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Effects of partial slip on chemically reactive solute transfer in the boundary layer flow over an exponentially stretching sheet with suction/blowing

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Abstract

The boundary layer flow and mass transfer toward an exponentially stretching porous sheet are analyzed in this paper. Velocity slip is considered instead of the no-slip condition on the boundary. Self-similar equations are obtained by using similarity transformations. Numerical solutions of these equations are obtained by the shooting method. It is found that the fluid velocity and concentration decrease with increasing slip parameter. The fluid velocity decreases with increasing suction parameter.

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References

  1. L. J. Crane, “Flow Past a Stretching Plate,” Z. Angew. Math. Phys. 21, 645–647 (1970).

    Article  Google Scholar 

  2. P. S. Gupta and A. S. Gupta, “Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing,” Canad. J. Chem. Eng. 55, 744–746 (1977).

    Article  Google Scholar 

  3. B. K. Datta, P. Roy, and A. S. Gupta, “Temperature Field in the Flow over a Stretching Sheet with Uniform Heat Flux,” Int. Comm. Heat Mass Transfer 12, 89–94 (1985).

    Article  Google Scholar 

  4. C. K. Chen, and M. I. Char, “Heat Transfer of a Continuous Stretching Surface with Suction or Blowing,” J. Math. Anal. Appl. 135, 568–580 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  5. V. Kumaran and G. Ramanaiah, “A Note on the Flow over a Stretching Sheet,” Acta Mech. 116, 229–233 (1996).

    Article  MATH  Google Scholar 

  6. H. Xu and S. J. Liao, “Series Solutions of Unsteady Magnetohydrodynamics Flows of Non-Newtonian Fluids Caused by an Impulsively Stretching Plate,” J. Non-Newtonian Fluid Mech. 159, 46–55 (2005).

    Article  Google Scholar 

  7. R. Cortell, “Flow and Heat Transfer of a Fluid Through a Porous Medium Over a Stretching Surface with Internal Heat Generation/Absorption and Suction/Blowing,” Fluid Dyn. Res. 37, 231–245 (2005).

    Article  ADS  MATH  Google Scholar 

  8. R. Cortell, “Effects of Viscous Dissipation and Work Done by Deformation on the MHD Flow and Heat Transfer of a Viscoelastic Fluid over a Stretching Sheet,” Phys. Lett. A 357, 298–305 (2006).

    Article  ADS  MATH  Google Scholar 

  9. T. Hayat, Z. Abbas, and M. Sajid, “Series Solution for the Upper-Convected Maxwell Fluid over a Porous Stretching Plate,” Phys. Lett. A 358, 396–403 (2006).

    Article  ADS  MATH  Google Scholar 

  10. T. Hayat and M. Sajid, “Analytic Solution for Axi-Symmetric Flow and Heat Transfer of a Second Grade Fluid Past a Stretching Sheet,” Int. J. Heat Mass Transfer 50, 75–84 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  11. M. E. Ali, “On Thermal Boundary Layer on a Power Law Stretched Surface with Suction or Injection,” Int. J. Heat Fluid Flow 16, 280–290 (1995).

    Article  Google Scholar 

  12. E. Magyari and B. Keller, “Heat and Mass Transfer in the Boundary Layers on an Exponentially Stretching Continuous Surface,” J. Phys., D: Appl. Phys. 32, 577–585 (2000).

    Article  ADS  Google Scholar 

  13. E. M. A. Elbashbeshy, “Heat Transfer over an Exponentially Stretching Continuous Surface with Suction,” Arch. Mech. 53, 643–651 (2001).

    MATH  Google Scholar 

  14. K. Vajravelu, “Viscous Flow over a Nonlinearly Stretching Sheet,” Appl. Math. Comput. 124, 281–288 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  15. K. Vajravelu and J. R. Cannon, “Fluid Flow over a Nonlinear Stretching Sheet,” Appl. Math. Comput. 181, 609–618 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  16. S. K. Khan, “Boundary Layer Viscoelastic Fluid Flow over an Exponentially Stretching Sheet,” Int. J. Appl. Mech. Eng. 11, 321–335 (2006).

    MATH  Google Scholar 

  17. E. Sanjayanand and S. K. Khan, “On Heat and Mass Transfer in a Visco-Elastic Boundary Layer Flow over an Exponentially Stretching Sheet,” Int. J. Thermal Sci. 45, 819–828 (2006).

    Article  Google Scholar 

  18. M. Sajid and T. Hayat, “Influence of Thermal Radiation on the Boundary Layer Flow Due to an Exponentially Stretching Sheet,” Int. Comm. Heat Mass Transfer 35, 347–356 (2008).

    Article  Google Scholar 

  19. B. Bidin and R. Nazar, “Numerical Solution of the Boundary Layer Flow over an Exponentially Stretching Sheet with Thermal Radiation,” Eur. J. Sci. Res. 33(4), 710–717 (2009).

    Google Scholar 

  20. T. Akyildiz, D. A. Siginer, K. Vajravelu, et al., “Similarity Solutions of the Boundary Layer Equations for a Nonlinearly Stretching Sheet,” Math. Meth. Appl. Sci. 33, 601–606 (2010).

    MATH  MathSciNet  Google Scholar 

  21. R. A. Van Gorder and K. Vajravelu, “A Note on Flow Geometries and the Similarity Solutions of the Boundary Layer Equations for a Nonlinearly Stretching Sheet,” Arch. Appl. Mech. 80, 1329–1332 (2010).

    Article  ADS  MATH  Google Scholar 

  22. A. Ishak, “MHD Boundary Layer Flow due to an Exponentially Stretching Sheet with Radiation Effect,” Sains Malaysiana 40, 391–395 (2011).

    Google Scholar 

  23. K. Bhattacharyya and K. Vajravelu, “Stagnation-Point Flow and Heat Transfer over an Exponentially Shrinking Sheet,” Comm. Nonlinear Sci. Numer. Simul. 17, (iss. 7), 2728–2734 (2011).

    Article  Google Scholar 

  24. H. I. Andersson, O. R. Hansen, and B. Olmedal, “Diffusion of a Chemically Reactive Species from a Stretching Sheet,” Int. J. Heat Mass Transfer 37, 659–664 (1994).

    Article  MATH  Google Scholar 

  25. H. S. Takhar, A. J. Chamkha, and G. Nath, “Flow and Mass Transfer on a Stretching Sheet with a Magnetic Field and Chemically Reactive Species,” Int. J. Eng. Sci. 38, 1303–1314 (2000).

    Article  MATH  Google Scholar 

  26. A. Afify, “MHD Free Convective Flow and Mass Transfer over a Stretching Sheet with Chemical Reaction,” Heat Mass Transfer 40, 495–500 (2004).

    ADS  Google Scholar 

  27. I. C. Liu, “A Note on Heat and Mass Transfer for a Hydromagnetic Flow over a Stretching Sheet,” Int. Comm. Heat Mass Transfer 32, 1075–1084 (2005).

    Article  Google Scholar 

  28. T. F. Akyildiz, H. Bellout, and K. Vajravelu, “Diffusion of Chemically Reactive Species in a Porous Medium over a Stretching Sheet,” J. Math. Anal. Appl. 320, 322–339 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  29. R. Cortell, “MHD Flow and Mass Transfer of an Electrically Conducting Fluid of Second Grade in a Porous Medium over a Stretching Sheet with Chemically Reactive Species,” Chem. Eng. Process 46, 721–728 (2007).

    Article  Google Scholar 

  30. R. Kandasamy, M. Ismoen, and H. B. Saim, “Lie Group Analysis for the Effects of Temperature-Dependent Fluid Viscosity and Chemical Reaction on MHD Free Convective Heat and Mass Transfer with Variable Stream Conditions,” Nucl. Eng. Des. 240, 39–46 (2010).

    Article  Google Scholar 

  31. A. Yoshimura and R. K. Prudhomme, “Wall Slip Corrections for Couette and Parallel Disc Viscometers,” J. Rheol. 32, 53–67 (1998).

    Article  Google Scholar 

  32. C. Y. Wang, “Flow Due to a Stretching Boundary with Partial Slip—an Exact Solution of the Navier-Stokes Equations,” Chem. Eng. Sci. 57, 3745–3747 (2002).

    Article  Google Scholar 

  33. H. I. Andersson, “Slip Flow Past a Stretching Surface,” Acta Mech. 158, 121–125 (2002).

    Article  MATH  Google Scholar 

  34. P. D. Ariel, T. Hayat, and S. Asghar, “The Flow of an Elastico-Viscous Fluid Past a Stretching Sheet with Partial Slip,” Acta Mech. 187, 29–35 (2006).

    Article  MATH  Google Scholar 

  35. P. D. Ariel, “Two Dimensional Stagnation Point Flow of an Elastico-Viscous Fluid with Partial Slip,” Z. Angew. Math. Mech. 88, 320–324 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  36. Z. Abbas, Y. Wang, T. Hayat, and M. Oberlack, “Slip Effects and Heat Transfer Analysis in a Viscous Fluid over an Oscillatory Stretching Surface,” Int. J. Numer. Meth. Fluids 59, 443–458 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  37. S. Mukhopadhyay and H. I. Andersson, “Effects of Slip and Heat Transfer Analysis of Flow over an Unsteady Stretching Surface,” Heat Mass Transfer 45, 1447–1452 (2009).

    Article  ADS  Google Scholar 

  38. S. Mukhopadhyay, “Effects of Slip on Unsteady Mixed Convective Flow and Heat Transfer Past a Stretching Surface,” Chinese Phys. Lett. 27(12), 124401 (2010).

    Article  ADS  Google Scholar 

  39. K. Bhattacharyya, “Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet,” Chinese. Phys. Lett. 28(7), 074701 (2011).

    Article  Google Scholar 

  40. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Slip Effects on Boundary Layer Stagnation-Point Flow and Heat Transfer Towards a Shrinking Sheet,” Int. J. Heat Mass Transfer 54, 308–313 (2011).

    Article  MATH  Google Scholar 

  41. S. Mukhopadhyay, and R. S. R. Gorla, “Effects of Partial Slip on Boundary Layer Flow Past a Permeable Exponential Stretching Sheet in Presence of Thermal Radiation,” Heat Mass Transfer 48(10), 1773–1781 (2012).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Burdwan, Burdwan, 713104, India

    S. Mukhopadhyay

  2. Administration, Institute of Business University of Rajshahi, Rajshahi, 6205, Bangladesh

    M. Golam Arif

  3. University of Rajshahi, Rajshahi, 6205, Bangladesh

    M. Wazed Ali

Authors
  1. S. Mukhopadhyay
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  2. M. Golam Arif
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  3. M. Wazed Ali
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Correspondence to S. Mukhopadhyay.

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Original Russian Text © S. Mukhopadhyay, M. Golam Arif, M. Wazed Ali.

__________

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 6, pp. 77–86, November–December, 2013.

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Mukhopadhyay, S., Arif, M.G. & Ali, M.W. Effects of partial slip on chemically reactive solute transfer in the boundary layer flow over an exponentially stretching sheet with suction/blowing. J Appl Mech Tech Phy 54, 928–936 (2013). https://doi.org/10.1134/S0021894413060084

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  • DOI: https://doi.org/10.1134/S0021894413060084

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