General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid

M. A. Imran; Shakila Sarwar; D. Vieru; M. Nazar

doi:doi:10.11648/j.ajam.s.2015030301.12

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General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid

M. A. Imran, Shakila Sarwar, D. Vieru, M. Nazar

Published in American Journal of Applied Mathematics (Volume 3, Issue 3-1)

Received: 19 May 2015 Accepted: 20 May 2015 Published: 9 June 2015

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Abstract

An analysis is carried out to the unsteady free convection flow of a rotating, incompressible viscous fluid near an infinite vertical plate that applies a time-dependent shear stress f(t) to the fluid. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. At the final stage, the effects of pertinent parameters on the fluid motion are numerically and graphically illustrated. A comparison between the numerical values of the velocity components given by the analytical solution and, by the Stehfest's algorithm for the inverse Laplace transform is presented.

Published in	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.2015030301.12
Page(s)	6-13
Creative Commons	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.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Free Convection, Shear Stress, Rotating Fluid, Viscous Flow, Isothermal Vertical Plate

References

[1]	A. S. Gupta, I. Pop, V. M. Sounalgekar , Free convection effects on the flow past an accelerated vertical plate in an incompressible dissipative fluid , Rev. Roum. Sci. Techn. Mec. Apl.24, (1979) 561-568.
[2]	N.G. Kafousias and A .A. Raptis, Mass transfer and free convection effects on the flow past an accelerated vertical infinite plate with variable suction or injection, Rev. Roum. Sci. Techn. Mec. Apl. 26, (1986)11-22.
[3]	P. Chandran, N. C. Sacheti, Ak. Singh, Natural convection near a vertical plate with ramped wall temperature, Heat Mass Trans.41, (2005) 459- 464.
[4]	U. S. Rajput, S. Kumar, Rotation and radiation effects on MHD flow past an impulsively started vertical plate with variable temperature, Int. Journal of Math. Analysis, 5(24), (2011) 1155 – 1163.
[5]	V.M. Soundalgekar, Free convection effects on the Stokes problem for an infinite vertical plate, J. Heat Trans , (Tr. ASME) , 99 , (1977) 499-501.
[6]	S. Asghar, Masood Khan, A. M. Siddiqui, T. Hayat, Exact solutions for magnetohydrodynamic flow in a rotating, Acta Mech. Sinica 18 (3), (2002), 244-251.
[7]	S. Abelman, E. Momoniat, T. Hayat, Steady MHD flow of a third fluid in a rotating frame and porous space, Nonlinear Analysis: Real World Appl., 10 (2009), 3322-3328.
[8]	T. Hayat, Liaqat Ali Khan, R. Ellahi, S. Obaidat, Exact Solutions on MHD Flow Past an Accelerated Porous Plate in a Rotating Frame, Chinese Physics Letters, 28(5), 2011, 054701. doi:10.1088/0256-307X/28/5/054701.
[9]	T. Hayat, S. Abelman, M. Hamese, Oscilatory Couette flow of rotating Sisko fluid, Appl. Math. Mech.-Engl. Ed. 35 (10) (2014), 1301-1310.
[10]	M. Kumari, G. Nath, Transient rotating flow over a moving surface with a magnetic field, Int. J. Heat Mass Transfer, 48, (2005) 2878 – 2885.
[11]	R. Muthucumaraswamy, N. Dhanasekar, G. E. Prasad, Rotation effects on unsteady flow past an accelerated isothermal vertical plate withvariable mass transfer in the presence of chemical reaction of first order, J. Appl. Fluid Mech., 6 (4), (2013) 485 – 490.
[12]	M.A. Imran, D. Vieru, I. Mirza, The influence of Ekman number on flows over an oscillating isothermal vertical plate in a rotating frame (JAFM in press (2014)).
[13]	N. D. Waters, M. J. King, Unsteady flow of an elastico-viscous liquid , Rheol. Acta. 9(3), (1970) 345-355.
[14]	D. Vieru, C. Fetecau, A. Sohail, Flow due to a plate that applies an accelerated shear to a second grade fluid between two parallel walls perpendicular to the plate, Z. Angew. Math. Phys. 62, (2011) 161-172.
[15]	C. Fetecau, D. Vieru, C. Fetecau, Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid, Cent. Eur. J. Phys. 9, (2011) 816 - 824.
[16]	C. Fetecau, C. Fetecau, M. Rana, General solutions for the unsteady flow of second-grade fluids over an infinite plate that applies arbitrary shear to the fluid, Z. Naturforsch. 66a, (2011) 753 - 759.
[17]	N. Ahmed, S. Talukdar, Transient magnetohydrodynamic (MHD) flow of a visco-elastic fluid past an infinite vertical porous plate embedded in a porous medium with Hall current and slip condition in a rotating system, Int. J. of Physical Sciences 7(45), (2012) 5942-5953.
[18]	A. Q. Mohamed, I. Khan, Z. Ismail, S. Shafie, The unsteady free convection flow of second grade fluid in rotating frame with ramped wall temperature, AIP Proceedings 1605, 398 (2014), doi:10.1063/1.4887622.
[19]	C. Fetecau, . Vieru, Corina Fetecau, S. Akhtar, General solutions for magnetohydrodynamic natural convection flow with radiative heat transfer and slip condition over a moving plate, Zeitschrift Naturforshung A, 68a, (2013) 659 -667.
[20]	A. P. Prudnikov, Y. A. Brychkov, I. O. Marichev, Integrals and Series, vol. 4: Direct Laplace Transforms, Gordn and Brech, New York, (1992).
[21]	A. P. Prudnikov, Y. A. Brychkov, I. O. Marichev, Integrals and Series, vol. 5: Inverse Laplace Transforms, Gordn and Brech, New York, (1992).
[22]	R. B. Hetnarski, An algorithm for generating some inverse Laplace transform of exponential form, J. Appl. Math. Physics (ZAMP), 26, (1975) 249-253.
[23]	H. Stehfest, Algorithm 368: Numerical inversion of Laplace transforms, Communication of the ACM 13(1), (1970) 47-49.

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APA Style

M. A. Imran, Shakila Sarwar, D. Vieru, M. Nazar. (2015). General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid. American Journal of Applied Mathematics, 3(3-1), 6-13. https://doi.org/10.11648/j.ajam.s.2015030301.12

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ACS Style

M. A. Imran; Shakila Sarwar; D. Vieru; M. Nazar. General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid. Am. J. Appl. Math. 2015, 3(3-1), 6-13. doi: 10.11648/j.ajam.s.2015030301.12

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AMA Style

M. A. Imran, Shakila Sarwar, D. Vieru, M. Nazar. General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid. Am J Appl Math. 2015;3(3-1):6-13. doi: 10.11648/j.ajam.s.2015030301.12

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@article{10.11648/j.ajam.s.2015030301.12,
  author = {M. A. Imran and Shakila Sarwar and D. Vieru and M. Nazar},
  title = {General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3-1},
  pages = {6-13},
  doi = {10.11648/j.ajam.s.2015030301.12},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.12},
  abstract = {An analysis is carried out to the unsteady free convection flow of a rotating, incompressible viscous fluid near an infinite vertical plate that applies a time-dependent shear stress f(t) to the fluid. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. At the final stage, the effects of pertinent parameters on the fluid motion are numerically and graphically illustrated. A comparison between the numerical values of the velocity components given by the analytical solution and, by the Stehfest's algorithm for the inverse Laplace transform is presented.},
 year = {2015}
}

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TY  - JOUR
T1  - General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid
AU  - M. A. Imran
AU  - Shakila Sarwar
AU  - D. Vieru
AU  - M. Nazar
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PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.s.2015030301.12
DO  - 10.11648/j.ajam.s.2015030301.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 6
EP  - 13
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.s.2015030301.12
AB  - An analysis is carried out to the unsteady free convection flow of a rotating, incompressible viscous fluid near an infinite vertical plate that applies a time-dependent shear stress f(t) to the fluid. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. At the final stage, the effects of pertinent parameters on the fluid motion are numerically and graphically illustrated. A comparison between the numerical values of the velocity components given by the analytical solution and, by the Stehfest's algorithm for the inverse Laplace transform is presented.
VL  - 3
IS  - 3-1
ER  -

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Author Information

M. A. Imran

Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Shakila Sarwar

Department of Mathematics, Bahauddin Zakariya University, Multan, Pakistan
D. Vieru

Department of Theoretical Mechanics, Technical University of Iasi, Iasi, Romania
M. Nazar

Department of Mathematics, Bahauddin Zakariya University, Multan, Pakistan

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APA Style

M. A. Imran, Shakila Sarwar, D. Vieru, M. Nazar. (2015). General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid. American Journal of Applied Mathematics, 3(3-1), 6-13. https://doi.org/10.11648/j.ajam.s.2015030301.12

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ACS Style

M. A. Imran; Shakila Sarwar; D. Vieru; M. Nazar. General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid. Am. J. Appl. Math. 2015, 3(3-1), 6-13. doi: 10.11648/j.ajam.s.2015030301.12

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AMA Style

M. A. Imran, Shakila Sarwar, D. Vieru, M. Nazar. General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid. Am J Appl Math. 2015;3(3-1):6-13. doi: 10.11648/j.ajam.s.2015030301.12

Copy | Download

@article{10.11648/j.ajam.s.2015030301.12,
  author = {M. A. Imran and Shakila Sarwar and D. Vieru and M. Nazar},
  title = {General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3-1},
  pages = {6-13},
  doi = {10.11648/j.ajam.s.2015030301.12},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.12},
  abstract = {An analysis is carried out to the unsteady free convection flow of a rotating, incompressible viscous fluid near an infinite vertical plate that applies a time-dependent shear stress f(t) to the fluid. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. At the final stage, the effects of pertinent parameters on the fluid motion are numerically and graphically illustrated. A comparison between the numerical values of the velocity components given by the analytical solution and, by the Stehfest's algorithm for the inverse Laplace transform is presented.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid
AU  - M. A. Imran
AU  - Shakila Sarwar
AU  - D. Vieru
AU  - M. Nazar
Y1  - 2015/06/09
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.s.2015030301.12
DO  - 10.11648/j.ajam.s.2015030301.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 6
EP  - 13
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.s.2015030301.12
AB  - An analysis is carried out to the unsteady free convection flow of a rotating, incompressible viscous fluid near an infinite vertical plate that applies a time-dependent shear stress f(t) to the fluid. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. At the final stage, the effects of pertinent parameters on the fluid motion are numerically and graphically illustrated. A comparison between the numerical values of the velocity components given by the analytical solution and, by the Stehfest's algorithm for the inverse Laplace transform is presented.
VL  - 3
IS  - 3-1
ER  -

Copy | Download