In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of an Oldroyd-B fluid, between two infinite coaxial circular cylinders, are determined by applying the finite Hankel transforms. The motion is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent rotational shear stress. The solutions that have been obtained are presented under series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for Maxwell, second grade and Newtonian fluids are obtained as limiting case of general solutions. Finally, the influence of the pertinent parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.
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American Journal of Applied Mathematics (Volume 3, Issue 3-1)
This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015) |
DOI | 10.11648/j.ajam.s.2015030301.15 |
Page(s) | 25-31 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
Taylor-Couette Flow, Oldroyd-B Fluid, Velocity Field, Shear Stress
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APA Style
M. Imran, Madeeha Tahir, M. A. Imran, A. U. Awan. (2015). Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation. American Journal of Applied Mathematics, 3(3-1), 25-31. https://doi.org/10.11648/j.ajam.s.2015030301.15
ACS Style
M. Imran; Madeeha Tahir; M. A. Imran; A. U. Awan. Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation. Am. J. Appl. Math. 2015, 3(3-1), 25-31. doi: 10.11648/j.ajam.s.2015030301.15
AMA Style
M. Imran, Madeeha Tahir, M. A. Imran, A. U. Awan. Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation. Am J Appl Math. 2015;3(3-1):25-31. doi: 10.11648/j.ajam.s.2015030301.15
@article{10.11648/j.ajam.s.2015030301.15, author = {M. Imran and Madeeha Tahir and M. A. Imran and A. U. Awan}, title = {Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation}, journal = {American Journal of Applied Mathematics}, volume = {3}, number = {3-1}, pages = {25-31}, doi = {10.11648/j.ajam.s.2015030301.15}, url = {https://doi.org/10.11648/j.ajam.s.2015030301.15}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.15}, abstract = {In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of an Oldroyd-B fluid, between two infinite coaxial circular cylinders, are determined by applying the finite Hankel transforms. The motion is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent rotational shear stress. The solutions that have been obtained are presented under series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for Maxwell, second grade and Newtonian fluids are obtained as limiting case of general solutions. Finally, the influence of the pertinent parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.}, year = {2015} }
TY - JOUR T1 - Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation AU - M. Imran AU - Madeeha Tahir AU - M. A. Imran AU - A. U. Awan Y1 - 2015/06/15 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.s.2015030301.15 DO - 10.11648/j.ajam.s.2015030301.15 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 25 EP - 31 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.s.2015030301.15 AB - In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of an Oldroyd-B fluid, between two infinite coaxial circular cylinders, are determined by applying the finite Hankel transforms. The motion is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent rotational shear stress. The solutions that have been obtained are presented under series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for Maxwell, second grade and Newtonian fluids are obtained as limiting case of general solutions. Finally, the influence of the pertinent parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations. VL - 3 IS - 3-1 ER -