Abstract
This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters. While the MATHEMATICA package is used to draw the figures velocity components in the plane.
Highlights
The interest for flow of nonNewtonian fluids has considerably grown in recent years because of the advance in technological applications
A thermodynamic framework has been put into place to develop a rate type model known as Burgers' model that is used to describe the motion of earth's mantle
Hyder [7] discussed some unidirectional flows of a viscoelastic fluid between two parallel plates with fractional Burgers' fluid models
Summary
The interest for flow of nonNewtonian fluids has considerably grown in recent years because of the advance in technological applications. It is difficult to suggest a single model which exhibits all properties of non-Newtonian fluids as it done for Newtonian fluids For this reason, a number of constitutive equations have been proposed. A thermodynamic framework has been put into place to develop a rate type model known as Burgers' model that is used to describe the motion of earth's mantle This model is used to characterize diverse viscoelastic materials, such as asphalt in geomechanics and cheese in food products. Khan [6] Studied the accelerated flows for a viscoelastic fluid governed by the fractional Burgers’ model. Hyder [7] discussed some unidirectional flows of a viscoelastic fluid between two parallel plates with fractional Burgers' fluid models. The paper ends with drawing the figures of velocity component in the plane
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