Abstract
In this paper fractional Maxwell fluid equation has been solved. The solution is in the Mettag-Leffler form. For the corresponding solutions for ordinary Maxwell fluid are obtained as limiting case of general solutions. Finally, the effects of different parameters on the velocity and shear stress profile are analyzed through plotting the velocity and shear stress profile.
Highlights
Fluids are classified into Newtonian and non-Newtonian where in the second case the relation between the rate of strain and shear stress is nonlinear
A thermodynamic framework has been put into place to develop a rate type model known as Maxwell which is non-Newtonian model, in which the ordinary Maxwell model has been replaced by the Maxwell model with fractional calculus such that the time derivative of an integer order replacing by the so-called Riemann-Liouville fractional differential operator [3,4,5,6]
Exact analytical solutions for a longitudinal flow of a fractional Maxwell fluid between two coaxial cylinders are investigated by Awan [9]
Summary
Fluids are classified into Newtonian and non-Newtonian where in the second case the relation between the rate of strain and shear stress is nonlinear. Hyder [7] in his paper solved the Fractional Burgers’ model for the flow of fluid with viscoelastic property. Zheng [8] discussed the slip effects on MHD flow of a generalized Oldroyd- B fluid with fractional derivative. Exact analytical solutions for a longitudinal flow of a fractional Maxwell fluid between two coaxial cylinders are investigated by Awan [9].
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