Journal of Applied Mathematics

Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface

Wubshet Ibrahim and Gosa Gadisa

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The nonlinear convective flow of Eyring-Powell nanofluid using Catteneo-Christov model with heat generation or absorption term and chemical reaction rate over nonlinear stretching surface is analyzed. The simultaneous nonlinear partial differential equations governing the boundary layer flow are transformed to the corresponding nonlinear ordinary differential equations using similarity solution and then solved using Galerkin finite element method (GFEM). The impacts of pertinent governing parameters like Brownian diffusion, thermophoresis, mixed convection, heat generation or absorption, chemical reaction rate, Deborah numbers, Prandtl number, magnetic field parameter, Lewis number, nonlinear stretching sheet, and Eyring-Powell fluid parameters on velocity field, temperature, and nanoparticle concentration are given in both figures and tabular form. The result shows that the rise in chemical reaction rate will improve mass transfer rate and reduce heat transfer rate and local buoyancy parameter has quit opposite effect. The attributes of local skin friction coefficient, Nusselt number, and Sheer wood number are investigated and validated with existing literatures.

Article information

J. Appl. Math., Volume 2019 (2019), Article ID 3472518, 16 pages.

Received: 13 February 2019
Revised: 10 May 2019
Accepted: 28 May 2019
First available in Project Euclid: 22 August 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Ibrahim, Wubshet; Gadisa, Gosa. Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface. J. Appl. Math. 2019 (2019), Article ID 3472518, 16 pages. doi:10.1155/2019/3472518.

Export citation


  • S. Panigrahi, M. Reza, and A. K. Mishra, “Mixed convective flow of a powell-eyring fluid over a non-linear stretching surface with thermal diffusion and diffusion thermo,” Procedia Engineering, vol. 127, pp. 645–651, 2015.
  • I. Khan, M. Qasim, and S. Shafie, “Flow of an Erying-Powell fluid over a stretching sheet in presence of chemical reaction,” Thermal Science International Scientific Journal, vol. 20, pp. 1903–1912, 2016.
  • S. Abdul Gaffar, V. E. Ramachandra Prasad, and K. Reddy, “Non-Newtonian thermal convection of Eyring-Powell fluid from an isothermal sphere with biot number effects,” International Journal of Industrial Mathematics, vol. 8, no. 2, 2016.
  • S. Alharbi, A. Dawar, Z. Shah et al., “Entropy generation in MHD eyring–powell fluid flow over an unsteady oscillatory porous stretching surface under the impact of thermal radiation and heat source/sink,” Applied Sciences, vol. 8, no. 12, article 2588, 2018.
  • B. Ahmad and Z. Iqbal, “An effect of Cattaneo Christov heat flux model for eyring powell fluid over an exponentially stretching sheet,” Frontiers in Heat and Mass Transfer, vol. 8, no. 22, 2017.
  • A. M. Megahed, “Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation,” Rheologica Acta, vol. 51, no. 9, pp. 841–847, 2012.
  • A. M. Megahed, “Flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching vertical surface with heat flux and thermal radiation,” Meccanica, vol. 50, no. 7, pp. 1693–1700, 2015.
  • A. M. Megahed, “Flow and heat transfer of non-Newtonian Sisko fluid past a nonlinearly stretching sheet with heat generation and viscous dissipation,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 40, no. 492, 2018.
  • M. S. Upadhay, Mahesha, and C. S. K. Raju, “Cattaneo-Christov on heat and mass transfer of unsteady Eyring-Powell dusty nanofluid over sheet with heat and mass flux conditions,” Informatics in Medicine Unlocked, vol. 9, pp. 76–85, 2017.
  • K. Anantha Kumar, J. V. Ramana Reddy, V. Sugunamma, and N. Sandeep, “Magnetohydrodynamic Cattaneo-Christov flow past a cone and a wedge with variable heat source/sink,” Alexandria Engineering Journal, vol. 571, pp. 435–443, 2016.
  • A. Kumar, V. Sugunamma, and N. Sandeep, “Impact of non-linear radiation on mhd non-aligned stagnation point flow of micropolar fluid over a convective surface,” Journal of Non-Equilibrium Thermodynamics, vol. 43, no. 4, pp. 327–345, 2018.
  • K. Anantha Kumar, V. Sugunamma, N. Sandeep, and J. V. Ramana Reddy, “Impact of Brownianmotion and thermophoresis on bioconvective flow of nanoliquids past a variable thickness surface with slip effects,” Multidiscipline Modeling in Materials and Structures, 2018.
  • T. Hayat, R. Sajjad, T. Muhammad, A. Alsaedi, and R. Ellahi, “MHD nonlinear stretching flow of Powell–Eyring nanomaterial,” Results in Physics, vol. 7, pp. 535–543, 2017.
  • M. Madhu and N. Kishan, “MHD Boundary-layer flow of a non-Newtonian nanofluid Past a Stretching sheet with a heat source/sink,” Journal of Applied Mechanics and Technical Physics, vol. 57, no. 5, pp. 908–915, 2016.
  • J. Rahimi, D. D. Ganji, M. Khaki, and K. Hosseinzadeh, “Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet by collocation method,” Alexandria Engineering Journal, vol. 56, no. 4, pp. 621–627, 2017.
  • A. T. Akinshilo and O. Olaye, “On the analysis of the Eyring Powell model based fluid flow in a pipe with temperature dependent viscosity and internal heat generation,” Journal of King Saud University - Engineering Sciences, vol. 31, no. 3, pp. 271–279, 2019.
  • M. Madhu and N. Kishan, “Finite element analysis of heat and mass transfer by MHD mixed convection stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface with radiation,” Journal of the Egyptian Mathematical Society, vol. 24, no. 3, pp. 458–470, 2016.
  • M. Jayachandra Babu, N. Sandeep, and S. Saleem, “Free convective MHD Cattaneo-Christov flow over three different geometries with thermophoresis and Brownian motion,” Alexandria Engineering Journal, vol. 56, no. 4, pp. 659–669, 2017.
  • K. Vajravelu and K. S. Sastri, “Fully developed laminar free convection flow between two parallel vertical walls-I,” International Journal of Heat and Mass Transfer, vol. 20, no. 6, pp. 655–660, 1977.
  • R. Bhargava and R. S. Agarwal, “Fully developed free convection flow in a circular pipe,” Indian Journal of Pure and Applied Mathematics, vol. 10, pp. 357–365, 1979.
  • M. I. Khan, S. Qayyum, T. Hayat, M.. Khan, A. Alsaedi, and T. A. Khan, “Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection,” Physics Letters A, vol. 382, no. 31, pp. 2017–2026, 2018.
  • K. Vajravelu, J. R. Cannon, J. Leto et al., “Nonlinear convection at a porous flat plate with application to heat transfer from a dike,” Journal of Mathematical Analysis and Applications, vol. 277, no. 2, pp. 609–623, 2003.
  • M. I. Khan, M. Waqas, T. Hayat, M. I. Khan, and A. Alsaedi, “Numerical simulation of nonlinear thermal radiation and homogeneous-heterogeneous reactions in convective flow by a variable thicked surface,” Journal of Molecular Liquids, vol. 246, pp. 259–267, 2017.
  • T. Hayat and S. Nadeem, “Flow of 3D Eyring-Powell fluid by utilizing Cattaneo-Christov heat flux model and chemical processes over an exponentially stretching surface,” Results in Physics, vol. 8, pp. 397–403, 2018.
  • S. Noreen, “Magneto-thermo hydrodynamic peristaltic flow of Eyring-Powell nanofluid in asymmetric channel,” Nonlinear Engineering, vol. 7, no. 2, pp. 83–90, 2018.
  • W. Ibrahim and B. Hindebu, “Magnetohydrodynamic (MHD) boundary layer flow of eyring-powell nanofluid past stretching cylinder with cattaneo-christov heat flux model,” Nonlinear Engineering, 2018.
  • K. Anantha Kumar, B. Ramadevi, and V. Sugunamma, “Impact of lorentz force on unsteady bio convective flow of carreau fluid across a variable thickness sheet with non-fourier heat flux model,” Defect and Diffusion Forum, vol. 387, pp. 474–497, 2018.
  • B. Ramadevi, V. Sugunamma, K. Anantha Kumar, and J. V. Ramana Reddy, “MHD flow of Carreau fluid over a variable thickness melting surface subject to Cattaneo-Christov heat flux,” Multidiscipline Modeling in Materials and Structures, 2018.
  • K. Anantha Kumar, J. V. Ramana Reddy, V. Sugunamma, and N. Sandeep, “MHD carreau fluid flow past a melting surface with cattaneo-christov heat flux,” in Applied Mathematics and Scientific Computing, Trends in Mathematics, 336, p. 325, 2019.
  • R. E. Powell and H. Eyring, “Mechanisms for the relaxation theory of viscosity,” Nature, vol. 154, no. 3909, pp. 427-428, 1944.
  • M. Y. Malik, I. Khan, A. Hussain, and T. Salahuddin, “Mixed convection flow of MHD Eyring-Powell nanofluid over a stretching sheet,” A numerical study AIP Advances, vol. 5, no. 11, Article ID 117118, 2015.
  • J. N. Reddy, An Introduction to the Finite Element Method, McGraw– Hill, New York, NY, USA, 1985.
  • E. B. G. F. Becker and J. T. Oden, Finite Elements an Introduction, Texas Institute for Computational Mechanics, UT Austin, 1981.
  • O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Volume 1: Basic Formulations and Linear Problems, McGraw Hill, London, UK, 4th edition, 2013.
  • W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” International Journal of Heat and Mass Transfer, vol. 53, no. 11-12, pp. 2477–2483, 2010.
  • M. Goyal and R. Bhargava, “Finite element solution of double-diffusive boundary layer flow of viscoelastic nanofluids over a stretching sheet,” Computational Mathematics and Mathematical Physics, vol. 54, no. 5, pp. 848–863, 2014. \endinput