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Effect of Mhd on Accelerated Flows of A Viscoelastic Fluid with The Fractional Burgers’ Model | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 54, Issue 2, 2013, Pages 419-426 | ||
| Authors | ||
| Hind S. Mahmood; Ahmed M. Abdulhadi | ||
| 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 . While the MATHEMATICA package is used to draw the figures velocity components in the plane. | ||
| Keywords | ||
| Fractional derivative; Laplace transform; Fourier transform | ||
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