Slip Effects on Fractional Viscoelastic Fluids. (20th December 2011)

• Record Type: Journal Article
• Authors: Jamil, Muhammad; Khan, Najeeb Alam
• Other Names: Chen Wen Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2011(2011)
• Publication Date: 2011-12-20
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2011/193813
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions p Ψ q, by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter isθ → 0 . Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally, the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations.