The Approximate Analytical Solution of the MHD Flow of a Power-Law Fluid

Abstract:

This paper presents a theoretical analysis for the incompressible MHD stagnation-point flows of a Non-Newtonian Fluid over stretching sheets.The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. By using the homotopy analysis method, a convergent series solution is obtained. The reliability and efficiency of series solutions are illustrated by good agreement with numerical results in the literature.Besides, the effects of the power-law indexthe magnetic field parameter and velocity ratio parameter on the flow are investigated.

• Periodical: Applied Mechanics and Materials (Volume 431)
• Pages: 198-201
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.431.198
• Online since: October 2013
• Authors: Jing Zhu*, Lian Cun Zheng
• Keywords: Approximate Solution, Homotopy Analysis Method, Non-Newtonian Fluid

References

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

DOI: 10.1002/aic.690070108

[2] L.J. Crane. Flow past a stretching sheet. Z. Angew. Math. Phys, 21 (1970): 645-647.

[3] T.C. Chiam. Stagnation-point flow towards a stretching plate. J. Phys. Soc. Jpn, 63 (1994): 2443-2444.

DOI: 10.1143/jpsj.63.2443

[4] W.R. Schowalter. The application of boundary-layer theory to power-law pseudoplastic fluids: Similar solution. AIChE J. 6(1960): 24-28.

DOI: 10.1002/aic.690060105

[5] H.I. Andersson, K.H. Bech, B.S. Dandapat. Flow of a power-law fluid film on an unsteady stretching surface. J. Non-Newtonian Fluid Mech, 62(1996): 1-8.

DOI: 10.1016/0377-0257(95)01392-x

[6] L. Zheng, L. Ma, J. He. Bifurcation solution to a boundary layer problems arising in theory of power law fluids. Acta Math. Sci, 20(2000): 19-26.

DOI: 10.1016/s0252-9602(17)30727-0

[7] D.S. Djukic. On the use of Crocco's equation for the flow of power-law fluids in transverse magnetic fields. AIChE J. 19 (1973): 1159-1163.

DOI: 10.1002/aic.690190612

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

DOI: 10.1016/0020-7462(92)90045-9

[9] S.J. Liao: The Proposed Homopoty Analysis Technique for the Solution of Nonlinear Problems. Ph.D., Shanghai Jiao Tong University, (1992).

[10] K. Yabushita, M. Yamashita, K. Tsubo: An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method. J. Phys. A: Mathematical and Theoretical, 40(2007)8403-8416.

DOI: 10.1088/1751-8113/40/29/015

[11] V. Marinca, N. Herisanu: Application of optional homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate. Applied Mathematics Letters, 22(2009)245-251.

DOI: 10.1016/j.aml.2008.03.019

[12] M.M. Zhao, Y.B. Zhou: The Further Discussion for Homotopy Analysis Method and Their Modification. Lan Zhou University, (2009).

[13] J Zhu, L C Zheng, Z G Zhang. Effect of slip condition on MHD stagnation-point flow over a power-law stretching sheet, Applied Mathematics and Mechanics. 2010, 31(4), 439-448.

DOI: 10.1007/s10483-010-0404-z