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Non-Dimensional Optimization of Magnetohydrodynamic Falkner–Skan Fluid Flow

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Abstract

This paper focuses on the optimized solution of magnetohydrodynamic (MHD) Falkner–Skan fluid flow. To this end, an optimal homotopy analysis method (OHAM) is utilized to solve the governing equation with the corresponding boundary conditions. A convergence and comparison study is also conducted to show accuracy and reliability of the presented OHAM series solution. It is shown that utilizing the OHAM can accelerate convergence of the series solution.

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References

  • Abbasbandy S, Hayat T (2009) Solution of the MHD Falkner–Skan flow by homotopy analysis method. Commun Nonlinear Sci Numer Simul 14(9–10):3591–3598

    Article  MathSciNet  MATH  Google Scholar 

  • Abbasbandy S, Naz R, Hayat T, Alsaedi A (2014) Numerical and analytical solutions for Falkner–Skan flow of MHD Maxwell fluid. Appl Math Comput 242:569–575

    MathSciNet  MATH  Google Scholar 

  • Eurdum B, Eerdum Q, Huhe B, Temuer C, Wang JY (2014) Variational iteration method with He’s polynomials for MHD Falkner–Skan flow over permeable wall based on Lie symmetry method. Int J Numer Methods Heat Fluid Flow 24(6):1348–1362

    Article  MathSciNet  MATH  Google Scholar 

  • Falkner VM, Skan SW (1931) Some approximate solutions of the boundary layer equations. Philos Mag 12(80):865–896

    Article  MATH  Google Scholar 

  • Fang T, Yao S, Zhang J, Zhong Y, Tao H (2012) Momentum and heat transfer of the Falkner–Skan flow with algebraic decay: an analytical solution. Commun Nonlinear Sci Numer Simul 17(6):2476–2488

    Article  MathSciNet  MATH  Google Scholar 

  • Ganapathirao M, Ravindran R, Momoniat E (2015) Effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a wedge with heat generation/absorption in the presence of suction or injection. Heat Mass Trans 51(2):289–300

    Article  Google Scholar 

  • Harris SD, Ingham DB, Pop I (2008) Unsteady heat transfer in impulsive Falkner–Skan flows: constant wall heat flux case. Acta Mech 201:185–196

    Article  MATH  Google Scholar 

  • Hartree DR (1937) On an equation occurring in Falkner–Skan approximate treatment of the equations of the boundary layer. Proc Camb Philos Soc 33(2):223–239

    Article  MATH  Google Scholar 

  • Ishak A, Nazar R, Pop I (2007) Falkner–Skan equation for flow past a moving wedge with suction or injection. J Appl Math Comput 25(1–2):67–83

    Article  MathSciNet  MATH  Google Scholar 

  • Khan M, Azam M, Munir A (2017) On unsteady Falkner–Skan flow of MHD Carreau nanofluid past a static/moving wedge with convective surface condition. J Mol Liq 230:48–58

    Article  Google Scholar 

  • Liao SJ (1992) On the proposed homotopy analysis techniques for nonlinear problems and its application, Ph.D. Dissertation, Shanghai Jiao Tong University

  • Liao SJ (2004a) Beyond perturbation: introduction to the homotopy analysis method. Chapman & Hall/CRC, Boca Raton

    MATH  Google Scholar 

  • Liao SJ (2004b) On the homotopy analysis method for nonlinear problems. Appl Math Comput 147(2):499–513

    MathSciNet  MATH  Google Scholar 

  • Liao SJ (2010) An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun Nonlinear Sci Numer Simul 15(8):2003–2016

    Article  MathSciNet  MATH  Google Scholar 

  • Liu CS (2017) An iterative method based-on eigenfunctions and adjoint eigenfunctions for solving the Falkner–Skan equation. Appl Math Lett 67:33–39

    Article  MathSciNet  MATH  Google Scholar 

  • Marinca V, Herisanu N (2015) The optimal homotopy asymptotic method. Springer, Berlin

    Book  MATH  Google Scholar 

  • Merkin JH (1986) On dual solutions occurring in mixed convection in a porous medium. J Eng Math 20(2):171–179

    Article  MathSciNet  MATH  Google Scholar 

  • Nadeem S, Ahmad S, Muhammad N (2018) Computational study of Falkner–Skan problem for a static and moving wedge. Sens Actuators B Chem 263:69–76

    Article  Google Scholar 

  • Olagunju DO (2006) The Falkner–Skan flow of a viscoelastic fluid. Int J Nonlinear Mech 41(6–7):825–829

    Article  Google Scholar 

  • Postelnicu A, Pop I (2011) Falkner–Skan boundary layer flow of a power-law fluid past a stretching wedge. Appl Math Comput 217(9):4359–4368

    MathSciNet  MATH  Google Scholar 

  • Rahman MM, Merkin JH, Pop I (2015) Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition. Acta Mech 226(8):2441–2460

    Article  MathSciNet  Google Scholar 

  • Schlichting H (1978) Boundary-layer theory, 7th edn. McGraw-Hill, New York

    MATH  Google Scholar 

  • Su XH, Zheng LC (2011) Approximate solutions to MHD Falkner–Skan flow over permeable wall. Appl Math Mech Eng Ed 32(4):401–408

    Article  MATH  Google Scholar 

  • Ullah I, Shafie S, Makinde OD, Khan LI (2017) Unsteady MHD Falkner–Skan flow of Casson nanofluid with generative/destructive chemical reaction. Chem Eng Sci 172:694–706

    Article  Google Scholar 

  • Watanabe T (1990) Thermal boundary layers over a wedge with uniform suction or injection in forced flow. Acta Mech 83(3–4):119–126

    Article  MathSciNet  Google Scholar 

  • White FM (1991) Viscous fluid flow, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Yacob NA, Ishak A, Pop I (2011) Falkner–Skan problem for a static or moving wedge in nanofluids. Int J Therm Sci 50(2):133–139

    Article  Google Scholar 

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Correspondence to Reza Saleh.

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Khoshrouye Ghiasi, E., Saleh, R. Non-Dimensional Optimization of Magnetohydrodynamic Falkner–Skan Fluid Flow. INAE Lett 3, 143–147 (2018). https://doi.org/10.1007/s41403-018-0043-2

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  • DOI: https://doi.org/10.1007/s41403-018-0043-2

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