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Variable viscosity effect on free convection of a non-Newtonian power-law fluid over a vertical cone in a porous medium with variable heat flux

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Abstract.

The effect of variable viscosity on the free-convection boundary layer over a permeable vertical cone in a porous medium saturated with non-Newtonian power-law fluid has been studied numerically. The governing equations describing the problem are transformed into a system of nonlinear ordinary differential equations by using a similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the power-law index, blowing/suction parameter and the viscosity parameter on the temperature profiles and the local Nusselt number are discussed.

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References

  1. P. Cheng, W.J. Minkowycz, J. Geophys. Res. 82, 2040 (1977)

    Article  ADS  Google Scholar 

  2. C.H. Johson, P. Cheng, Int. J. Heat Mass Transfer 21, 709 (1978)

    Article  ADS  Google Scholar 

  3. J.H. Merkin, Int. J. Heat Mass Transfer 21, 1499 (1978)

    Article  Google Scholar 

  4. T.Y. Na, I. Pop, Int. J. Eng. Sci. 21, 517 (1983)

    Article  Google Scholar 

  5. M. Kumari, I. Pop, G. Nath, Int. Commun. Heat Mass Transfer 12, 337 (1985)

    Article  Google Scholar 

  6. A. Bejan, K.R. Khair, Int. J. Heat Mass Transfer 28, 909 (1985)

    Article  Google Scholar 

  7. W.J. Minkowycz, P. Cheng, Lett. Heat Mass Transfer 9, 159 (1982)

    Article  Google Scholar 

  8. P. Cheng, T.T. Le, I. Pop, Int. Commun. Heat Mass Transfer 12, 705 (1985)

    Article  Google Scholar 

  9. K.A. Yih, Int. Commun. Heat Mass Transfer 24, 1195 (1997)

    Article  Google Scholar 

  10. C.Y. Cheng, Int. Commun. Heat Mass Transfer 27, 537 (2000)

    Article  ADS  Google Scholar 

  11. I. Pop, D.B. Ingham, Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluid and Porous Media (Pergamon, Oxford, 2001)

  12. D.A. Nield, A. Bejan, Convection in Porous Media, 3rd ed. (Springer, New York, 2006)

  13. K.N. Mehta, S. Sood, Int. J. Eng. Sci. 30, 1083 (1992)

    Article  Google Scholar 

  14. N.G. Kafoussias, E.W. Williams, Acta Mech. 110, 123 (1995)

    Article  Google Scholar 

  15. F.M. Hady, A.Y. Bakier, R.S.R. Gorla, Heat and Mass Transfer 31, 169 (1996)

    Article  ADS  Google Scholar 

  16. N.G. Kafoussias, D.A.S. Rees, J.E. Daskalakis, Acta Mech. 127, 39 (1998)

    Article  Google Scholar 

  17. M.A.A. Mahmoud, Math. Probl. Eng. V (2007) 41323

  18. M. Kumari, Mech. Res. Commun. 28, 339 (2001)

    Article  ADS  Google Scholar 

  19. H.T. Chen, C.K. Chen, ASME J. Heat Transfer 110, 257 (1988)

    Article  Google Scholar 

  20. K.N. Mehta, K.N. Rao, Int. J. Eng. Sci. 32, 297 (1994)

    Article  Google Scholar 

  21. H.T. Chen, C.K. Chen, Trans. ASME, J. Energ. Resour. Techn. 109, 119 (1987)

    Article  Google Scholar 

  22. K.N. Mehta, K.N. Rao, Int. J. Eng. Sci. 32, 521 (1994)

    Article  Google Scholar 

  23. M. Kumari, S. Jayanathi, J. Porous Media 8, 73 (2005)

    Article  Google Scholar 

  24. K.A. Yih., Int. Commun. Heat Mass Transfer 25, 959 (1998)

    Article  Google Scholar 

  25. T. Groşan, A. Postenlnicu, I. Pop, Techn. Mechanik 24, 91 (2004)

    Google Scholar 

  26. M. Massoudi, T.X. Phuoc, Continuum Mech. Thermodyn. 16, 529 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  27. S. Bagai, Acta Mech. 169, 187 (2004)

    Article  Google Scholar 

  28. Y. Ke, V.S. Solomatov, Phys. Fluids 16, 1059 (2004)

    Article  ADS  Google Scholar 

  29. T.G. Myers, J.P.F. Charpin, M.S. Tshehla, Appl. Math. Model. 30, 799 (2006)

    Article  Google Scholar 

  30. M. Massoudi, A. Vaidya, R. Wulandana, Nonlinear Anal., Real World Appl. 9, 80 (2008)

    Article  MathSciNet  Google Scholar 

  31. A.S. Dehkordi, M. Memari, Energy Conversion and Management 51, 1065 (2010)

    Article  Google Scholar 

  32. A.A. Soares, J.M. Ferreira, J. Caramelo, R.P. Chhabra, Int. J. Heat Mass Transfer 53, 4728 (2010)

    Article  Google Scholar 

  33. K.-H. Sun, D.L. Pyle, A.D. Fitt, C.P. Please, M.J. Baines, N. Hall-Taylor, Computers & Fluids 33, 869 (2004)

    Article  Google Scholar 

  34. S.E. El-Gendi, Computer J. 12, 282 (1969)

    Article  MathSciNet  Google Scholar 

  35. Y. Morchoisne, AIAA J. 19, 81 (1981)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Benha University, Benha, (13518), Egypt

    M. A. A. Mahmoud

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  1. M. A. A. Mahmoud
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Mahmoud, M.A.A. Variable viscosity effect on free convection of a non-Newtonian power-law fluid over a vertical cone in a porous medium with variable heat flux. Eur. Phys. J. Plus 126, 5 (2011). https://doi.org/10.1140/epjp/i2011-11005-1

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  • DOI: https://doi.org/10.1140/epjp/i2011-11005-1

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