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Slip flow and variable properties of viscoelastic fluid past a stretching surface embedded in a porous medium with heat generation

  • Geological, Civil, Energy and Traffic Engineering
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Abstract

This study examines theoretically and computationally the non-Newtonian boundary layer flow and heat transfer for a viscoelastic fluid over a stretching continuous sheet embedded in a porous medium with variable fluid properties, slip velocity, and internal heat generation/absorption. The flow in boundary layer is considered to be generated solely by the stretching of the sheet adjacent to porous medium with boundary wall slip condition. Highly nonlinear momentum and thermal boundary layer equations governing the flow and heat transfer are reduced to set of nonlinear ordinary differential equations by appropriate transformation. The resulting ODEs are successfully solved numerically with the help of shooting method. Graphical results are shown for non-dimensional velocities and temperature. The effects of heat generation/absorption parameter, the porous parameter, the viscoelastic parameter, velocity slip parameter, variable thermal conductivity and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction coefficient and Nusselt number are presented. Comparison of numerical results is made with the earlier published results under limiting cases.

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References

  1. CRANE L J. Flow past a stretching plate [J]. Z Angew Math Physk 1970, 21: 645–647.

    Article  Google Scholar 

  2. GUPTA P S, GUPTA A S. Heat and mass transfer on a stretching sheet with suction and blowing [J]. The Canadian Journal of Chemical Engineering 1977, 55: 744–746.

    Article  Google Scholar 

  3. CARRAGHER P, CRANE L J. Heat transfer on a continuous stretching sheet [J]. Zeitschrift fur Angewandte Mathematik und Mechanik 1982, 62: 564–565.

    Article  Google Scholar 

  4. POP I, NA T Y. A note on MHD flow over a stretching permeable surface [J]. Mechanics Research Communications 1988, 25: 263–269.

    Article  MathSciNet  MATH  Google Scholar 

  5. VAJRAVELU K, NAYFEH J. Convective heat transfer at a stretching sheet [J]. Acta Mechanica 1993, 96: 1227–1235.

    Article  MATH  Google Scholar 

  6. ALI M E. Heat transfer characteristics of a continuous stretching surface [J]. Warme-Stoffubertrag 1994, 29: 227–234.

    Article  Google Scholar 

  7. ALI M E. On thermal boundary layer on a power law stretched surface with suction or injection [J]. International Journal Heat and Mass Flow 1995, 16: 280–290.

    Article  Google Scholar 

  8. KUMARAN V, RAMANAIAH G. A note on the flow over a stretching sheet [J]. Acta Mechanica 1996, 116: 229–233.

    Article  MATH  Google Scholar 

  9. MAHAPATRA T R, GUPTA A S. Stagnation-point flow towards a stretching surface [J]. The Canadian Journal of Chemical Engineering 2003, 81: 258–263.

    Article  Google Scholar 

  10. MAHMOUD M A A, MEGAHED A M. Effect of suction and injection on MHD heat transfer in an electrically conducting fluid at a stretching vertical plate embedded in a porous medium with uniform free stream [J]. Il Nuovo Cimento B 2006, 121: 923–935.

    Google Scholar 

  11. CORTELL R. Viscous flow and heat transfer over a nonlinearly stretching sheet [J]. Applied Mathematics and Computation 2007, 184: 864–873.

    Article  MathSciNet  MATH  Google Scholar 

  12. ABDEL-RAHMAN REDA G, MEGAHED A M. Lie group analysis for a mixed convective flow and heat mass transfer over a permeable stretching surface with Soret and Dufour effects [J]. Journal of Mechanics 2014, 30: 67–75.

    Article  Google Scholar 

  13. RAJAGOPAL K R, NA T Y, GUPTA A S. Flow of a viscoelastic fluid over a stretching sheet [J]. Rheologica Acta 1984, 23: 213–215.

    Article  Google Scholar 

  14. VAJRAVELU K, ROLLINS D. Heat transfer in a viscoelastic fluid over a stretching sheet [J]. Journal of Mathematical Analysis and Applications 1991, 158: 241–255.

    Article  MathSciNet  MATH  Google Scholar 

  15. ANDERSSON H I. MHD flow of a viscoelastic fluid past a stretching surface [J]. Acta Mechanica 1992, 95: 227–230.

    Article  MathSciNet  MATH  Google Scholar 

  16. SARMA M S, NAGESWARA RAO B. Heat transfer in a viscoelastic fluid over a stretching sheet [J]. Journal of Mathematical Analysis and Applications 1998, 222: 268–275.

    Article  MathSciNet  MATH  Google Scholar 

  17. SUBHAS A, VEENA P. Viscoelastic fluid flow and heat transfer in a porous medium over a stretching sheet [J]. International Journal of Nonlinear Mechanics 1998, 33: 531–540.

    Article  MATH  Google Scholar 

  18. SANJAYANAND E, KHAN S K. On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet [J]. International Journal of Thermal Sciences 2006, 45: 819–828.

    Article  Google Scholar 

  19. NANDEPPANAVAR M M, ABEL M S, VAJRAVELU K. Flow and heat transfer characteristics of a viscoelastic fluid in a porous medium over an impermeable stretching sheet with viscous dissipation [J]. International Journal of Heat Mass Transfer 2010, 53: 4707–4713.

    Article  MATH  Google Scholar 

  20. COTTIN-BIZONNE C, CROSS B, STEINBERGER A, CHARLAIX E. Boundary slip on smooth hydrophobic surfaces: intrinsic effects and possible artifacts [J]. Physical Review Letters 2005, 94: 056–102.

    Article  Google Scholar 

  21. NAVIER C L M H. Memory on the laws of motion of fluids [J]. Memoires Académie des Sciences Institut de France 1823, 6: 389–416. (in French)

    Google Scholar 

  22. THOMPSON P A, TROIAN S M. A general boundary condition for liquid flow at solid surfaces [J]. Nature 1997, 389: 360–362.

    Article  Google Scholar 

  23. TURKYILMAZOGLU M. Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet [J]. International Journal of Thermal Sciences 2011, 50: 2264–2276.

    Article  Google Scholar 

  24. MEGAHED A M. Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation [J]. Rheologica Acta 2012, 51: 841–847.

    Article  Google Scholar 

  25. EL-HAWARY H M, MOSTAFA A A MAHMOUD, ABDELRAHMAN REDA G, ABEER S E. Similarity analysis for effects of variable diffusivity and heat generation/absorption on heat and mass transfer for a MHD stagnation-point flow of a convective viscoelastic fluid over a stretching sheet with a slip velocity [J]. Mathematical Problems in Engineering 2013: 1–11.

    Google Scholar 

  26. MOSTAFA A A M. The effects of variable fluid properties on MHD Maxwell fluids over a stretching surface in the presence of heat generation/absorption [J]. Chemical Engineering Communications 2011, 198: 131–146.

    Google Scholar 

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Authors and Affiliations

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

    Ahmed M. Megahed

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  1. Ahmed M. Megahed
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Correspondence to Ahmed M. Megahed.

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Megahed, A.M. Slip flow and variable properties of viscoelastic fluid past a stretching surface embedded in a porous medium with heat generation. J. Cent. South Univ. 23, 991–999 (2016). https://doi.org/10.1007/s11771-016-3147-4

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  • DOI: https://doi.org/10.1007/s11771-016-3147-4

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