Abstract
In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fractional calculus approach is used in the governing equations. The exact solutions are established by means of the Fourier sine transform and N-transform. The series solutions of velocity field and associated shear stress in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. The similar solutions for ordinary Jeffrey fluid, performing the same motion, appear as limiting case of the solutions are also obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.
Highlights
Impressive advancement has been made in examining streams of non-Newtonian fluids in the most recent couple of decades
We presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate
In this paper we establish exact solutions for the velocity field and the associated shear stress corresponding to the unsteady flow of an incompressible generalized Jeffrey fluid between two side walls perpendicular to the plate
Summary
Impressive advancement has been made in examining streams of non-Newtonian fluids in the most recent couple of decades. Non-Newtonian fluids have both the properties of elasticity as well as viscosity The examples of such fluids are very large but we give some of them like honey, toothpaste, ketchup, oils and paints etc. Amongst non-Newtonian fluids the Jeffrey model is considered to be one of the simplest model which best explains the rheological effects of viscoelastic fluids. The fractional derivative [8] [9] approach has proved to be an important tool for considering behaviors of such types of fluids. Integer order time derivatives in the constitutive models for generalized Jeffrey fluids were replaced by the Riemann-Liouville fractional derivatives. Bagley [10] proved that fractional derivative models of viscoelastic type fluids were in harmony with the molecular theory and attains the fractional differential equation of order 1/2.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
