Approximate analytical solution of the MHD Powell-Eyring fluid flow near accelerated plate


  • Fawzia Mansour Elniel Universiti Teknologi Malaysia
  • Zainal Abdul Aziz Universiti Teknologi Malaysi
  • Faisal Salah Universiti Teknologi Malaysi
  • Shaymaa Mustafa Universiti Teknologi Malaysi



non -Newtonian, ADM, Powell-Eyring fluid



In this article, the non-linear equation of unsteady flow of Powell-Eyring fluid is solved by using Adomian Decomposition Method (ADM). The fluid is assumed to be flowing under the effect of magnetic field. The model is developed for the case of constant accelerated plate. Sensitivity analysis is performed to show the effects of material parameters on the velocity profile and shear stress at the wall. The results confirmed the suitability of ADM in solving nonlinear equations.



Khan, I., Malik, M., Salahuddin, T., Khan, M., and Rehman, K. U. 2017. Homogenous–heterogeneous reactions in MHD flow of Powell–Eyring fluid over a stretching sheet with Newtonian heating. Neural Computing and Applications. 1-8.

Hayat, T., Iqbal, Z., Qasim, M., and Obaidat, S. 2012. Steady flow of an Eyring Powell fluid over a moving surface with convective boundary conditions. International Journal of Heat and Mass Transfer. 55(7), 1817-1822.

Fetecau, C., Zierep, J., Bohning, R., and Fetecau, C. 2010. On the energetic balance for the flow of an Oldroyd-B fluid due to a flat plate subject to a time-dependent shear stress. Computers & Mathematics with Applications. 60(1), 74-82.

Ishak, A., Nazar, R., and Pop, I. 2006. Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica. 41(5), 509-518.

Fetecau, C., Prasad, S. C., and Rajagopal, K. R. A 2007. note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid. Applied Mathematical Modelling. 31(4), 647-654.

Jamil, M., Rauf, A., Fetecau, C., and Khan, N. Helical flows of second grade fluid due to constantly accelerated shear stresses. Communications in Nonlinear Science and Numerical Simulation. 16(4), 1959-1969.

Adesanya, S. O., Falade, J. A., and Rach, R. 2015. Effect of couple stresses on hydromagnetic Eyring-Powell fluid flow through a porous channel. Theoretical and Applied Mechanics. 42(2), 135-150.

Siddiqui, A., Haroon, T., and Zeb, M. 2014. Analysis of Eyring-Powell fluid in helical screw rheometer. The Scientific World Journal. 382(2015), 355-358.

Zaman, H., Zaman, H., and Zaman, H. 2013. for the Eyring-Powell model with porous walls Unsteady incompressible Couette flow problem. American Journal of Computational Mathematics. 3(4), 313-325 .

Akbar, N. S., Ebaid, A., and Khan, Z. 2015. Numerical analysis of magnetic field effects on Eyring-Powell fluid flow towards a stretching sheet. Journal of Magnetism and Magnetic Materials. 382, 355-358.

Ellahi, R., Shivanian, E., Abbasbandy, S., and Hayat, T. 2016. Numerical study of magnetohydrodynamics generalized Couette flow of Eyring- Powell fluid with heat transfer and slip condition. International Journal of Numerical Methods for Heat & Fluid Flow. 26(5), 1433-1445.

Powell, R. E. and Eyring, H. 1944. Mechanism for relaxation theory of viscosity. Nature. 154(55), 427-428.

Sirohi, V., Timol, M., and Kalthia, N. 1987. Powell-Eyring model flow near an accelerated plate. Fluid Dynamics Research. 2(3), 193-204.

Khan, N. A., Aziz, S., and Khan, N. A. 2014. MHD flow of Powell–Eyring fluid over a rotating disk. Journal of the Taiwan Institute ofChemical Engineers. 45(6), 2859-2867.

Khan, M., Saleem, M., Fetecau, C., and Hayat, T. 2007. Transient oscillatory and constantly accelerated non-Newtonian flow in a porous medium. International Journal of Non-Linear Mechanics. 42(10), 1224-1239.

Khan, M., Ali, S. H., and Qi, H. 2009. Some accelerated flows for a generalized Oldroyd-B fluid. Nonlinear analysis. Real World Applications. 10(2), 980-991.

Khan, M., Ali, S. H., and Qi, H. 2009. On accelerated flows of a viscoelastic fluid with the fractional Burgers’ model. Nonlinear Analysis Real World Applications. 10(4), 2286-2296.

Aziz, Z. A., Salah, F., and Ching, D. L. C. 2011. On accelerated flow for MHD generalized burgers' fluid in a porous medium and rotating frame. IAENG International Journal of Applied Mathematics. 41(3), 199-205.

Khan, I., Ali, F., Mustapha, N., and Shafie, S. 2015. Closed-form solutions for accelerated MHD flow of a generalized Burgers’ fluid in a rotating frame and porous medium. Boundary Value Problems. 2015(8),


Jalil, M., Asghar, S., and Imran, S. 2013. Self similar solutions for the flow and heat transfer of Powell-Eyring fluid over a moving surface in a parallel free stream. International Journal of Heat and Mass Transfer. 65, 73-79.

Hansen, A. and Na, T. Y. 1986. Similarity solutions of laminar, incompressible boundary layer equations of non-Newtonian fluids. Journal of Basic Engineering. 90(1), 71-74.

Adomian, G. 1991. Solving frontier problems modelled by nonlinear partial differential equations. Computers & Mathematics with Applications. 22(8), 91-94.

Wazwaz, A.-M. 2010. Partial Differential Equations and Solitary Waves Theory. Springer Science & Business Media.

Gul, T., Ghani, F., Islam, S., Shah, R. A., Khan, I., Nasir, S., and Sharidan, S. 2016. Unsteady thin film flow of a fourth grade fluid over a vertical moving and oscillating belt. Propulsion and Power Research. 5(3), 223-235.