American Journal of Applied Mathematics

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The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid

Received: 14 April 2017    Accepted: 27 April 2017    Published: 23 June 2017
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Abstract

In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.

DOI 10.11648/j.ajam.20170503.13
Published in American Journal of Applied Mathematics (Volume 5, Issue 3, June 2017)
Page(s) 78-90
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), 2024. Published by Science Publishing Group

Keywords

Viscoelastic Fluid, MHD, Couette Channel Walls, Permeability of Porous Medium

References
[1] K. Walters, Non-Newtonian effects in some elastic-viscous liquids whose behavior at small rates of shear is characterized by a general linear equation of state. Quant. J. Mech. Appl. Math, 15, 1962, 63-76.
[2] Bhaskara Reddy N. and Bathaiah, D., Reg. J. of Energy Heat Mass Transfer, 3 (4), 1981, 239-255.
[3] Bhaskara Reddy N. and Bathaiah, D., Acta Mechanica, 42, 1982, 239-251.
[4] Chowdhury M. K. and Islam M. N., MHD-free convection flow of viscoelastic fluid past an infinite porous plate, Int. J. Heat Mass Trans., 36, 2000, 439-447.
[5] Rajgopal K., Veena P. H. and Parvin V. K., Oscillatory Motion of an Electrically Conducting Viscoelastic Fluid over a Stretching Sheet in Saturated Porous Medium with Suction / Blowing. Mathematical Problems in Engineering, 1, 2006, 1-14.
[6] P. R. Sharma and D. Pareek, Unsteady flow and heat transfer through an elastic viscous liquid along an infinite hot vertical porous moving plate with variable free stream suction. Bull. Cal. Math. Sec. 98, 2006, 97-108.
[7] Pravat Kumar Rath, G. C. Dash, and P. K. Rath, Flow and heat transfer of an electrically conducting viscoelastic fluid between two horizontal squeezing/stretching plates. AMSE Modeling Measurement and Control 70, 2001, 45-63.
[8] S. M. B. Alhari, A. A. Mohamed and M. S. E. L. Gerdy, Heat and Mass transfer in MHD viscous elastic fluid flow through a porous medium over a stretching sheet with chemical reaction. Applied Mathematics 1, 2010, 446-455.
[9] B. Kumar and R. Sivaraj, MHD mixed convective viscoelastic fluid flow in a permeable vertical channel with Dufour effect and chemical reaction. Int. J. of Appl. Math. & Mech. 14, 2011, 79-96.
[10] R. A. Damesh and B. A. Shannak, Viscoelastic fluid flow past infinite vertical porous plates in the presence of first order chemical reaction, Int. J. of Appl. Math. Mech. Engl. Ed. 31, 2010, 955-962.
[11] S. Dash, G. C. Dash and D. P. Mishra, MHD flow through a porous medium past a stretched vertical permeable surface in the presence of heat source/sink and a chemical reaction. Proc. Nat. Acad. Sci. India., 78A, 2008, 49-55.
[12] P. K. Rath, T. Parida and G. C. Dash, Three-Dimension free convective flow through porous medium in a vertical channel with heat source and chemical reaction. Proc. Nat. Acad. Sci. India, 82A, 2012, 225-232.
[13] P. R. Sharma and S. Sharma, Unsteady two dimensional flow and heat transfer through an elastic viscous liquid along an infinite hot vertical porous surface bounded by porous medium. Bull. Cal. Math. Sec. 97, 2005; 477-488.
[14] Arpita Mohanty, Pravat Kumar Rath, G. C. Dash, Unsteady MHD flow of a viscoelastic fluid a long a vertical porous surface with fluctuating temperature and concentration IOSR Journal of Engineering, ISSN (e); 2250-3021, ISSN (p); 2278-8719, 4, 2014, 46-57.
[15] Pawan Kumar Sharma, Mukesh Dutt, MHD oscillatory free convection flow past parallel plates with periodic temperature and concentration, Universal Journal of Applied Mathematics, 2 (7), 2014, 264 – 75, Doi: 10.13189/ujam.2014,020702.
[16] T. Sarpkaya, Flow of non-Newtonian fluids in a magnetic field, AICHE Journal 7, 1961, 324-328.
[17] Cogley A. C., Vinceti W. C. and Gilles S. E. Differential Approximation for Radiation Transfer in a Nongray Gas near Equilibrium. American Institute of Aeronautics and Astronautics Journal, 6, 1968, 551-555.
[18] Mansour M. A. Radiative and Free Convection Effects on the Oscillatory Flow past a Vertical Plate. Astrophysics and Space Science, 166, 1990, 269-275.
[19] Hossain M. A. and Thakar, H. S. Radiation Effect on Mixed Convection along a Vertical Plate with Uniform Surface Temperature. Heat and Mass Transfer, 314, 1996, 243-248.
[20] Hossain M. A., Alim M. A. and Rees S. The Effect of Radiation on Free Convection from a Porous Vertical Plate. International Journal of Heat and Mass Transfer, 42, 1999, 181-191.
[21] Muthucumarswamy R. and Senthil G. K., Effect of Heat and Mass Transfer on Moving Vertical Plate in the Presence of Thermal Radiation. Journal of Theoretical and Applied Mechanics, 31, 2004, 35-46.
[22] Aydin A. and Kaya A. Radiation Effect on MHD Mixed Convection Flow about a Permeable Vertical Plate. Heat and Mass Transfer, 45, 2008, 239-246.
[23] Muthucumarswamy R. and Janakiraman B. Mass Transfer Effects on Isothermal Vertical Oscillating Plate in the Presence of Chemical Reaction. International Journal of Applied Mathematics and Mechanics, 4, 2008, 66-74.
[24] Sudheer Babu M. and Satya Narayan P. V. Effects of the Chemical Reaction and Radiation Absorption on Free Convection Flow through Porous Medium with Variable Suction in the Presence of Uniform Magnetic Field. Journal of Heat and Mass Transfer, 3, 2009, 219-234.
[25] Makinde D. and Chinyoka T. Numerical Study of Unsteady Hydromagnetic Generalized Couette Flow of a Reactive Third-Grade Fluid with Asymmetric Convective Cooling. Computers and Mathematics with Applications, 61, 2011, 1167-1179.
[26] Skelland A. H. P. Non-Newtonian Flow and Heat Transfer, John Wiley, Sons, New York, 1976.
[27] Brewster M. A Thermal Radiative Transfer and Properties.– New York: John Wiley and Sons, 1992.
Author Information
  • School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

  • School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

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  • APA Style

    Binyam Zigta, Purnachandra Rao Koya. (2017). The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. American Journal of Applied Mathematics, 5(3), 78-90. https://doi.org/10.11648/j.ajam.20170503.13

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    Binyam Zigta; Purnachandra Rao Koya. The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. Am. J. Appl. Math. 2017, 5(3), 78-90. doi: 10.11648/j.ajam.20170503.13

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    AMA Style

    Binyam Zigta, Purnachandra Rao Koya. The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. Am J Appl Math. 2017;5(3):78-90. doi: 10.11648/j.ajam.20170503.13

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  • @article{10.11648/j.ajam.20170503.13,
      author = {Binyam Zigta and Purnachandra Rao Koya},
      title = {The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid},
      journal = {American Journal of Applied Mathematics},
      volume = {5},
      number = {3},
      pages = {78-90},
      doi = {10.11648/j.ajam.20170503.13},
      url = {https://doi.org/10.11648/j.ajam.20170503.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20170503.13},
      abstract = {In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid
    AU  - Binyam Zigta
    AU  - Purnachandra Rao Koya
    Y1  - 2017/06/23
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajam.20170503.13
    DO  - 10.11648/j.ajam.20170503.13
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 78
    EP  - 90
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20170503.13
    AB  - In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.
    VL  - 5
    IS  - 3
    ER  - 

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