Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

• Autorzy: Constantin Fetecau , Dumitru Vieru , Corina Fetecau
• Języki publikacji: EN

Abstrakty

EN

The velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.

Słowa kluczowe

EN

unsteady motion; side walls; oscillating shear stress; exact solutions

• Czasopismo: Open Physics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 816-824

Daty

wydano

2011-06-01

online

2011-02-26

Twórcy

autor

Constantin Fetecau

• Department of Theoretical Mechanics, Technical University of Iasi, 700050, Iasi, Romania

autor

Dumitru Vieru

• Department of Theoretical Mechanics, Technical University of Iasi, 700050, Iasi, Romania,

autor

Corina Fetecau

• Department of Theoretical Mechanics, Technical University of Iasi, 700050, Iasi, Romania

Bibliografia

• [1] H. Schlichting, Boundary Layer Theory, Sixth ed. (McGraw Hill, New York, 1968)
• [2] Y. Zeng, S. Weinbaum, J. Fluid Mech. 287, 59 (1995) http://dx.doi.org/10.1017/S0022112095000851[Crossref]
• [3] R. Penton, J. Fluid Mech. 31, 819 (1968) http://dx.doi.org/10.1017/S0022112068000509[Crossref]
• [4] M.E. Erdogan, Int. J. Nonlin. Mech. 35, 1 (2000) http://dx.doi.org/10.1016/S0020-7462(99)00019-0[Crossref]
• [5] C. Fetecau, D. Vieru, C. Fetecau, Int. J. Nonlin. Mech. 43, 451 (2008) http://dx.doi.org/10.1016/j.ijnonlinmec.2007.12.022[Crossref]
• [6] M.E. Erdogan, C.E. Imrak, Math. Probl. Eng. Volume 2009, 725196 (2009)
• [7] K.R. Rajagopal, In: A. Sequira (Ed.), Navier-Stokes Equations and Related Non-Linear Problems (Plenum Press, New York, 1995)
• [8] I.N. Sneddon, Fourier transforms (McGraw Hill Book Company, Inc., New York, Toronto, London, 1951)
• [9] I.N. Sneddon, Functional Analysis, Encyclopedia of Physics, vol. II (Springer, Berlin, Göttingen, Heidelberg, 1955)
• [10] C. Fetecau, C. Fetecau, Int. J. Eng. Sci. 43, 781 (2005) http://dx.doi.org/10.1016/j.ijengsci.2004.12.009[Crossref]
• [11] H.G. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Clarendon Press, Oxford, 1995)
• [12] D. Vieru, C. Fetecau, A. Sohail, Z. Angew. Math. Phys., DOI:10.1007/s00033-010-0073-4 [Crossref]
• [13] M. Abramovitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965)
• [14] R. BandellI, K.R. Rajagopal, G.P. Galdi, Arch. Mech. 47, 661 (1995)

Identyfikatory

DOI

10.2478/s11534-010-0073-1