Slip Effects on Fractional Viscoelastic Fluids
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induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid.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 gen...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/193813 |
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| author | Muhammad Jamil Najeeb Alam Khan |
| author_facet | Muhammad Jamil Najeeb Alam Khan |
| author_sort | Muhammad Jamil |
| collection | DOAJ |
| description | 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plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid.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 𝑝Ψ𝑞,
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 is 𝜃→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. |
| format | Article |
| id | doaj-art-e74622d969c14291b640a08e765fdbc6 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-e74622d969c14291b640a08e765fdbc62025-02-03T01:02:55ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/193813193813Slip Effects on Fractional Viscoelastic FluidsMuhammad Jamil0Najeeb Alam Khan1Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, PakistanDepartment of Mathematics, University of Karachi, Karachi 75270, PakistanUnsteady 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 𝑝Ψ𝑞, 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 is 𝜃→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.http://dx.doi.org/10.1155/2011/193813 |
| spellingShingle | Muhammad Jamil Najeeb Alam Khan Slip Effects on Fractional Viscoelastic Fluids International Journal of Differential Equations |
| title | Slip Effects on Fractional Viscoelastic Fluids |
| title_full | Slip Effects on Fractional Viscoelastic Fluids |
| title_fullStr | Slip Effects on Fractional Viscoelastic Fluids |
| title_full_unstemmed | Slip Effects on Fractional Viscoelastic Fluids |
| title_short | Slip Effects on Fractional Viscoelastic Fluids |
| title_sort | slip effects on fractional viscoelastic fluids |
| url | http://dx.doi.org/10.1155/2011/193813 |
| work_keys_str_mv | AT muhammadjamil slipeffectsonfractionalviscoelasticfluids AT najeebalamkhan slipeffectsonfractionalviscoelasticfluids |