Show Summary Details
More options …

# International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

8 Issues per year

IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
Source Normalized Impact per Paper (SNIP) 2017: 0.636

Mathematical Citation Quotient (MCQ) 2017: 0.12

Online
ISSN
2191-0294
See all formats and pricing
More options …
Volume 19, Issue 3-4

# Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation

G.C. Layek
/ Bidyut Mandal
/ Krishnendu Bhattacharyya
• Corresponding author
• Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh 221005, India
• Email
• Other articles by this author:
/ Astick Banerjee
Published Online: 2018-05-19 | DOI: https://doi.org/10.1515/ijnsns-2017-0211

## Abstract

A symmetry analysis of steady two-dimensional boundary layer stagnation-point flow and heat transfer of viscous incompressible non-Newtonian power-law fluids over a nonlinearly shrinking/stretching sheet with thermal radiation effect is presented. Lie group of continuous symmetry transformations is employed to the boundary layer flow and heat transfer equations, that gives scaling laws and self-similar equations for a special type of shrinking/stretching velocity ($c{x}^{1/3}$) and free-stream straining velocity ($a{x}^{1/3}$) along the axial direction to the sheet. The self-similar equations are solved numerically using very efficient shooting method. For the above nonlinear velocities, the unique self-similar solution is obtained for straining velocity being always less than the shrinking/stretching velocity for Newtonian and non-Newtonian power-law fluids. The thickness of velocity boundary layer becomes thinner with power-law index for shrinking as well as stretching sheet cases. Also, the thermal boundary layer thickness decreases with increasing values the Prandtl number and the radiation parameter.

## References

• [1]

B.C. Sakiadis, Boundary layer behavior on continuous solid surfaces: I. Boundary layer equations for two-dimensional and axisymmetric flow, AIChE J. 7 (1961), 26–28.

• [2]

L.J. Crane, Flow past a stretching plate, Zamp. 21 (1970), 645–647.

• [3]

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

• [4]

C.D. Surma Devi, H.S. Takhar and G. Nath, Unsteady, three-dimensional, boundary-layer flow due to a stretching surface, Int. J. Heat Mass. Transfer. 29 (12) (1986), 1996–1999.

• [5]

K.R. Rajagopal, T.Y. Na and A.S. Gupta, Flow of viscoelastic fluid over a stretching sheet, Rheol Acta. 23 (1984), 213–215.

• [6]

W.C. Troy, E.A. Overman, H.G.B. Ermentrout and J.P. Keerner, Uniqueness of the flow of a second order fluid past a stretching sheet, Quart. Appl. Math. 44 (1987), 753–755.

• [7]

B.S. Dandapat and A.S. Gupta, Flow and heat transfer in a viscoelastic fluid over a stretching sheet, Int. J. Non-Linear Mech. 24 (3) (1989), 215–219.

• [8]

K.R. Rajagopal, T.Y. Na and A.S. Gupta, A non-similar boundary layer on a stretching sheet in a non-Newtonian fluid with uniform free stream, J. Math. Phys. Sci. 21 (1987), 189–200.Google Scholar

• [9]

R. Cortell, Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl. Math. Comput. 184 (2007), 864–873.

• [10]

H.I. Andersson and T.H. Toften, Numerical solution of a laminar boundary layer equations for power-law-fluid, J. non-Newtonian Fluid Mech. 32 (1989), 175–195.

• [11]

A.K. Sahu, M.N. Mathur, P. Chaturani and S.S. Bharatiya, Momentum and heat transfer from a continuous moving surface to a power law fluid, Acta Mech. 142 (2000), 119–131.

• [12]

L.C. Zhang and X.X. Zhang, Skin friction and heat transfer in a power law fluid in a laminar boundary layer along a moving surface, Int. J. Heat Mass. Transfer. 45 (2002), 2667–2672.

• [13]

J. Nagler, Generalized similarity transformation model for Power-law laminar boundary layer fluids with non-linear dynamic viscosity, WSEAS Trans. Fluid Mech. 9 (2014), 168–177.Google Scholar

• [14]

B.S. Reddy, N. Kishan and M.N. Rajasekhar, MHD boundary layer flow of a non-Newtonian power-law fluid on a moving at plate, Adv. Appl. Sci. Res. 3 (2012), 1472–1481.Google Scholar

• [15]

H.I. Andersson, K.H. Bech and B.S. Dandapat, Magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Int. J. Non-Linear Mech. 27 (6) (1992), 929–936.

• [16]

R. Cortell, A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Appl. Math. Comput. 168 (2005), 557–566.Google Scholar

• [17]

K.V. Prasad, S.R. Santhi and P.S. Datti, Non-Newtonian power-law fluid flow and heat transfer over a non-linearly stretching surface, Appl. Math. 3 (2012), 425–435.

• [18]

M. Miklavčič and C.Y. Wang, Viscous flow due a shrinking sheet, Q. Appl. Math. 64 (2006), 283–290.

• [19]

C.Y. Wang, Stagnation flow towards a shrinking sheet, Int. J. Nonlinear Mech. 43 (2008), 377–382.

• [20]

A. Ishak, Y.Y. Lok and I. Pop, Stagnation-point flow over a shrinking sheet in a micropolar fluid, Chem. Eng. Commun. 197 (2010), 1417–1427.

• [21]

K. Bhattacharyya and G.C. Layek, Effects of suction/blowing on steady boundary layer stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation, Int. J. Heat Mass. Transfer. 54 (2011), 302–307.

• [22]

K. Bhattacharyya, S. Mukhopadhyay and G.C. Layek, Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet, Int. J. Heat Mass. Transfer. 54 (2011), 308–313.

• [23]

Y.Y. Lok, A. Ishak and I. Pop, MHD stagnation-point flow towards a shrinking sheet, Int. J. Numer. Meth. Heat Fluid Flow. 21 (2011), 61–72.

• [24]

N.A. Yacob and A. Ishak, Flow and heat transfer of a power-law fluid over a permeable shrinking sheet, Sains Malaysiana. 43 (3) (2014), 491–496.Google Scholar

• [25]

T.R. Mahapatra, S.K. Nandy, K. Vajravelu and R.A. Van Gorder, Dual solutions for the magnetohydrodynamic stagnation-point flow of a power-law fluid over a shrinking sheet, ASME J. Appl. Mech. 79 (2012), 024503.

• [26]

N. Bachok and A. Ishak, Similarity solutions for the stagnation-point flow and heat transfer over a nonlinearly stretching/shrinking sheet, Sains Malaysiana. 40 (11) (2011), 1297–1300.Google Scholar

• [27]

G.C. Layek, An introduction to dynamical system and chaos, India: Springer, 2015.Google Scholar

• [28]

B.J. Cantwell, Introduction to symmetry analysis, Cambridge, New York: Cambridge University Press, 2002.Google Scholar

• [29]

G.W. Bluman and S. Kumei, Symmetries and differential equations, Springer, New York, 1989.Google Scholar

• [30]

M. Oberlack, A unified approach for symmetries in plane parallel turbulent shear flows, J. Fluid Mech. 427 (2001), 299–328.

• [31]

Z.-S. She, X. Chen and F. Hussain, Lie-group derivation of a multi-layer mixing length formula for turbulent channel and pipe flows, arXiv, 1112.6312v3 [physics.flu-dyn].Google Scholar

• [32]

Z.-S. She, X. Chen and F. Hussain, Quantifying wall turbulence via a symmetry approach: A Lie group theory, J. Fluid Mech. 827 (2017), 322–356.

• [33]

X. Chen and F. Hussain, Similarity transformation for equilibrium boundary layers, including effects of blowing and suction, Phys. Rev. Fluids. 2 (2017), art. id 034605.

• [34]

M. Jalil and S. Asghar, Flow and heat transfer of Powell-Eyring fluid over a stretching surface: A Lie group analysis, J. Fluids Eng. 135 (2013), art. id 121201.

• [35]

H.S. Hassan, S.A. Mahrous, A. Sharara and A. Hassan, A study for MHD boundary layer flow of variable viscosity over a heated stretching sheet via Lie-group method, Appl. Math. Inf. Sci. 9 (2015), 1327–1338.Google Scholar

• [36]

M.Q. Brewster, Thermal radiative transfer properties, Chichester: John Wiley and Sons, 1972.Google Scholar

• [37]

K. Bhattacharyya and G.C. Layek, Magnetohydrodynamic boundary layer flow of nanofluid over an exponentially stretching permeable sheet, Phys. Res. Int. 2014 (2014), art id 592536.Google Scholar

Accepted: 2018-01-20

Published Online: 2018-05-19

Published in Print: 2018-06-26

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 3-4, Pages 415–426, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339,

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.