Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere

Mwangi Wanjiku Lucy; Mathew Ngugi Kinyanjui; Surindar Mohan Uppal

doi:doi:10.11648/j.ajam.20160401.15

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Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal

Published in American Journal of Applied Mathematics (Volume 4, Issue 1)

Received: 8 January 2016 Accepted: 30 January 2016 Published: 25 February 2016

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Abstract

In this study, the effects of temperature dependent viscosity on MHD natural convection flow past an isothermal sphere are determined. The uniformly heated sphere is immersed in a viscous and incompressible fluid where viscosity of the fluid is taken as a non-linear function of temperature. The Partial Differential Equations governing the flow are transformed into non dimensional form and solved using the Direct Numerical Scheme and implemented in MATLAB. The numerical results obtained are presented graphically and in tables and are discussed. In this study, it has been observed that increasing the Magnetic parameter M leads to decrease in velocity, temperature, skin friction and the rate of heat transfer. It has also been noted that increase in the Grashof number G_r leads to increase in velocity and temperature whereas increase in the values of eta η leads to increase in temperature but there is a decrease in velocity. These results are applicable to engineers in designing electricity plants which have higher life expectancy.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 1)
DOI	10.11648/j.ajam.20160401.15
Page(s)	53-61
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), 2016. Published by Science Publishing Group

Keywords

Natural Convection Flow, Temperature Dependent Viscosity, Magnetohydrodynamic (MHD), Isothermal Sphere

References

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[2]	Miraj M., Alim M. A. and Andallah L. S. (2011). Effects of Viscous Dissipation and Radiation on Magnetohydrodynamic Free Convection Flow along sphere with joule Heating and Heat Generation. Thanmasat International Journal. Of Science and Technology. 16(4): 52-64.
[3]	Kabir K. H., Alim A. and Andallah L. S (2013). Effects of viscous dissipation on MHD natural convection flow along a vertical wavy surface. Journal of Theoretical and Applied Physics. 7(31): 4-8.
[4]	Soares A. A, Ferreira J. M., Caramelo L., Anacleto J., and Chhabra R. P. (2010). The effects of temperature-dependent Viscosity on Forced Convection heat transfer from a cylinder in crossflow of power-law fluids. International Journal of heat and mass transfer. 53(21-22): 4728-4740.
[5]	Morris S. (1982). The effects of a strongly temperature dependent viscosity on a slow flow past a hot sphere. Journal of Fluid Mechanics. 124: 1-26.
[6]	Molla M., Suvash C. S., and Khan M. A. I. (2012). MHD Natural Convection Flow from an Isothermal Circular Cylinder under the consideration of Temperature Dependent Viscosity. Engineering Computations. 29(8): 875-887.
[7]	Huang M. J., and Chen C. K. (1987). Laminar Free Convection Flow from a Sphere with Blowing and Suction. ASME Journal of Heat transfer. 86(4), 537-541.
[8]	Molla M. M, Hossain M. A. and Taher M. A. (2005). Magnetohydrodynamic natural Convection Flow on a sphere with Uniform Heat flux in presence of Heat Generation. Acta Mechanica. 186: 75-86.
[9]	Shrama P. R. and Gurminder S. (2010). Steady MHD natural convection flow with variable electrical conductivity and heat generation along an isothermal vertical plate. Tamkang Journal of Science and Engineering. 13(3), 235-242.
[10]	Chaudhary R. C. and Jain A. (2007). Combined Heat and Mass Transfer Effects on MHD Free Convection Flow Past an Oscillating Plate Embedded in Porous Medium. Rom. Journal. Physics. 52(5-7), 505-524.
[11]	Molla M., Taher M. A., Chowdhury M. K. and Hossain A. (2005). Magnetohydrodynamic Natural Convection Flow from an Isothermal Sphere with Temperature Dependent Heat Generation. Nonlinear Analysis: Modelling and Control. 10(4), 349-363.
[12]	Molla M. M, Biswas A., Al-Mamun A. and Hossain A. (2014). Natural Convection Flow along an Isothermal Vertical Flat Plate with Temperature Dependent Viscosity and Heat Generation. Journal of Computational Engineering, Volume 2014(2014), Article ID 712147, 13 pages.
[13]	Perot J. B. and Subramanian V. (2007). A Discrete Calculus Analysis of the Keller Box Scheme and a Generalization of the Method to Arbitrary Meshes. Journal of Computational Physics. 226(1), 494-508.
[14]	Haque R., Alam M., Ali M. M and Sheikh N. M. A. (2014). Effects of viscous dissipation on MHD natural convection flow over a sphere with temperature dependent thermal conductivity in presence of heat generation. Journal of Computer and Mathematical Sciences. 5(1), (1-122).
[15]	Kang'ethe G. (2011). Magnetohydrodynamic Flow in Porous Media over A Stretching Surface in a Rotating System with Heat and Mass Transfer (Doctoral Thesis). Retrieved from http://ir.jkuat.ac.ke/bitstream/handle/123456789/867/Giterere,Kang'ethe_PhD.Applied%20Mathematics-2011.pdf?sequence=1.

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APA Style

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. (2016). Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere. American Journal of Applied Mathematics, 4(1), 53-61. https://doi.org/10.11648/j.ajam.20160401.15

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ACS Style

Mwangi Wanjiku Lucy; Mathew Ngugi Kinyanjui; Surindar Mohan Uppal. Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere. Am. J. Appl. Math. 2016, 4(1), 53-61. doi: 10.11648/j.ajam.20160401.15

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AMA Style

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere. Am J Appl Math. 2016;4(1):53-61. doi: 10.11648/j.ajam.20160401.15

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@article{10.11648/j.ajam.20160401.15,
  author = {Mwangi Wanjiku Lucy and Mathew Ngugi Kinyanjui and Surindar Mohan Uppal},
  title = {Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {1},
  pages = {53-61},
  doi = {10.11648/j.ajam.20160401.15},
  url = {https://doi.org/10.11648/j.ajam.20160401.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160401.15},
  abstract = {In this study, the effects of temperature dependent viscosity on MHD natural convection flow past an isothermal sphere are determined. The uniformly heated sphere is immersed in a viscous and incompressible fluid where viscosity of the fluid is taken as a non-linear function of temperature. The Partial Differential Equations governing the flow are transformed into non dimensional form and solved using the Direct Numerical Scheme and implemented in MATLAB. The numerical results obtained are presented graphically and in tables and are discussed. In this study, it has been observed that increasing the Magnetic parameter M leads to decrease in velocity, temperature, skin friction and the rate of heat transfer. It has also been noted that increase in the Grashof number Gr leads to increase in velocity and temperature whereas increase in the values of eta η leads to increase in temperature but there is a decrease in velocity. These results are applicable to engineers in designing electricity plants which have higher life expectancy.},
 year = {2016}
}

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TY  - JOUR
T1  - Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere
AU  - Mwangi Wanjiku Lucy
AU  - Mathew Ngugi Kinyanjui
AU  - Surindar Mohan Uppal
Y1  - 2016/02/25
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160401.15
DO  - 10.11648/j.ajam.20160401.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 53
EP  - 61
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160401.15
AB  - In this study, the effects of temperature dependent viscosity on MHD natural convection flow past an isothermal sphere are determined. The uniformly heated sphere is immersed in a viscous and incompressible fluid where viscosity of the fluid is taken as a non-linear function of temperature. The Partial Differential Equations governing the flow are transformed into non dimensional form and solved using the Direct Numerical Scheme and implemented in MATLAB. The numerical results obtained are presented graphically and in tables and are discussed. In this study, it has been observed that increasing the Magnetic parameter M leads to decrease in velocity, temperature, skin friction and the rate of heat transfer. It has also been noted that increase in the Grashof number Gr leads to increase in velocity and temperature whereas increase in the values of eta η leads to increase in temperature but there is a decrease in velocity. These results are applicable to engineers in designing electricity plants which have higher life expectancy.
VL  - 4
IS  - 1
ER  -

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Author Information

Mwangi Wanjiku Lucy

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mathew Ngugi Kinyanjui

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Surindar Mohan Uppal

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. (2016). Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere. American Journal of Applied Mathematics, 4(1), 53-61. https://doi.org/10.11648/j.ajam.20160401.15

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ACS Style

Mwangi Wanjiku Lucy; Mathew Ngugi Kinyanjui; Surindar Mohan Uppal. Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere. Am. J. Appl. Math. 2016, 4(1), 53-61. doi: 10.11648/j.ajam.20160401.15

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AMA Style

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere. Am J Appl Math. 2016;4(1):53-61. doi: 10.11648/j.ajam.20160401.15

Copy | Download

@article{10.11648/j.ajam.20160401.15,
  author = {Mwangi Wanjiku Lucy and Mathew Ngugi Kinyanjui and Surindar Mohan Uppal},
  title = {Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {1},
  pages = {53-61},
  doi = {10.11648/j.ajam.20160401.15},
  url = {https://doi.org/10.11648/j.ajam.20160401.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160401.15},
  abstract = {In this study, the effects of temperature dependent viscosity on MHD natural convection flow past an isothermal sphere are determined. The uniformly heated sphere is immersed in a viscous and incompressible fluid where viscosity of the fluid is taken as a non-linear function of temperature. The Partial Differential Equations governing the flow are transformed into non dimensional form and solved using the Direct Numerical Scheme and implemented in MATLAB. The numerical results obtained are presented graphically and in tables and are discussed. In this study, it has been observed that increasing the Magnetic parameter M leads to decrease in velocity, temperature, skin friction and the rate of heat transfer. It has also been noted that increase in the Grashof number Gr leads to increase in velocity and temperature whereas increase in the values of eta η leads to increase in temperature but there is a decrease in velocity. These results are applicable to engineers in designing electricity plants which have higher life expectancy.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Effects of Temperature Dependent Viscosity on Magnetohydrodynamic Natural Convection Flow Past an Isothermal Sphere
AU  - Mwangi Wanjiku Lucy
AU  - Mathew Ngugi Kinyanjui
AU  - Surindar Mohan Uppal
Y1  - 2016/02/25
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160401.15
DO  - 10.11648/j.ajam.20160401.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 53
EP  - 61
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160401.15
AB  - In this study, the effects of temperature dependent viscosity on MHD natural convection flow past an isothermal sphere are determined. The uniformly heated sphere is immersed in a viscous and incompressible fluid where viscosity of the fluid is taken as a non-linear function of temperature. The Partial Differential Equations governing the flow are transformed into non dimensional form and solved using the Direct Numerical Scheme and implemented in MATLAB. The numerical results obtained are presented graphically and in tables and are discussed. In this study, it has been observed that increasing the Magnetic parameter M leads to decrease in velocity, temperature, skin friction and the rate of heat transfer. It has also been noted that increase in the Grashof number Gr leads to increase in velocity and temperature whereas increase in the values of eta η leads to increase in temperature but there is a decrease in velocity. These results are applicable to engineers in designing electricity plants which have higher life expectancy.
VL  - 4
IS  - 1
ER  -

Copy | Download