Effect of Mhd on accelerated flows of a viscoelastic fluid with the fractional burgers’ model

Abstract EN

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.