Effect of Mhd on Accelerated Flows of A Viscoelastic Fluid with The Fractional Burgers’ Model

Authors

  • Hind Mahmood Department of Mathematics, College of Science, University of Baghdad, Baghdad ,Iraq.
  • Ahmed Abdulhadi Department of Mathematics, College of Science, University of Baghdad, Baghdad ,Iraq.

Keywords:

Fractional derivative, , Laplace transform,

Abstract

In this paper, we studied the effect of magnetic hydrodynamic (MHD) on accelerated flows of a viscoelastic fluid with the fractional Burgers’ model. The velocity field of the flow is described by a fractional partial differential equation of fractional order by using Fourier sine transform and Laplace transform, an exact solutions for the velocity distribution are obtained for the following two problems: flow induced by constantly accelerating plate, and flow induced by variable accelerated plate. These solutions, presented under integral and series forms in terms of the generalized Mittag-Leffler function, are presented as the sum of two terms. The first term, represent the velocity field corresponding to a Newtonian fluid, and the second term gives the non-Newtonian contributions to the general solutions. The similar solutions for second grad, Maxwell and Oldroyd-B fluids with fractional derivatives, as well as, those for the ordinary models are obtained as the limiting cases of our solutions. Moreover, in the special cases when 1==βα . While the
MATHEMATICA package is used to draw the figures velocity components in the
plane.

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Published

2024-01-26

Issue

Section

Mathematics

How to Cite

Effect of Mhd on Accelerated Flows of A Viscoelastic Fluid with The Fractional Burgers’ Model. (2024). Iraqi Journal of Science, 54(2), 419-426. https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/12312

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