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Mixed convection stagnation-point flow on vertical stretching sheet with external magnetic field

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Abstract

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection stagnation-point flow of an incompressible viscous fluid over a vertical stretching sheet is studied. The effect of an externally magnetic field is taken into account. The transformed boundary layer equations are solved numerically by using an implicit finite-difference scheme. Numerical results are obtained for various values of the mixed convection parameter, Hartmann number, and Prandtl number. The effects of an externally magnetic field on the skin friction coefficient, local Nusselt number, velocity, and temperature profiles for both A > 1 and A < 1, where A is the velocity ratio parameter, are presented graphically and discussed in detail. Both assisting and opposing flows are considered, and it is found that dual solutions exist for the opposing flow.

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References

  1. Ahmad, N., Siddiqui, Z. U., and Mishra, M. K. Boundary layer flow and heat transfer past a stretching plate with variable thermal conductivity. Int. J. Non-Linear Mech., 45, 306–309 (2010)

    Article  Google Scholar 

  2. Kumari, M. and Nath, G. Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid. Int. J. Non-Linear Mech., 45, 310–319 (2010)

    Article  Google Scholar 

  3. Prasad, K. V., Vajravelu, K., and Datti, P. S. Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties. Int. J. Non-Linear Mech., 45, 320–330 (2010)

    Article  Google Scholar 

  4. Ali, F. M., Nazar, R., Arifin, N. M., and Pop, I. MHD boundary layer flow and heat transfer over a stretching sheet with induced magnetic field. Heat and Mass Transfer, 47, 155–162 (2011)

    Article  Google Scholar 

  5. Hiemenz, K. Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder. Dingler’s Polytech. J., 3326, 321–324 (1911)

    Google Scholar 

  6. Eckert, E. R. G. Die Berechnung des Wärmeubergangs in der laminaren Grenzschicht umstromter Körpe. VDI Forschungsheft, 41416, 1–23 (1942).

    Google Scholar 

  7. Mahapatra, T. R. and Gupta, A. S. Heat tansfer in stagnation-point flow towards a stretching sheet. Heat and Mass Transfer, 38, 517–521 (2002)

    Article  Google Scholar 

  8. Andersson, H. I. MHD flow of a viscoelastic fluid past a stretching sheet. Acta Mech., 95, 227–230 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ishak, A., Nazar, R., and Pop, I. Magnetohydrodynamic (MHD) flow of a micropolar fluid towards a stagnation point on a vertical surface. Comp. Math. Appl., 56, 3188–3194 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mahapatra, T. R., Nandy, S. K., and Gupta, A. S. Magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface. Int. J. Non-Linear Mech., 44, 124–129 (2009)

    Article  MATH  Google Scholar 

  11. Gupta, A. S., Pal, A., Pal, B., and Takhar, H. S. Hall effects on MHD flow and heat transfer over a stretching surface. Int. J. Appl. Mech. Eng., 8, 219–232 (2003)

    MATH  Google Scholar 

  12. Ali, F. M., Nazar, R., Arifin, N. M., and Pop, I. Effect of Hall current on MHD mixed convection boundary layer flow over a stretched vertical flat plate. Meccanica, 46, 1103–1112 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ishak, A., Nazar, R., and Pop, I. Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat and Mass Transfer, 44, 921–927 (2008)

    Article  Google Scholar 

  14. Pop, S. R., Grosan, T., and Pop, I. Radiation effect on the flow near the stagnation point of a stretching sheet. Technische Mechanik, 25, 100–106 (2004)

    Google Scholar 

  15. Pal, D. Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation. Meccanica, 44, 145–158 (2009)

    Article  MATH  Google Scholar 

  16. Hayat, T., Javed, T., and Abbas, Z. MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface. Nonlinear Analysis: Real World Applications, 10, 1514–1526 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Shokouhmand, H., Fakoor Pakdaman, M., and Kooshkbaghi, M. A similarity solution in order to solve the governing equations of laminar separated fluids with a flat plate. Commun. Nonlinear Sci. Numer. Simulat., 15, 3965–3973 (2010)

    Article  Google Scholar 

  18. Vajravelu, K. and Hadijinicolaou, A. Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream. Int. J. Eng. Sci., 35, 1237–1244 (1997)

    Article  MATH  Google Scholar 

  19. Xu, H. An explicit analytic solution for convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream. Int. J. Eng. Sci., 43, 859–874 (2005)

    Article  MATH  Google Scholar 

  20. Ishak, A., Jafar, K., Nazar, R., and Pop, I. MHD stagnation point flow towards a stretching sheet. Physica A, 388, 3377–3383 (2009)

    Article  Google Scholar 

  21. Bachok, N., Ishak, A., and Pop, I. Mixed convection boundary layer flow near the stagnation point on a vertical surface embedded in a porous medium with anisotropy effect. Transport Porous Media, 82, 363–373 (2010)

    Article  MathSciNet  Google Scholar 

  22. Sutton, G. W. and Sherman, A. Engineering Magnetohydrodynamics, McGraw-Hill, New York (1965)

    Google Scholar 

  23. Ramachandran, N., Chen, T. S., and Armaly, B. F. Mixed convection in stagnation flows adjacent to vertical surfaces. Journal of Heat Transfer, 110, 373–377 (1988)

    Article  Google Scholar 

  24. Cebeci, T. and Bradshaw, P. Physical and Computational Aspects of Convective Heat Transfer, Springer, New York (1988)

    Book  MATH  Google Scholar 

  25. Cebeci, T. and Cousteix, J. Modeling and Computing of Boundary-Layer Flows: Laminar, Turbulent and Transitional Boundary Layers in Incompressible and Compressible Flows, Springer, New York (2005)

    Google Scholar 

  26. Hassanien, I. A. and Gorla, R. S. R. Combined forced and free convection in stagnation flows of micropolar fluids over vertical non-isothermal surfaces. Int. J. Eng. Sci., 28, 783–792 (1990)

    Article  Google Scholar 

  27. Lok, Y. Y., Amin, N., and Pop, I. Unsteady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface. Int. J. Therm. Sci., 45, 1149–1157 (2006)

    Article  Google Scholar 

  28. Ishak, A., Nazar, R., and Pop, I. Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate. Int. J. Therm. Sci., 47, 417–422 (2008)

    Article  Google Scholar 

  29. Ishak, A., Nazar, R., and Pop, I. Mixed convection boundary layers in the stagnation-point flow towards a stretching vertical sheet. Meccanica, 41, 509–518 (2006)

    Article  MATH  Google Scholar 

  30. Rosca, A. V. and Pop, I. Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. Int. J. Heat Mass Transfer, 60, 355–364 (2013)

    Article  Google Scholar 

  31. Merkin, J. H. Mixed convection boundary-layer flow on a vertical surface in a saturated porous medium. J. Eng. Math., 14, 301–313 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  32. Merkin, J. H. On dual solutions occurring in mixed convection in a porous medium. J. Eng. Math., 20, 171–179 (1985)

    Article  MathSciNet  Google Scholar 

  33. Hoog, F. R., Laminger, B., and Weiss, R. A numerical study of similarity solutions for combined forced and free convection. Acta Mech., 51, 139–149 (1984)

    Article  MATH  Google Scholar 

  34. Afzal, N. and Hussain, T. Mixed convection over a horizontal plate. Journal of Heat Transfer, 106, 240–241 (1984)

    Article  Google Scholar 

  35. Harris, S. D., Ingham, D. B., and Pop, I. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport Porous Media, 77, 267–285 (2009)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia

    F. M. Ali & N. M. Arifin

  2. School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, UKM Bangi, 43600, Selangor, Malaysia

    R. Nazar

  3. Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, R-400084, Romania

    I. Pop

Authors
  1. F. M. Ali
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  2. R. Nazar
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  3. N. M. Arifin
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  4. I. Pop
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Corresponding author

Correspondence to F. M. Ali.

Additional information

Project supported by the Fundamental Research Grant Scheme (FRGS) from the Ministry of Higher Education in Malaysia (No. 5524295), and the Research University Grant from the Universiti Kebangsaan Malaysia (No.GUP-2013-040)

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Ali, F.M., Nazar, R., Arifin, N.M. et al. Mixed convection stagnation-point flow on vertical stretching sheet with external magnetic field. Appl. Math. Mech.-Engl. Ed. 35, 155–166 (2014). https://doi.org/10.1007/s10483-014-1780-8

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  • DOI: https://doi.org/10.1007/s10483-014-1780-8

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