This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular cases, all the solutions of Moro et al. [1990, “Steady Flows of a Third Grade Fluid by Transformation Methods,” ZAMM, 70(3), pp. 189–198]
Issue Section:
Techniques and Procedures
1.
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, K. R.
, 1984, “On the Creeping Flow of the Second-Order Fluid
,” J. Non-Newtonian Fluid Mech.
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, pp. 239
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.2.
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, 1995, “Plane Surface Suddenly Set in Motion in a Non-Newtonian Fluid
,” Acta Mech.
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.3.
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, K. R.
, and Gupta
, A. S.
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, R.
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, and Kaloni
, P. N.
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0020-7462, 21
, pp. 459
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.6.
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, A. M.
, and Siddiqui
, A. M.
, 1992, “Certain Solutions of the Equations of the Planar Motion of a Second Grade Fluid for Steady and Unsteady Cases
,” Acta Mech.
0001-5970, 94
, pp. 85
–96
.7.
Ariel
, P. D.
, 1994, “The Flow of a Viscoelastic Fluid Past a Porous Plate
,” Acta Mech.
0001-5970, 107
, pp. 199
–204
.8.
Ariel
, P. D.
, 2003, “Flow of a Third Grade Fluid Through a Porous Flat Channel
,” Int. J. Eng. Sci.
0020-7225, 41
, pp. 1267
–1285
.9.
Fetecau
, C.
, 1977, “Cone and Plate Flow of a Second Grade
,” Acta Mech.
0001-5970, 122
, pp. 225
–230
.10.
Hayat
, T.
, Kara
, A. H.
, and Momoniat
, E.
, 2003, “Exact Flow of a Third Grade Fluid on a Porous Wall
,” Int. J. Non-Linear Mech.
0020-7462, 38
, pp. 1533
–1537
.11.
Hayat
, T.
, Wang
, Y.
, and Hutter
, K.
, 2004, “Hall Effects on the Unsteady Hydromagnetic Oscillatory Flow of a Second Grade Fluid
,” Int. J. Non-Linear Mech.
0020-7462, 39
, pp. 1027
–1037
.12.
Hayat
, T.
, Khan
, M.
, Siddiqui
, A. M.
, and Asghar
, S.
, 2004, “Transient Flows of a Second Grade Fluid
,” Int. J. Non-Linear Mech.
0020-7462, 39
, pp. 1621
–1633
.13.
Moro
, L.
, Siddiqui
, A. M.
and Kaloni
, P. N.
, 1990, “Steady Flows of a Third Grade Fluid by Transformation Methods
,” ZAMM
0044-2267, 70
(3
), pp. 189
–198
.14.
Rivlin
, R. S.
, and Ericksen
, J. L.
, 1955, “Stress-Deformation Relations for Isotropic Materials
,” J. Rational Mech. Anal.
, 4
, pp. 323
–425
.15.
Fosdic
, R. L.
, and Rajagopal
, K. R.
, 1980, “Thermodynamics and Stability of Fluids of Third Grade
,” Proc. R. Soc. London, Ser. A
1364-5021, 339
, pp. 351
–377
.16.
Truessdell
, C.
, and Noll
, W.
, 1965, “The Non-Linear Field Theories of Mechanics
,” in Handbuch der physik III, No. 3
, Springer
, Berlin
, pp. 494
–513
.17.
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, M. P.
, 1983, “A Class of Exact Solution of the Navier-Stokes Equations. Plane Unsteady Flow
,” Lett. Appl. Eng. Sci.
0090-6913, 21
(2
), pp. 179
–186
.Copyright © 2008
by American Society of Mechanical Engineers
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