# Stagnation point flow of a MHD Powell-Eyring fluid over a nonlinearly stretching sheet in the presence of heat source/sink

### Abstract

This study investigates the stagnation point flow of a MHD Powell-Eyring fluid over a nonlinearly stretching sheet in the presence of heat source/sink. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. The transformed nonlinear boundary layer equations are then solved numerically using Keller Box method. The effects of various physical parameters on the dimensionless velocity and temperature profiles are depicted graphically. Present results are compared with previously published work and the results are found to be in very good agreement. Numerical results for local skin-friction and local Nusselt number are tabulated for different physical parameters.

### Downloads

### References

Harris J (1977) Rheology and non-Newtonian flow, Longman.

Bird RB, Curtiss CF, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids. Wiley.

K. R. Rajagopal, “A note on unsteady unidirectional lows of a non-Newtonian fluid,” International Journal of Non-Linear Mechanics,vol.17,no.5-6,pp.369–373,1982.

K.R.Rajagopal and R.K.Bhatnagar,“Exact solutions for some simple flows of an Oldroyd-B fluid,” Acta Mechanica, vol. 113, no. 1–4, pp. 233–239, 1995.

K. R. Rajagopal, “On the creeping flow of the second-order fluid,” Journal of Non-Newtonian Fluid Mechanics,vol.15,no. 2, pp. 239–246, 1984.

T. Hayat, S. Asghar, and A. M. Siddiqui, “Periodic unsteady flows of a non-Newtonian fluid,” Acta Mechanica,vol.131,no.3-4, pp. 169–175, 1998.

T. Hayat, S. Asghar, and A. M. Siddiqui, “Some unsteady unidirectional flows of a non-Newtonian fluid,” International Journal of Engineering Science,vol.38,no.3,pp.337–346,2000.

R. E. Powell and H. Eyring, “Mechanism for Relaxation Theory of Viscosity,” Nature 154, 427–428 (1944)

M. Patel and M. G. Timol, “Numerical Treatment of Powell–Eyring Fluid Flow Using Method of Asymptotic Boundary Conditions,” Appl. Numer. Math. 59, 2584–2592 (2009).

T. Hayat, Z. Iqbal, M. Qasim, and S. Obaidat, “Steady Flow of an Eyring–Powell Fluid over a Moving Surface with Convective Boundary Conditions,” Int. J. Heat Mass Transfer. 55, 1817–1822 (2012).

T. Javed, N. Ali, Z. Abbas, M. Sajid, Flow of an Eyring-Powell Non-Newtonian Fluid over a Stretching Sheet Chemical Engineering Communications 200 (2013) 327-336.

M. Jalil, S. Asghar, S. M. Imran, 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 (2013) 73-79.

Mushtaq A, Mustafa M, Hayat T, Rahi M, Alsaedi A (2013) Exponentially stretching sheet in a Powell-Eyring fluid: Numerical and series solutions. Z.Naturforsch. 68a: 791–798.

Khader MM, Megahed AM (2013) Numerical studies for flow and heat transfer of the Powell-Eyring fluid thin film over an unsteady stretching sheet with internal heat generation using the chebyshev finite difference method. J. Applied Mechanics Technical Phys, 54: 440–450.

V. Sirohi, M. G. Timol, and N. L. Kalathia, “Numerical Treatment of Powell–Eyring Fluid Flow Past a 90 degree Wedge,” Reg. J. Energy Heat Mass Transfer 6 (3), 219–228 (1984).

Zaman H (2013) Unsteady Incompressible Couette Flow Problem for the Eyring-Powell Model with Porous Walls. American J. Computational Math, 3:313–325.

Crane L J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik, 1970, 21(4): 645–647

Wang C Y. The three dimensional flow due to a stretching flat surface. Physics of Fluids, 1984, 27(8): 1915–1917

McLeod J B, Rajagopal K R. On the uniqueness of flow of a Navier–Stokes fluid due to a stretching boundary. Archive for Rational Mechanics and Analysis, 1987, 98(4): 385–393

Chiam TC. Stagnation-point ﬂow towards a stretching plate. J Phys Soc Jpn 1994;63:2443–4.

Mahapatra TR, Gupta AS. Magnetohydrodynamic stagnation-point flow towards a stretching sheet. Acta Mech 2001;152:191–6.

A. Ishak, K. Jafar, R. Nazar, I. Pop, MHD stagnation point flow towards a stretching sheet, Physics A 388 (2009) 3377–3383.

S.R. Pop, T. Grosan, I. Pop, Radiation effects on the flow near the stagnation point of a stretching sheet, Tech. Mech. 29 (2004) 100–106.

K. Vajravelu, Viscous flow over a nonlinearly stretching sheet, Appl. Math. Comput. 124 (2001) 281–288.

K.V. Prasad, K. Vajravelu, P.S. Dattri, Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties, Int. J. Non-linear Mech. 45 (2010) 320–330.

M.S. Abel, K.A. Kumar, R. Ravikumara, MHD flow and heat transfer with effects of buoyancy, viscous and joule dissipation over a nonlinear vertical stretching porous sheet with partial slip, Engineering 3 (2011) 285–291.

T. Hayat, T. Javed, and Z. Abbas, “MHD low of a micropolar fluid near a stagnation-point towards a non-linear stretching surface,” Nonlinear Analysis: Real World Applications, vol.10, no.3, pp. 1514–1526, 2009.

P. Rana, R. Bhargava, Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study, Commun.Nonlinear Sci. Numer. Simul. 17 (2012) 212–226.

Z. Abbas,T. Hayat, Stagnation Slip Flow and Heat Transfer over a Nonlinear Stretching Sheet.

T. Hayat,T. Javed, Z. Abbas MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface Volume 10, Issue 3, June 2009, Pages 1514–1526

Mabood, F., Khan, W.A. and Ismail, A.I.M. (2015) MHD Boundary Layer Flow and Heat Transfer of Nanofluids over a Nonlinear Stretching Sheet: A Numerical Study. Journal of Magnetism and Magnetic Materials, 374, 569-576.

W Ibrahim and B. Shanker Int. J. Appl. Math. Mech. 8 18 (2012)

Khan, S.K.: Heat transfer in a viscoelastic fluid flow over a stretching surface with heat source/sink, suction/blowing and radiation. Int. J. Heat Mass Tran. 49, 628–639 (2006).

Vajravelu, K. and Hadjinicolaou, A. Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation. International Communications in Heat and Mass Transfer, 20(3), 417–430 (1993)

Veena, P. H., Subhas-Abel, M., Rajagopal, K., and Pravin, V. K. Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation. Zeitschrift f ur Angewandte Mathematik und Physik (ZAMP), 57(3), 447–463 (2006)

Abo-Eldahab Emad, M., El Aziz Mohamed, A., 2004. Blowing suction effect on hydro magnetic heat transfer by mixed convection from an inclined continuously stretching surface with internal heat generation/absorption. Int. J. Therm. Sci. 43, 709–719.

Sharma, P. R. and Singh, G. 2008. Effect of variable thermal conductivity and heat source/sink on Magnetohydrodynamic flow near a stagnation point on a linearly stretching sheet. Journal of Applied Fluid Mechanics, 1: 13-21.

Mohamed RA, Abo-Dahab SM. Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation. Int J Thermal Science 2009;48:1800–13.

Grubka LG, and Bobba KM (1985). Heat transfer characteristics of a continuous stretching surface with variable temperature. ASME J. Heat Transfer. 107, pp. 248–250.

Chen CK, and Char MI (1988). Heat transfer of a continuous stretching surface with suction or blowing. J. Math. Anal. Appl.135, pp. 568–580.

K. V. Prasad , P. S. Datti and B. T. Raju, "Momentum and Heat transfer of a Non-Newtonian Eyring-Powell fluid over a non-isothermal stretching sheet ". International Journal of Mathematical Archive- 4(1), 2013, 230-241.

*Journal of Progressive Research in Mathematics*,

*8*(2), 1290-1300. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/843

Copyright (c) 2016 Journal of Progressive Research in Mathematics

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.