Abstract

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 @a=@b=1, M=0, the solutions corresponds to the ordinary Oldroyd-B fluids, while @q=0 and @l=0 describe the Maxwell fluid and the generalized second grade fluid, as limiting cases of present results, respectively.