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A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid. (English) Zbl 1287.76047
Summary: The velocity field and the adequate tangential stress that is induced by the flow due to a constantly accelerating plate in an Oldroyd-B fluid, are determined by means of Fourier sine transforms. The solutions corresponding to a Maxwell, Second grade and Navier-Stokes fluid appear as limiting cases of the solutions obtained here. However, in marked contrast to the solution for a Navier-Stokes fluid, in the case of an Oldroyd-B fluid oscillations are set up which decay exponentially with time.

MSC:
76A10 Viscoelastic fluids
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[1] Maxwell, J.C., On the dynamical theory of gases, Philos. trans. R. soc. London A, 157, 26-78, (1866)
[2] Rajagopal, K.R.; Srinivasa, A.R., A thermodynamical frame-work for rate type fluid models, J. non-Newtonian fluid mech., 88, 207-227, (2000) · Zbl 0960.76005
[3] Oldroyd, J.G., On the formulation of rheological equations of state, Proc. R. soc. London ser. A, 200, 523-541, (1950) · Zbl 1157.76305
[4] Frohlick, H.; Sack, R., Theory of rheological properties of dispersions, Proc. R. soc. London ser. A, 185, 415-430, (1946)
[5] Burgers, J.M., First report on viscosity and plasticity, (1935), Royal Netherlands Academy of Sciences Amsterdam, (Chapter 1) · JFM 61.1514.03
[6] Böhme, G., Strömungsmechanik nicht-newtonscher fluide, (2000), B.G. Teubner Stuttgart, Leipzig, Wiesbaden · Zbl 0465.76002
[7] Fetecau, C.; Fetecau, C., Flow induced by a constantly accelerating plate in a Maxwell fluid, Bull. acad. stiinte repub. mold. mat., 2, 45, 55-61, (2004) · Zbl 1187.76614
[8] Fetecau, C.; Zierep, J., On a class of exact solutions of the equations of motion of a second grade fluid, Acta mech., 150, 135-138, (2001) · Zbl 0992.76006
[9] Waters, N.D.; King, M.J., Unsteady flows of an elastico-viscous liquid in a straight pipe of circular cross-section, J. phys. D: appl. phys., 4, 204-211, (1971)
[10] Akyildiz, F.T.; Jones, R.S., The generation of steady flow in a rectangular duct, Rheolog. acta, 32, 499-504, (1993)
[11] Rahaman, K.D.; Ramkissoon, H., Unsteady axial viscoelastic pipe flows, J. non-Newtonian fluid mech., 57, 27-38, (1995)
[12] Wood, W.P., Transient viscoelastic helical flows in pipes of circular and annular cross-section, J. non-Newtonian fluid mech., 100, 115-126, (2001) · Zbl 1014.76004
[13] Bandelli, R.; Rajagopal, K.R.; Galdi, G.P., On some unsteady motions of fluids of second grade, Arch. mech., 47, 4, 661-676, (1995) · Zbl 0835.76002
[14] R. Bandelli, Unsteady flows of Non-Newtonian fluids, Ph.D thesis, University of Pittsburgh, Pittsburgh, 1995. · Zbl 0837.76004
[15] Rajagopal, K.R., Mechanics of non-Newtonian fluids, (), 129-162 · Zbl 0818.76003
[16] Bandelli, R.; Rajagopal, K.R., Start-up flows of second grade fluids in domains with one finite dimension, Int. J. non-linear mech., 30, 817-839, (1995) · Zbl 0866.76004
[17] Erdogan, M.E., On unsteady motions of a second-order fluid over a plane wall, Int. J. non-linear mech., 38, 1045-1051, (2003) · Zbl 1348.76061
[18] Sneddon, I.N., Fourier transforms, (1951), McGraw-Hill Book Company, Inc. New York, Toronto, London · Zbl 0099.28401
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