Erratum to: Unsteady flow of an Oldroyd-B fluid induced by the impulsive motion of a plate between two side walls perpendicular to the plate

Exact solutions for the unsteady flow of an Oldroyd-B fluid produced by a suddenly moved plane wall between two side walls perpendicular to the plane are established by means of the Fourier sine transforms. The similar solutions for Maxwell, Newtonian and second grade fluids, performing the same motion, appear as limiting cases of the solutions obtained here. In the absence of the side walls, the solutions corresponding to the motion over an infinite suddenly moved plate are also obtained as the limiting cases. Finally, for comparison, the velocity field in the middle of the channel and the shear stress at the bottom wall are plotted for different values of the material constants.

[1]  C. Christov,et al.  Comment on “Stokes’ first problem for an Oldroyd-B fluid in a porous half space” [Phys. Fluids 17, 023101 (2005)] , 2009 .

[2]  The Rayleigh–Stokes problem for an edge in an Oldroyd-B fluid☆ , 2002 .

[3]  K. Rajagopal,et al.  A thermodynamic frame work for rate type fluid models , 2000 .

[4]  Constantin Fetecau Analytical solutions for non-Newtonian fluid flows in pipe-like domains , 2004 .

[5]  Kumbakonam R. Rajagopal,et al.  Exact solutions for some simple flows of an Oldroyd-B fluid , 1995 .

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

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

[8]  Tasawar Hayat,et al.  Unsteady flow of a second grade fluid between two side walls perpendicular to a plate , 2008 .

[9]  Constantin Fetecau,et al.  UNSTEADY FLOWS OF OLDROYD-B FLUIDS IN A CHANNEL OF RECTANGULAR CROSS SECTION , 2005 .

[10]  Cha'o-Kuang Chen,et al.  Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions , 2004 .

[11]  J. Oldroyd On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  James Clerk Maxwell,et al.  IV. On the dynamical theory of gases , 1868, Philosophical Transactions of the Royal Society of London.

[13]  Tasawar Hayat,et al.  Exact solutions of flow problems of an Oldroyd-B fluid , 2004, Appl. Math. Comput..

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

[15]  Wenchang Tan,et al.  STOKES FIRST PROBLEM FOR AN OLDROYD-B FLUID IN A POROUS HALF SPACE , 2005 .

[16]  Tasawar Hayat,et al.  Some simple flows of an Oldroyd-B fluid , 2001 .

[17]  Markus Scholle,et al.  Starting solutions for some unsteady unidirectional flows of Oldroyd-B fluids , 2006 .

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

[19]  Tasawar Hayat,et al.  Influence of Hall current on the flows of a generalized Oldroyd-B fluid in a porous space , 2006 .

[20]  Tasawar Hayat,et al.  Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law , 2006 .

[21]  W. P. Wood Transient viscoelastic helical flows in pipes of circular and annular cross-section , 2001 .

[22]  Tasawar Hayat,et al.  Hall effect on flows of an Oldroyd-B fluid through porous medium for cylindrical geometries , 2006, Comput. Math. Appl..

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