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Solving the Boundary Layer Flow of Eyring–Powell Fluid Problem via Quasilinearization–Collocation Method Based on Hermite Functions

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Abstract

In this paper, the combination of quasilinearization and collocation methods is used for solving the problem of the boundary layer flow of Eyring–Powell fluid over a stretching sheet. The proposed approach is based on Hermite function collocation method. The quasilinearization method is used for converting the non-linear Eyring–Powell problem to a sequence of linear equations and the Hermite collocation method is applied for solving linear equations at each iteration. In the end, the obtained result of the present work is compared with the obtained results in other papers.

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References

  • Alsaedi A, Awais M, Hayat T (2012) Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions. Commun Nonlinear Sci Number Simul 17:4210–4223

    Article  MathSciNet  MATH  Google Scholar 

  • Ara A, Alamkhan N, Khan H, Sultan F (2014) Radiation effect on boundary layer flow of an Eyring–Powell fluid over an exponentially shrinking sheet. Ain Shams Eng 5(4):1337–1342

    Article  Google Scholar 

  • Boyd JP (1987) Spectral methods using rational basis functions on an infinite interval. J Comput Phys 69:112–142

    Article  MathSciNet  MATH  Google Scholar 

  • Boyd JP (2000) Chebyshev and Fourier spectral methods, 2nd edn. Dover, NewYork

    Google Scholar 

  • Boyd JP, Rangan C, Bucksbaum PH (2003) Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: a comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions. J Comput Phys 188:56–74

    Article  MATH  Google Scholar 

  • Christov CI (1982) A complete orthogonal system of functions in \(L^{2(-\infty, \infty )}\) space. SIAM J Appl Math 42:1337–1344

    Article  MathSciNet  MATH  Google Scholar 

  • Crane LJ (1970) Flow past a stretching plate. Z Angew Math Phys 21:645–647

    Article  Google Scholar 

  • Funaro D, Kavian O (1991) Approximation of some diffusion evolution equations in unbounded domains by Hermite functions. Math Comput 57:597–619

    Article  MathSciNet  MATH  Google Scholar 

  • Grubka LJ, Bobba KM (1985) Heat transfer characteristics of continuous stretching surface with variable temperature. J Heat Transf 107:248–250

    Article  Google Scholar 

  • Guo BY (1999) Error estimation of Hermite spectral method for nonlinear partial differential equations. Math Comput 68(227):1067–1078

    Article  MathSciNet  MATH  Google Scholar 

  • Guo BY (2000) Jacobi spectral approximation and its applications to differential equations on the half line. J Comput Math 18:95–112

    MathSciNet  MATH  Google Scholar 

  • Guo BY (2000) Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations. J Math Anal Appl 243:373–408

    Article  MathSciNet  MATH  Google Scholar 

  • Guo BY, Shen J, Wang ZQ (2000) A rational approximation and its applications to differential equations on the half line. J Sci Comput 15:117–147

    Article  MathSciNet  MATH  Google Scholar 

  • Hayat T, Iqbal Z, Qasim M, Obaidat S (2012) Steady flow of an Eyring–Powell fluid over a moving surface with convective boundary conditions. Int J Heat Mass Transf 55:1817–1822

    Article  Google Scholar 

  • Jalil M, Asghar S, Imran SM (2013) Self-similar solutions for the flow and heat transfer of Eyring–Powell fluid over a moving surface in a parallel free stream. Int J Heat Mass Transf 65:73–79

    Article  Google Scholar 

  • Javed T, Ali N, Abbas Z, Sajid M (2013) Flow of an Eyring–Powell non Newtonian fluid over a stretching sheet. Chem Eng Commun 200:327–336

    Article  Google Scholar 

  • Liverts EZ, Krivec R, Mandelzweig VB (2008) Quasilinearization approach to the resonance calculations: the quartic oscillator. Phys Scripta 77(4):045004

    Article  MATH  Google Scholar 

  • Magyari E, Kaller B (2000) Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls. Eur J Mech B Fluids. 19:109–122

    Article  MathSciNet  MATH  Google Scholar 

  • Mahapatra TR, Gupta AS (2003) Stagnation-point flow towards a stretching surface. Can J Chem Eng 81(2):258–263

    Article  Google Scholar 

  • Malvandi A, Hedayati F, Gangi DD (2014) slip effects on unsteady stagnation point flow of a nanofluid over a stretching sheet. Power Technol 253:377–384

    Article  Google Scholar 

  • Mandelzweig VB (1999) Quasilinearization method and its verification on exactly solvable models in quantum mechanics. J Math Phys 40:6266–6291

    Article  MathSciNet  MATH  Google Scholar 

  • Megahed AM (2015) Flow and heat transfer of Eyring-Powell fluid due to an exponential stretching sheet with heat flux and variable thermal conductivity. Z Naturforsch 70(3):163–169

    Google Scholar 

  • Mukhopadhyay S (2013) Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction/blowing and thermal radiation. Ain Shams Eng J 4:485–491

    Article  Google Scholar 

  • Parand K, Dehghan M, Baharifard F (2013) Solving a laminar boundary layer equation with the rational Gegenbauer functions. Appl Math Model 37(3):851–863

    Article  MathSciNet  MATH  Google Scholar 

  • Parand K, Dehghan M, Rezaeia AR, Ghaderi SM (2010) An approximation algorithm for the solution of the nonlinear Lane–Emden type equations arising in astrophysics using Hermite functions collocation method. Comput Phys Commun 181:1096–1108

    Article  MathSciNet  MATH  Google Scholar 

  • Parand K, Delkhosh M (2017a) Solving the nonlinear Schlomilch’s integral equation arising in ionospheric problems. Afr Mat 28(3):459–480

    Article  MathSciNet  MATH  Google Scholar 

  • Parand K, Delkhosh M (2017b) Accurate solution of the Thomas–Fermi equation using the fractional order of rational Chebyshev functions. J Comput Appl Math 317:624–642

    Article  MathSciNet  MATH  Google Scholar 

  • Parand K, Ghaderi A, Yousefi H, Delkhosh M (2016) A new approach for solving nonlinear Thomas–Fermi equation based on fractional order of rational Bessel functions. Electron J Diff Equ 2016:331

    MathSciNet  MATH  Google Scholar 

  • Parand K, Ghasemi M, Rezazadeh S, Peiravi A, Ghorbanpour A, Tavakoli Golpaygani A (2010) Quasilinearization approach for solving Volterra’s population model. Appl Comput Math 9(1):95–103

    MathSciNet  MATH  Google Scholar 

  • Parand K, Lotfi Y, Rad JA (2017) An accurate numerical analysis of the laminar two-dimensional of an incompressible Eyring–Powell fluid over a linear stretching sheet. Eur Phys J Plus 132(9):397

    Article  Google Scholar 

  • Parand K, Mazaheri P, Yousefi H, Delkhosh M (2017) Fractional order of rational Jacobi functions for solving the non-linear singular Thomas–Fermi equation. Eur Phys J Plus 132(2):77

    Article  Google Scholar 

  • Parand K, Rezaei AR, Taghavi A (2010) Numerical approximations for population growth model by rational Chebyshev and Hermite functions collocation approach: a comparison. Math Method Appl Sci 33(17):2076–2086

    Article  MathSciNet  MATH  Google Scholar 

  • Parand K, Taghavi A, Shahini M (2009) Comparison between rational Chebyshev and modified generalized Laguerre functions pseudospectral methods for solving Lane-Emden and unsteady gas equations. Acta Phys Pol B 40(6):1749–1763

    MATH  Google Scholar 

  • Parand K, Yousefi H, Delkhosh M, Ghaderi A (2016) A novel numerical technique to obtain an accurate solution to the Thomas–Fermi equation. Eur Phys J Plus 131(7):228

    Article  Google Scholar 

  • Rahimi J, Ganji DD, Khaki M, Hosseinzadeh KH (2016) Solution of the boundary layer flow of an Eyring–Powell non Newtonian fluid over a linear stretching sheet by collocation method. Alexandria Eng J. https://doi.org/10.1016/j.aej.2016.11.006

  • Rezaei A, Baharifard F, Parand K (2011) Quasilinearization–Barycentric approach for numerical investigation of the boundary value Fin problem. Int J Comput Electr Autom Control Info Eng 5(2):194–201

    Google Scholar 

  • Shen J (2000) Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J Numer Anal 38:1113–1133

    Article  MathSciNet  MATH  Google Scholar 

  • Shen J, Tang T (2005) High order numerical methods and algorithms. Chinese Science Press, Beijing

    Google Scholar 

  • Shen J, Tang T, Wang L-L (2010) Spectral methods algorithms, analyses and applications, 1st edn. Springer, Berlin

    Google Scholar 

  • Shen J, Wang L-L (2009) Some recent advances on spectral methods for unbounded domains. Commun Comput Phys 5:195–241

    MathSciNet  MATH  Google Scholar 

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Correspondence to Kourosh Parand.

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Parand, K., Kalantari, Z. & Delkhosh, M. Solving the Boundary Layer Flow of Eyring–Powell Fluid Problem via Quasilinearization–Collocation Method Based on Hermite Functions. INAE Lett 3, 11–19 (2018). https://doi.org/10.1007/s41403-018-0033-4

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  • DOI: https://doi.org/10.1007/s41403-018-0033-4

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