Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper, a two-dimensional steady flow of a viscous fluid due to a stretching sheet in the presence of a magnetic field is considered. We proposed two new numerical schemes based on the Haar wavelet coupled with a collocation approach and quasi-linearization process for solving the Falkner-Skan equation representing the governing problem. The important derived quantities representing the fluid velocity and wall shear stress for various values of flow parameters Mand βare calculated. The proposed methods enable us to obtain the solutions even for negative β, nonlinear stretching parameter, and smaller values of the magnetic parameter ()M1< which was missing in the earlier findings. Numerical and graphical results obtained show an excellent agreement with the available findings and demonstrate the efficiency and accuracy of the developed schemes. Another significant advantage of the present method is that it does not depends on small parameters and initial presumptions unlike in traditional semi-analytical and numerical methods.
Rocznik
Tom
Strony
84--103
Opis fizyczny
Bibliogr. 33 poz., wykr.
Twórcy
autor
- Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, 576104, INDIA
autor
- Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, 576104, INDIA
Bibliografia
- [1] Rashad A.M., Rashidi M.M., Giulio Lorenzini, Sameh E.A. and Abdelraheem M.A. (2017): Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu-water nanofluid.– International Journal of Heat and Mass Transfer, vol.104, pp.878-889.
- [2] Bhatti M.M., Mishra S.R., Abbas T. and Rashidi M.M. (2018): A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects.– Neural Computing and Applications, vol.30, pp.1237-1249.
- [3] Mansoury D., Doshmanziari F.I., Rezaie S. and Rashidi M.M. (2019): Effect of Al2O3/water nanofluid on performance of parallel flow heat exchangers.– Journal of Thermal Analysis and Calorimetry, vol.135, pp.625-643.
- [4] Crane L.J. (1970): Flow past a stretching plate.– Zeitschrift für angewandte Mathematik und Physik ZAMP, vol.21, pp.645-647.
- [5] Chakrabarti A. and Gupta A.S. (1979): Hydromagnetic flow and heat transfer over a stretching sheet.– Quarterly of Applied Mathematics, vol.37, pp.73-78.
- [6] Banks W.H.H. and Zaturska M.B. (1986): Eigen solutions in boundary-layer flow adjacent to a stretching wall.– IMA. J. Appl. Math., vol.36, pp.263-273.
- [7] Afzal N. (1993): Heat transfer from a stretching surface.– International Journal of Heat and Mass Transfer, vol.36, pp.1128-1131.
- [8] Chiam T.C. (1995): Hydromagnetic flow over a surface stretching with a power-law velocity.– International Journal of Engineering Science, vol.33, pp.429-435.
- [9] Liao S. (2005): A new branch of solutions of boundary-layer flows over an impermeable stretched plate.– International Journal of Heat and Mass Transfer, vol.48, pp.2529-2539.
- [10] Kudenatti R.B. (2012): A new exact solution for boundary layer flow over a stretching plate.– International Journal of Non-Linear Mechanics, vol.47, pp.727-733.
- [11] Hayat T., Hussain Q. and Javed T. (2009): The modified decomposition method and Padè approximants for the MHD flow over a non-linear stretching sheet.– Nonlinear Analysis: Real World Applications, vol.10, pp.966-973.
- [12] Rashidi M.M. (2009): The modified differential transform method for solving MHD boundary-layer equations.– Computer Physics Communications, vol.180, pp.2210-2217.
- [13] Mehmood A., Munawar S. and Ali A. (2010): Comments to: Homotopy analysis method for solving the MHD flow over a non-linear stretching sheet (Commun. Nonlinear Sci. Numer. Simul. 14(2009)2653-2663).– Communications in Nonlinear Science and Numerical Simulation, vol.15, pp.4233-4240.
- [14] Chen C.F. and Hsiao C.H. (1997): Haar wavelet method for solving lumped and distributed-parameter systems.– IEE Proc.-Control Theory Appl., vol.144, pp.87-94.
- [15] Lepik Ü. (2006): Haar wavelet method for nonlinear integro-differential equations.– Applied Mathematics and Computation, vol.176, pp.324-333.
- [16] Lepik Ü. (2007): Application of the Haar wavelet transform to solving integral and differential equations.– Proceedings-Estonian Academy of Sciences Physics Mathematics, vol.56, pp.28-46.
- [17] Lepik Ü. (2008): Haar wavelet method for solving higher order differential equations.– International Journal of Mathematics and Computation, vol.8, pp.84-94.
- [18] Lepik Ü. (2009): Solving fractional integral equations by the Haar wavelet method.– Applied Mathematics and Computation, vol.214, pp.468-478.
- [19] Bujurke N.M., Salimath C.S. and Shiralashetti S.C. (2008): Numerical solution of stiff systems from nonlinear dynamics using single-term Haar wavelet series.– Nonlinear Dynamics, vol.51, pp.595-605.
- [20] Hariharan G. and Kannan K. (2010): Haar wavelet method for solving some nonlinear Parabolic equations -Journal of Mathematical Chemistry, vol.48, pp.1044-1061.
- [21] Kanth A.S.V.R. and Kumar N.U. (2013): A Haar wavelet study on convective-radiative fin under continuous motion with temperature-dependent thermal conductivity.– Walailak Journal of Science and Technology, vol.11, pp.211- 224.
- [22] Aziz I., Islam S.U., Fayyaz M. and Azram M. (2014): New algorithms for numerical assessment of nonlinear integrodifferential equations of second-order using Haar wavelets.– Walailak Journal of Science and Technology, vol.12, pp.995-1007.
- [23] Saeed U. and Rehman M.U. (2013): Haar wavelet-quasilinearization technique for fractional nonlinear differential equations.– Applied Mathematics and Computation, vol.220, pp.630-648.
- [24] Kaur H., Mittal R.C. and Mishra V. (2011): Haar wavelet quasilinearization approach for solving nonlinear boundary value problems.– American Journal of Computational Mathematics, vol.1, pp.176-182.
- [25] Jiwari R. (2012): A Haar wavelet quasilinearization approach for numerical simulation of Burgers' equation.– Computer Physics Communications, vol.183, pp.2413-2423.
- [26] Lepik Ü. (2005): Numerical solution of differential equations using Haar wavelets.– Mathematics and Computers in Simulation, vol.68, pp.127-143.
- [27] Afzal N. (2003): Momentum transfer on power law stretching plate with free stream pressure gradient.–International Journal of Engineering Science, vol.41, pp.1197-1207.
- [28] Bellman R.E. and Kalaba R.E. (1965): Quasilinearization and Nonlinear Boundary-Value Problems.– American Elsevier Publishing Company, New York.
- [29] Majak J., Shvartsman B.S., Kirs M., Pohlak M. and Herranen H. (2015): Convergence theorem for the Haar wavelet based discretization method.– Composite Structures, vol.126, pp.227-232.
- [30] Sachdev P.L., Bujurke N.M. and Awati V.B. (2005): Boundary value problems for third-order nonlinear ordinary differential equations.– Studies in Applied Mathematics, vol.115, pp.303-318.
- [31] Kudenatti R.B., Awati V.B. and Bujurke N.M. (2011): Approximate analytical solutions of a class of boundary layer equations over nonlinear stretching surface.– Applied Mathematics and Computation, vol.218, pp.2952-2959.
- [32] Sakiadis B.C. (1961): Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface.– AIChE Journal, vol.7, pp.221-225.
- [33] Hayat T., Zaman H. and Ayub M. (2011): Analytical solution of hydromagnetic flow with Hall effect over a surface stretching with a power-law velocity.– Numerical Methods for Partial Differential Equations, vol.27, pp.937-959.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-21407188-ac09-4cdc-a460-b1376c6d40f1