Unsteady flow of a second grade fluid between two side walls perpendicular to a plate

Abstract Exact solutions for the unsteady flow of a second grade fluid induced by the time-dependent motion of a plane wall between two side walls perpendicular to the plane are established by means of the Fourier sine transforms. The similar solutions for Newtonian fluids, performing the same motions, are obtained as limiting cases for α 1 → 0 . The steady solutions, the same for Newtonian and non-Newtonian fluids, are also obtained as limiting cases for t → ∞ . In the absence of the side walls, all solutions that have been obtained reduce to those corresponding to the motion over an infinite plate. Graphical illustrations show that the diagrams corresponding to the velocity field in the middle of channel and the shear stress at the bottom wall for a second grade fluid are going to be those for a Newtonian fluid if the normal stress module α 1 → 0 .

[1]  C. Fetecau,et al.  Starting solutions for some unsteady unidirectional flows of a second grade fluid , 2005 .

[2]  C. Fetecau,et al.  On a class of exact solutions of the equations of motion of a second grade fluid , 2001 .

[3]  J. E. Dunn,et al.  Fluids of differential type: Critical review and thermodynamic analysis , 1995 .

[4]  K. Rajagopal.  On Boundary Conditions for Fluids of the Differential Type , 1995 .

[5]  Chun-I Chen,et al.  Unsteady unidirectional flow of second grade fluid between the parallel plates with different given volume flow rate conditions , 2003, Appl. Math. Comput..

[6]  K. Rajagopal,et al.  On a class of exact solutions to the equations of motion of a second grade fluid , 1981 .

[7]  K. Rajagopal,et al.  An existence theorem for the flow of a non-newtonian fluid past an infinite porous plate , 1986 .

[8]  Kumbakonam R. Rajagopal,et al.  Flow of viscoelastic fluids between rotating disks , 1992 .

[9]  Tasawar Hayat,et al.  Flow induced by non-coaxial rotation of a porous disk executing non-torsional oscillations and a second grade fluid rotating at infinity , 2004 .

[10]  Tasawar Hayat,et al.  Some analytical solutions for second grade fluid flows for cylindrical geometries , 2006, Math. Comput. Model..

[11]  Constantin Fetecau,et al.  The first problem of Stokes for an Oldroyd-B fluid , 2003 .

[12]  Kumbakonam R. Rajagopal,et al.  A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid , 2007 .

[13]  Giovanni P. Galdi,et al.  ON SOME UNSTEADY MOTIONS OF FLUIDS OF SECOND GRADE , 1995 .

[14]  Kumbakonam R. Rajagopal,et al.  On the creeping flow of the second-order fluid , 1984 .

[15]  C. Fetecau,et al.  Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder , 2006 .

[16]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[17]  C. Fetecau,et al.  On some axial Couette flows of non-Newtonian fluids , 2005 .

[18]  Tasawar Hayat,et al.  Transient flows of a second grade fluid , 2004 .

[19]  K. Rajagopal,et al.  An exact solution for the flow of a non-newtonian fluid past an infinite porous plate , 1984 .

[20]  T. Hayat,et al.  The unsteady Couette flow of a second grade fluid in a layer of porous medium , 2005 .

[21]  Wenchang Tan,et al.  Stokes’ first problem for a second grade fluid in a porous half-space with heated boundary , 2005 .

[22]  Tasawar Hayat,et al.  Hall effects on the unsteady hydromagnetic oscillatory flow of a second-grade fluid. , 2004 .

[23]  Kumbakonam R. Rajagopal,et al.  Start-up flows of second grade fluids in domains with one finite dimension , 1995 .

[24]  C. Fetecau,et al.  Decay of a potential vortex and propagation of a heat wave in a second grade fluid , 2002 .

[25]  Tasawar Hayat,et al.  Some unsteady unidirectional flows of a non-Newtonian fluid , 2000 .

[26]  Tasawar Hayat,et al.  Unsteady hydromagnetic rotating flow of a conducting second grade fluid , 2004 .

[27]  J. E. Dunn,et al.  Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade , 1974 .