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Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet

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Abstract

This article studies the three-dimensional boundary layer flow of an elasticoviscous fluid over a stretching surface. Velocity of the stretching sheet is assumed to be time-dependent. Effect of mass transfer with higher order chemical reaction is further considered. Computations are made by the homptopy analysis method (HAM). Convergence of the obtained series solutions is explicitly analyzed. Variations of embedding parameters on the velocity and concentration are graphically discussed. Numerical computations of surface mass transfer are reported. Comparison of the present results with the numerical solutions is also given.

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References

  1. Fetecau, C. and Fetecau, C. Starting solutions for some unsteady unidirectional flows of a second grade fluid. International Journal of Engineering Science, 43(10), 781–789 (2005)

    Article  MathSciNet  Google Scholar 

  2. Fetecau, C., Athar, M., and Fetecau, C. Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate. Computers and Mathematics with Applications, 57(4), 596–603 (2008)

    Article  MathSciNet  Google Scholar 

  3. Fetecau, C. and Fetecau, C. Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder. International Journal of Engineering Science, 44(11–12), 788–796 (2006)

    Article  MathSciNet  Google Scholar 

  4. Tan, W. C., Xiao, P. W., and Yu, X. M. A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model. International Journal of Nonlinear Mechanics, 38(5), 645–650 (2003)

    Article  MATH  Google Scholar 

  5. Hayat, T., Ahmad, N., and Ali, N. Effects of endoscope and magnetic field on the peristalsis involving Jeffrey fluid. Communications in Nonlinear Science and Numerical Simulation, 13(8), 1581–1591 (2008)

    Article  MathSciNet  Google Scholar 

  6. Hayat, T., Mustafa, M., and Asghar, S. Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in presence of chemical reaction. Nonlinear Analysis: Real World Applications, 11(4), 3186–3197 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hayat, T., Mustafa, M., and Pop, I. Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid. Communications in Nonlinear Science and Numerical Simulation, 15(5), 1183–1196 (2010)

    Article  MathSciNet  Google Scholar 

  8. Devi, C. D. S., Takhar, H. S., and Nath, G. Unsteady mixed convection flow in a stagnation region to adjacent to a vertical surface. Heat and Mass Transfer, 26(2), 71–79 (1991)

    Google Scholar 

  9. Andersson, H. I., Aarseth, J. B., and Dandapat, B. S. Heat transfer in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer, 43(1), 69–74 (2003)

    Article  Google Scholar 

  10. Nazar, R., Amin, N., and Pop, I. Unsteady boundary layer due to a stretching surface in a rotating fluid. Mechanics Research Communications, 31(1), 121–128 (2004)

    Article  MATH  Google Scholar 

  11. Elbashbeshy, E. M. A. and Bazid, M. A. A. Heat transfer over an unsteady stretching surface. Heat and Mass Transfer, 41(1), 1–4 (2004)

    Article  Google Scholar 

  12. Beard, D. W. and Walters, K. Elastico-viscous boundary layer flows I: two-dimensional flow near a stagnation point. Proceedings of the Cambridge Philosophical Society, 60(3), 667–674 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ariel, P. D. Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip. Zeitschrift für Angewandte Mathematik und Mechanik, 88(4), 320–324 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hayat, T., Abbas, Z., and Pop, I. Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluid. Numerical Methods for Partial Differential Equations, 26(2), 305–319 (2010)

    MATH  MathSciNet  Google Scholar 

  15. Cortell, R. MHD flow and mass transfer of an electrically fluid of second grade in a porous medium over a stretching sheet with chemically reactive species. Chemical Engineering Processing, 46(8), 721–728 (2007)

    Article  Google Scholar 

  16. Cortell, R. Towards an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet. Chemical Engineering Processing, 46(10), 982–989 (2007)

    Article  Google Scholar 

  17. Nazar, R. and Latip, N. A. Numerical investigation of three-dimensional boundary layer flow due to a stretching surface in a viscoelastic fluid. European Journal of Scientific Research, 29(4), 509–517 (2009)

    Google Scholar 

  18. Mukhopadhyay, S. Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in a porous medium. International Journal of Heat and Mass Transfer, 52(13–14), 3261–3265 (2009)

    Article  MATH  Google Scholar 

  19. Liao, S. J. A general approach to get series solution of nonsimilarity boundary layer flows. Communications in Nonlinear Science and Numerical Simulation, 14(5), 2144–2159 (2009)

    Article  MathSciNet  Google Scholar 

  20. Xu, H., Liao, S. J., and You, X. C. Analysis of nonlinear fractional partial differential equations with homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation, 14(4), 1152–1156 (2009)

    Article  MathSciNet  Google Scholar 

  21. Xu, H. and Liao, S. J. Dual solutions of boundary layer flow over an upstream moving plate. Communications in Nonlinear Science and Numerical Simulation, 13(2), 350–358 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  22. Liao, S. J. Notes on the homotopy analysis method: some definitions and theorems. Communications in Nonlinear Science and Numerical Simulation, 14(4), 983–997 (2009)

    Article  MathSciNet  Google Scholar 

  23. Tan, Y. and Abbasbandy, S. Homotopy analysis method for quadratic Recati differential equation. Communications in Nonlinear Science and Numerical Simulation, 13(3), 539–546 (2008)

    Article  MATH  Google Scholar 

  24. Abbasbandy, S. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Physics Letters A, 372(6), 613–618 (2008)

    MathSciNet  Google Scholar 

  25. Abbasbandy, S. and Zakaria, F. S. Soliton solution for the fifth-order KdV equation with homotopy analysis method. Nonlinear Dynamics, 51(1–2), 83–87 (2008)

    MATH  MathSciNet  Google Scholar 

  26. Kechil, S. and Hashim, I. Approximate analytical solution for MHD stagnation-point flow in porous media. Communications in Nonlinear Science and Numerical Simulation, 14(4), 1346–1354 (2009)

    Article  MathSciNet  Google Scholar 

  27. Hashim, I., Abdulaziz, O., and Momani, S. Homotopy analysis method for fractional IVPs. Communications in Nonlinear Science and Numerical Simulation, 14(3), 674–684 (2009)

    Article  MathSciNet  Google Scholar 

  28. Hayat, T., Maqbool, K., and Asghar, S. Hall and heat transfer effects on the steady flow of a Sisko fluid. Zeitschrift Für Naturforschung A, 64a(1), 769–782 (2009)

    Google Scholar 

  29. Hayat, T., Maqbool, K., and Asghar, S. The influence of Hall current and heat transfer on the flow of a fourth grade fluid. Numerical Methods for Partial Differential Equations, 26(3), 501–518 (2010)

    MATH  MathSciNet  Google Scholar 

  30. Hayat, T., Qasim, M., and Abbas, Z. Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet. Zeitschrift für Naturforschung A, 65a(1), 231–239 (2010)

    Google Scholar 

  31. Hayat, T., Qasim, M., and Abbas, Z. Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space. Communications in Nonlinear Science and Numerical Simulation, 15(9), 2375–2387 (2010)

    Article  MathSciNet  Google Scholar 

  32. Hayat, T. and Nawaz, M. Hall and ion-slip effects on three-dimensional flow of a second grade fluid. International Journal for Numerical Methods in Fluids DOI: 10.1002/fld.2251

  33. Hayat, T., Sajjad, R., and Asghar, S. Series solution for MHD channel flow of a Jeffery fluid. Communications in Nonlinear Science and Numerical Simulation, 15(9), 2400–2406 (2010)

    Article  MathSciNet  Google Scholar 

  34. Hayat, T., Qasim, M., and Mesloub, S. MHD flow and heat transfer over permeable stretching sheet with slip conditions. International Journal for Numerical Methods in Fluids DOI: 10.1002/fld.2294

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    T. Hayat & M. Mustafa

  2. Department of Physics, Faculty of Science, King Saud University, Riyadh, 11320, Saudi Arabia

    T. Hayat, M. Mustafa & A. A. Hendi

Authors
  1. T. Hayat
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  2. M. Mustafa
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  3. A. A. Hendi
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Correspondence to M. Mustafa.

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Hayat, T., Mustafa, M. & Hendi, A.A. Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet. Appl. Math. Mech.-Engl. Ed. 32, 167–178 (2011). https://doi.org/10.1007/s10483-011-1403-7

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  • DOI: https://doi.org/10.1007/s10483-011-1403-7

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