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Scaling group transformation for the effect of temperature-dependent nanofluid viscosity on an mhd boundary layer past a porous stretching surface

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Abstract

This paper deals with a steady two-dimensional flow of an electrically conducting incompressible fluid over a porous vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. The partial differential equations governing the problem under consideration are transformed by a special form of Lie group transformations, namely, scaling group of transformations, into a system of ordinary differential equations, which are solved numerically using the Runge-Kutta-Gill algorithm and the shooting method. The conclusion is drawn that the flow field and temperature profiles are significantly influenced by the Lewis number, Brownian motion number, and thermophoresis number.

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References

  1. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” in: D. A. Siginer and H. P. Wang (eds.), Developments and Applications of Non-Newtonian Flows, ASME, New York (1995); FED-Vol. 231/MD-Vol. 66, pp. 99–105.

    Google Scholar 

  2. H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles,” Netsu Bussei, 7, 227–233 (1993).

    Article  Google Scholar 

  3. J. Buongiorno and W. Hu, “Nanofluid coolants for advanced nuclear power plants,” ih: Proc. of the ICAPP’05 (Seoul, May 15–19, 2005), Paper No. 5705 (2005).

  4. J. Buongiorno, “Convective transport in nanofluids,” Trans. ASME, J. Heat Transfer, 128, 240–250 (2006).

    Article  Google Scholar 

  5. A. V. Kuznetsov and D. A. Nield, “Natural convective boundary-layer flow of a nanofluid past a vertical plate,” Int. J. Therm. Sci. [Electron. resource]; DOI: 10.1016/j.ijthermalsci.2009.07.015.

  6. D. A. Nield and A. V. Kuznetsov, “The Cheng-Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid,” Int. J. Heat Mass Transfer, 52, 5792–5795 (2009).

    Article  MATH  Google Scholar 

  7. P. Cheng and W. J. Minkowycz, “Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike,” J. Geophys. Res., 82, No. 14, 2040–2044 (1977).

    Article  ADS  Google Scholar 

  8. W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” Int. J. Heat Mass Transfer, 53, 2477–2483 (2010).

    Article  MATH  Google Scholar 

  9. M. Yurusoy and M. Pakdemirli, “Symmetry reductions of unsteady three-dimensional boundary layers of some non-Newtonian fluids,” Int. J. Eng. Sci., 35, 731–740 (1997).

    Article  MathSciNet  Google Scholar 

  10. M. Yurusoy and M. Pakdemirli, “Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet,” Mech. Res. Comm., 26, 171–175 (1999).

    Article  Google Scholar 

  11. M. Yurusoy, M. Pakdemirli, and O. F. Noyan, “Lie group analysis of creeping flow of a second grade fluid,” Int. J. Non-Linear Mech., 36, 955–960 (2001).

    Article  MathSciNet  Google Scholar 

  12. G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge Univ. Press, London (1987).

    Google Scholar 

  13. J. X. Ling and A. Dybbs, “Forced convection over a flat plate submersed in a porous medium: Variable viscosity case,” ASME Paper No. 87-WA/HT-23 (1987).

  14. S. Gill, “A process for the step-by-step integration of differential equations in an automatic digital computing machine,” Math. Proc. Cambridge Philos. Soc., 47, 96–108 (1951).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. C. Y. Wang, “Free convection on a vertical stretching surface,” Z. Angew. Math. Mech., 69, 418–420 (1989).

    Article  MATH  Google Scholar 

  16. R. S. R. Gorla and I. Sidawi, “Free convection on a vertical stretching surface with suction and blowing,” Appl. Sci. Res., 52, 247–257 (1994).

    Article  MATH  ADS  Google Scholar 

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Authors and Affiliations

  1. University Tun Hussein Onn, Parit Raja, Malaysia

    R. Kandasamy & I. Muhaimin

  2. Linton University college, Mantin, Malaysia

    G. Kamachi

Authors
  1. R. Kandasamy
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  2. I. Muhaimin
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  3. G. Kamachi
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Corresponding author

Correspondence to R. Kandasamy.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 52, No. 6, pp. 100–111, November–December, 2011.

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Kandasamy, R., Muhaimin, I. & Kamachi, G. Scaling group transformation for the effect of temperature-dependent nanofluid viscosity on an mhd boundary layer past a porous stretching surface. J Appl Mech Tech Phy 52, 931–940 (2011). https://doi.org/10.1134/S0021894411060113

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  • DOI: https://doi.org/10.1134/S0021894411060113

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