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Flow due to a plate that applies an accelerated shear to a second grade fluid between two parallel walls perpendicular to the plate

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Abstract

The velocity field and the shear stresses corresponding to the motion of a second grade fluid between two side walls, induced by an infinite plate that applies an accelerated shear stress to the fluid, are determined by means of the integral transforms. The obtained solutions, presented under integral form in term of the solutions corresponding to the flow due to a constant shear on the boundary, satisfy all imposed initial and boundary conditions. In the absence of the side walls, they reduce to the similar solutions over an infinite plate. The Newtonian solutions are obtained as limiting cases of the general solutions. The influence of the side walls on the fluid motion as well as a comparison between the two models is shown by graphical illustrations.

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Authors and Affiliations

  1. Department of Theoretical Mechanics, Technical University of Iasi, 700050, Iasi, Romania

    D. Vieru & Corina Fetecau

  2. Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

    A. Sohail

Authors
  1. D. Vieru
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  2. Corina Fetecau
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  3. A. Sohail
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Correspondence to D. Vieru.

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Vieru, D., Fetecau, C. & Sohail, A. Flow due to a plate that applies an accelerated shear to a second grade fluid between two parallel walls perpendicular to the plate. Z. Angew. Math. Phys. 62, 161–172 (2011). https://doi.org/10.1007/s00033-010-0073-4

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  • DOI: https://doi.org/10.1007/s00033-010-0073-4

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