Fractional MHD Oldroyd-B fluid over an oscillating plate

Abstract

This paper presents some new exact solutions corresponding to the oscillating flows of a MHD Oldroyd-B fluid with fractional derivatives. The fractional calculus approach in the governing equations is used. The exact solutions for the oscillating motions of a fractional MHD Oldroyd-B fluid due to sine and cosine oscillations of an infinite plate are established with the help of discrete Laplace transform. The expressions for velocity field and the associated shear stress that have been obtained, presented in series form in terms of Fox Hfunctions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary MHD Oldroyd-B , fractional and ordinary MHD Maxwell, fractional and ordinary MHD Second grade and MHD Newtonian fluid as well as those for hydrodynamic fluids are obtained as special cases of general solutions. Finally, the obtained solutions are graphically analyzed through various parameters of interest.

Keywords

Dates

  • Submission Date2011-07-31
  • Revision Date2011-10-22
  • Acceptance Date2011-10-26

DOI Reference

10.2298/TSCI110731140J

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Volume 17, Issue 4, Pages997 -1011