Advances in Applied Sciences

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Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity

Received: 19 July 2018    Accepted: 13 August 2018    Published: 06 September 2018
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Abstract

In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mux) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.

DOI 10.11648/j.aas.20180303.13
Published in Advances in Applied Sciences (Volume 3, Issue 3, June 2018)
Page(s) 34-42
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

Stretching Sheet, Slip Parameter, Heat Source, Thermal Radiation, Chemical Reaction, OHAM

References
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[7] P. Babu, J.A. Rao, and S. Sheri, “Radiation Effect on Mhd Heat and Mass Transfer Flow over a Shrinking Sheet with Mass Suction,” J. Appl. Fluid Mech., 2014, 7(4): 641–650.
[8] N. S. Akbar, S. Nadeem, R.U. Haq, and Z.H. Khan, “Radiation effects on MHD stagnation point flow of nanofluid towards a stretching surface with convective boundary condition,” Chin J Aeronaut, 2013, 26: 1389–97.
[9] B. C. Rout and S. R. Mishra, “Thermal energy transport on MHD nanofluid flow over a stretching surface: A comparative study,” Eng. Sci. Technol. an Int. J., 2018, 21: 60–69.
[10] N. S. Akbar, S. Nadeem, R. U. Haq, and Z. H. Khan, “Dual solutions in MHD stagnation point flow of a Prandtl fluid impinging on a shrinking sheet,” Appl Math Mech, 2014, 35: 813–20.
[11] O. D. Makinde and S. R. Mishra, “On Stagnation Point Flow of Variable Viscosity Nanofluids Past a Stretching Surface with Radiative Heat,” Int. J. Appl. Comput. Math., 2017, 3: 561-578
[12] D. Pal and G. Mandal, “Influence of Lorentz Force and Thermal Radiation on Heat Transfer of Nanofluids Over a Stretching Sheet with Velocity–Thermal Slip,” Int. J. Appl. Comput. Math., 2017, 3(4): 3001-3020.
[13] D. Pal and N. Roy, “Influence of Brownian Motion and Thermal Radiation on Heat Transfer of a Nanofluid Over Stretching Sheet with Slip Velocity,” Int. J. Appl. Comput. Math,2017, 3(4): 3355–3377.
[14] Y. S. Daniel, Z. A. Aziz, Z. Ismail, and F. Salah, “Effects of slip and convective conditions on MHD flow of nanofluid over a porous nonlinear stretching/shrinking sheet,” Aust. J. Mech. Eng., 2017.
[15] M. Sheikholeslami, H.. Ashorynejad, D.. Ganji, and A. Kolahdooz, “Investigation of rotating MHD viscous flow and heat transfer between stretching and porous surfaces using analytical method,” Math probl Eng, 2011: 1–17.
[16] G. Adamu and B. Shankar, “MHD Flow of Non-Newtonian Viscoelastic Fluid on Stretching Sheet With The Effect of Slip Velocity,” Int. J. Eng. Manuf. Sci., 2018, 8(1): 1–14.
[17] P. V. S. Narayana and D. H. Babu, “Numerical study of MHD heat and mass transfer of a Jeffrey fluid over a stretching sheet with chemical reaction and thermal radiation,” J. Taiwan Inst. Chem. Eng.,2016,59: 18–25.
[18] K. Ammad and A. Ishak, “Magnetohydrodynamic (MHD) Jeffrey fluid over a stretching vertical surface in a porous medium,” Propuls. Power Res., 2017, 6(4): 269–276.
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[21] A. Zeeshan and A. Majeed, “Heat transfer analysis of Jeffery fluid flow over a stretching sheet with suction/injection and magnetic dipole effect,” Alexandria Eng. J., 2016, 55: 2171–2181.
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Author Information
  • Department of Mathematics, College of Science, Osmania University, Hyderabad, India

  • Department of Mathematics, College of Science, Osmania University, Hyderabad, India

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  • APA Style

    Adamu Gizachew, Bandari Shankar. (2018). Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Advances in Applied Sciences, 3(3), 34-42. https://doi.org/10.11648/j.aas.20180303.13

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    ACS Style

    Adamu Gizachew; Bandari Shankar. Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Adv. Appl. Sci. 2018, 3(3), 34-42. doi: 10.11648/j.aas.20180303.13

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    AMA Style

    Adamu Gizachew, Bandari Shankar. Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Adv Appl Sci. 2018;3(3):34-42. doi: 10.11648/j.aas.20180303.13

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  • @article{10.11648/j.aas.20180303.13,
      author = {Adamu Gizachew and Bandari Shankar},
      title = {Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity},
      journal = {Advances in Applied Sciences},
      volume = {3},
      number = {3},
      pages = {34-42},
      doi = {10.11648/j.aas.20180303.13},
      url = {https://doi.org/10.11648/j.aas.20180303.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.aas.20180303.13},
      abstract = {In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mux) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.},
     year = {2018}
    }
    

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    AU  - Adamu Gizachew
    AU  - Bandari Shankar
    Y1  - 2018/09/06
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    JF  - Advances in Applied Sciences
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    AB  - In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mux) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.
    VL  - 3
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