Symmetries of boundary layer equations of power-law fluids of second grade

Acta Mechanica Sinica/Lixue Xuebao

Volumn 24, Issue 6, 2008, Pages 661-670

  Pakdemirli, Mehmet ^a   Aksoy, Yiǧit ^a   Yürüsoy, Muhammet ^b   Khalique, Chaudry Masood ^c  

^a CELAL BAYAR UNIVERSITY   (Turkey)

^b AFYON KOCATEPE UNIVERSITY   (Turkey)

^c NORTH WEST UNIVERSITY   (South Africa)

Author keywords

Boundary layers; Liegroup theory; Power law fluid of second grade

Indexed keywords

AERODYNAMICS; ALGEBRA; BOUNDARY LAYERS; DRAG REDUCTION; EQUATIONS OF MOTION; FLUIDS; INCOMPRESSIBLE FLOW; METEOROLOGY; THEOREM PROVING; WALL FLOW;

FLUID SOLUTIONS; GROUP CLASSIFICATIONS; LIE GROUPS; LIEGROUP THEORY; NORMAL STRESSES; ORDINARY DIFFERENTIAL SYSTEMS; PARTIAL DIFFERENTIALS; POWER-LAW FLUID OF SECOND GRADE; SCALING SYMMETRIES; SHEAR THICKENINGS;

HYDRODYNAMICS;

EID: 56749169218     PISSN: 05677718     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10409-008-0172-z     Document Type: Article

References (30)

1. C.S. Man Q.X. Sun 1987 On the significance of normal stress effects in the flow of glaciers J. Glaciology 33 268 273
2. C.S. Man 1992 Nonsteady channel flow of ice as a modified second-order fluid with power-law viscosity Arch. Rational Mech. Anal. 119 35 57
3. T. Hayat S. Asghar C.M. Khalique R. Ellahi 2007 Influence of partial slip on flows of second grade fluid in a porous medium J. Porous Media 10 797 805
4. T. Hayat Z. Abbas M. Sajid 2007 On the analytical solution of Magnetohydrodynamic flow of a second grade fluid over a shrinking sheet J. Appl. Mech. 74 1165 1171
5. T. Hayat R. Ellahi S. Asghar 2007 Unsteady magnetohydrodynamic non-Newtonian flow due to non-coaxial rotations of disk and a fluid at infinity Chem. Eng. Commun. 194 37 49
6. S. Asghar K. Hanif T. Hayat C.M. Khalique 2007 MHD non-Newtonian flow due to non-coaxial rotations of an accelerated disk and a fluid at infinity Comm. Nonlinear Sci. Num. Simul. 12 465 485
7. T. Hayat M. Sajid 2007 Analytical solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet Int. J. Heat Mass Transfer 50 75 84
8. T. Hayat Z. Abbas M. Sajid S. Asghar 2007 The influence of thermal radiation on MHD flow of a second grade fluid Int. J. Heat Mass Transfer 50 931 941
9. T. Hayat M. Khan M. Ayub 2007 Some analytical solutions for second grade fluid flows for cylindrical geometries Math. Comput. Model. 43 16 29
10. H. Franchi B. Straughan 1993 Stability and nonexistence results in the generalized theory of a fluid of second grade J. Math. Anal. Appl. 180 122 137
11. G. Gupta M. Massoudi 1993 Flow of a generalized second grade fluid between heated plates Acta Mech. 99 21 33
12. M. Massoudi T.X. Phuoc 2001 Fully developed flow of a modified second grade fluid with temperature dependent viscosity Acta Mech. 150 23 37
13. M. Massoudi T.X. Phuoc 2004 Flow of a generalized second grade non-Newtonian fluid with variable viscosity Continuum Mech. Thermodyn. 16 529 538
14. T. Hayat M. Khan 2005 Homotopy solutions for a generalized second-grade fluid past a porous plate Nonlinear Dyn. 42 395 405
15. J.E. Dunn R.L. Fosdick 1974 Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade Arch. Rational Mech. Anal. 56 191 252
16. K.R. Rajagopal R.L. Fosdick 1980 Thermodynamics and stability of fluids of third grade Proc. R. Soc. Lond. A. 369 351 377
17. J.E. Dunn K.R. Rajagopal 1995 Fluids of differential type: critical review and thermodynamic analysis Int. J. Eng. Sci. 33 689 729
18. Bluman G.W., Kumei S.: Symmetries and differential equations. Springer, New York (1989)
19. Stephani H.: Differential equations: their solution using symmetries. Cambridge University Press, New York (1989)
20. T. Hayat A.H. Kara E. Momoniat 2003 Exact flow of a third grade fluid on a porous wall Int. J. Non-Linear Mech. 38 1533 1537
21. M.R. Mohyuddin T. Hayat F.M. Mahomed S. Asghar 2004 On solutions of some non-linear differential equations arising in Newtonian and non-Newtonian fluids Nonlinear Dyn. 35 229 248
22. T. Hayat A.H. Kara E. Momoniat 2005 The unsteady flow of a fourth grade fluid past a porous plate Math. Comput. Model. 41 1347 1353
23. T. Hayat A.H. Kara 2006 A variational analysis of a non-Newtonian flow in a rotating system Int. J. Comput. Fluid Dyn. 20 157 162
24. T. Hayat A.H. Kara 2006 Couette flow of a third grade fluid with variable magnetic field Math. Comput. Model. 43 132 137
25. Y. Aksoy M. Pakdemirli C.M. Khalique 2007 Boundary layer equations and stretching sheet solutions for the modified second grade fluid Int. J. Eng. Sci. 45 829 841
26. M. Pakdemirli E.S. Şhubi 1992 Boundary layer theory for second order fluids Int. J. Eng. Sci. 30 523 532
27. M. Pakdemirli 1992 The boundary layer equations of third grade fluids Int. J. Non-Linear Mech. 27 785 793
28. M. Pakdemirli 1994 Conventional and multiple deck boundary layer approach to second and third grade fluids Int. J. Eng. Sci. 32 1 141 154
29. A.K. Head 1993 LIE a PC program for Lie analysis of differential equations Comput. Phys. Commun. 71 241 248
30. K.R. Rajagopal A.Z. Szeri W. Troy 1986 An existence theorem for the flow of a non-Newtonian fluid past an infinite porous plate Int. J. Non-Linear Mech. 21 279 289