Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere

Mwangi Wanjiku Lucy; Mathew Ngugi Kinyanjui; Roy Phineas Kiogora

doi:doi:10.11648/j.ajam.20160406.11

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Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Roy Phineas Kiogora

Published in American Journal of Applied Mathematics (Volume 4, Issue 6)

Received: 13 September 2016 Accepted: 2 October 2016 Published: 1 November 2016

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Abstract

In this study, the effects of variable viscosity on unsteady natural convection hydromagnetic 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 linear function of temperature. The Partial Differential Equations governing the flow are reduced into non dimensional form and since these equations are non-linear, they are solved numerically using finite difference methods. The numerical results obtained are presented graphically and discussed. It has been observed that there is a significant change in primary velocity, secondary velocity, temperature, skin friction and heat transfer of the fluid with changes in Reynolds number, Grashof number, Magnetic parameter and viscous variation parameter. These results are applicable in engineering, technology and biomedical fields.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 6)
DOI	10.11648/j.ajam.20160406.11
Page(s)	258-270
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, Hydrodynamics, Temperature Dependence of Liquid Viscosity, Isothermal Sphere, Finite Difference, Dimensional Analysis

References

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[2]	Selivanov N. V. and Kuz’min S. I. (2009). Numerical Simulation of Forced Flow in Boundary Layer and of Heat Transfer by Non-Newtonian Fluid in View of the Temperature Dependence of Viscosity. Heat and Mass Transfer and Physical Gasdynamics. 47 (6): 886-891.
[3]	Rahman M. M., Rahman M. A., Samad M., Alam S. (2009). Heat Transfer in Micropolar Fluid along a Non-Linear Stretching Sheet with Temperature Dependent Viscosity and Variable Surface Temperature. International Journal of Thermophysics. 30 (5): 1649-1670.
[4]	Gomathi P. and Kwang-Yong K. (2010). Numerical study on a vertical plate with variable viscosity and thermal conductivity. Archive of Applied Mechanics. 80 (7): 711-725.
[5]	Miyauchi A., Kameyama M., Ichikawa H. (2014). Linear stability analysis on the influences of the spatial variations in thermal conductivity and expansivity on the flow patterns of thermal convection with strongly temperature-dependent viscosity. Journal of Earth Science. 25 (1): 126-139.
[6]	Umavathi J. C. (2015). Combined Effect of Variable Viscosity and Variable Thermal Conductivity on Double Diffusive Convection Flow of a Permeable Fluid in a Vertical Channel. Transport in Porous Media. 108 (3).
[7]	Umavathi J. C. and Shekar M. (2015). Combined effect of variable viscosity and thermal conductivity on free convection flow of a viscous fluid in a vertical channel using DTM. Meccanica. pp 1-16.
[8]	B ´eg O. A, Zueco J., Ghosh S. K., Heidari A. (2011). Unsteady Magnetohydrodynamic Heat Transfer in a Semi-Infinite Porous Medium with Thermal Radiation Flux: Analytical and Numerical Study. Advances in Numerical Analysis: 2011 (304124), 17 pages.
[9]	Deka R. K. and Neog B. C (2009). Unsteady natural convection flow past an accelerated vertical plate in a thermally stratified fluid. Theoret. Appl. Mech. 36 (4): 261-274.
[10]	Mina B. A, Magda M. K, Mohammad L. M (2004). Similarity solutions for unsteady free-convection flow from a continuous moving vertical surface. Journal of Computational and Applied Mathematics. 11 – 24: 164–165.
[11]	Ramesh G. K., Mahesha, Gireesha B. J., Bagewadi C. S. (2011). Unsteady flow of a conducting dusty fluid between two circular cylinders. Acta Math. Univ. Comenianae. 80 (2): 171–184.
[12]	Mebine P. and Adigio E. M (2009). Unsteady Free Convection Flow with Thermal Radiation Past a Vertical Porous Plate with Newtonian Heating. Turk J Phys. 33: 109 – 119.
[13]	Deepa G. and Murali G. (2014). Effects of viscous dissipation on unsteady MHD free convective flow with thermophoresis past a radiate inclined permeable plate. Iranian Journal of Science & Technology. 38 (3): 379-388.
[14]	Sugunamma V. and Sandeep N. (2013). Effect of inclined magnetic field on unsteady free convection flow of a dusty viscous fluid between two infinite flat plates filled by a porous medium. International Journal of Applied Mathematics and Modeling. 1 (1): 16-33.

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APA Style

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Roy Phineas Kiogora. (2016). Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere. American Journal of Applied Mathematics, 4(6), 258-270. https://doi.org/10.11648/j.ajam.20160406.11

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ACS Style

Mwangi Wanjiku Lucy; Mathew Ngugi Kinyanjui; Roy Phineas Kiogora. Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere. Am. J. Appl. Math. 2016, 4(6), 258-270. doi: 10.11648/j.ajam.20160406.11

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AMA Style

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Roy Phineas Kiogora. Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere. Am J Appl Math. 2016;4(6):258-270. doi: 10.11648/j.ajam.20160406.11

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@article{10.11648/j.ajam.20160406.11,
  author = {Mwangi Wanjiku Lucy and Mathew Ngugi Kinyanjui and Roy Phineas Kiogora},
  title = {Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {258-270},
  doi = {10.11648/j.ajam.20160406.11},
  url = {https://doi.org/10.11648/j.ajam.20160406.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.11},
  abstract = {In this study, the effects of variable viscosity on unsteady natural convection hydromagnetic 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 linear function of temperature. The Partial Differential Equations governing the flow are reduced into non dimensional form and since these equations are non-linear, they are solved numerically using finite difference methods. The numerical results obtained are presented graphically and discussed. It has been observed that there is a significant change in primary velocity, secondary velocity, temperature, skin friction and heat transfer of the fluid with changes in Reynolds number, Grashof number, Magnetic parameter and viscous variation parameter. These results are applicable in engineering, technology and biomedical fields.},
 year = {2016}
}

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TY  - JOUR
T1  - Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere
AU  - Mwangi Wanjiku Lucy
AU  - Mathew Ngugi Kinyanjui
AU  - Roy Phineas Kiogora
Y1  - 2016/11/01
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.11
DO  - 10.11648/j.ajam.20160406.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 258
EP  - 270
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.11
AB  - In this study, the effects of variable viscosity on unsteady natural convection hydromagnetic 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 linear function of temperature. The Partial Differential Equations governing the flow are reduced into non dimensional form and since these equations are non-linear, they are solved numerically using finite difference methods. The numerical results obtained are presented graphically and discussed. It has been observed that there is a significant change in primary velocity, secondary velocity, temperature, skin friction and heat transfer of the fluid with changes in Reynolds number, Grashof number, Magnetic parameter and viscous variation parameter. These results are applicable in engineering, technology and biomedical fields.
VL  - 4
IS  - 6
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
Roy Phineas Kiogora

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, Roy Phineas Kiogora. (2016). Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere. American Journal of Applied Mathematics, 4(6), 258-270. https://doi.org/10.11648/j.ajam.20160406.11

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ACS Style

Mwangi Wanjiku Lucy; Mathew Ngugi Kinyanjui; Roy Phineas Kiogora. Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere. Am. J. Appl. Math. 2016, 4(6), 258-270. doi: 10.11648/j.ajam.20160406.11

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AMA Style

Mwangi Wanjiku Lucy, Mathew Ngugi Kinyanjui, Roy Phineas Kiogora. Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere. Am J Appl Math. 2016;4(6):258-270. doi: 10.11648/j.ajam.20160406.11

Copy | Download

@article{10.11648/j.ajam.20160406.11,
  author = {Mwangi Wanjiku Lucy and Mathew Ngugi Kinyanjui and Roy Phineas Kiogora},
  title = {Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {258-270},
  doi = {10.11648/j.ajam.20160406.11},
  url = {https://doi.org/10.11648/j.ajam.20160406.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.11},
  abstract = {In this study, the effects of variable viscosity on unsteady natural convection hydromagnetic 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 linear function of temperature. The Partial Differential Equations governing the flow are reduced into non dimensional form and since these equations are non-linear, they are solved numerically using finite difference methods. The numerical results obtained are presented graphically and discussed. It has been observed that there is a significant change in primary velocity, secondary velocity, temperature, skin friction and heat transfer of the fluid with changes in Reynolds number, Grashof number, Magnetic parameter and viscous variation parameter. These results are applicable in engineering, technology and biomedical fields.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Effects of Variable Viscosity on Unsteady Natural Convection Hydromagnetic Flow Past an Isothermal Sphere
AU  - Mwangi Wanjiku Lucy
AU  - Mathew Ngugi Kinyanjui
AU  - Roy Phineas Kiogora
Y1  - 2016/11/01
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.11
DO  - 10.11648/j.ajam.20160406.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 258
EP  - 270
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.11
AB  - In this study, the effects of variable viscosity on unsteady natural convection hydromagnetic 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 linear function of temperature. The Partial Differential Equations governing the flow are reduced into non dimensional form and since these equations are non-linear, they are solved numerically using finite difference methods. The numerical results obtained are presented graphically and discussed. It has been observed that there is a significant change in primary velocity, secondary velocity, temperature, skin friction and heat transfer of the fluid with changes in Reynolds number, Grashof number, Magnetic parameter and viscous variation parameter. These results are applicable in engineering, technology and biomedical fields.
VL  - 4
IS  - 6
ER  -

Copy | Download