Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate

The velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate have been established using Fourier sine and Laplace transforms. In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method has been used. The solutions that have been obtained, presented under integral and series forms in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. The similar solutions for generalized Maxwell fluids as well as those for Oldroyd-B, Maxwell and Newtonian fluids are obtained as limiting cases of our general solutions.

[1]  Haitao Qi,et al.  Unsteady flow of viscoelastic fluid with fractional Maxwell model in a channel , 2007 .

[2]  M. Erdoğan,et al.  On unsteady motions of a second-order fluid over a plane wall , 2003 .

[3]  Haitao Qi,et al.  Unsteady Rotating Flows of a Viscoelastic Fluid with the Fractional Maxwell Model Between Coaxial Cylinders , 2006 .

[4]  Haitao Qi,et al.  Some accelerated flows for a generalized Oldroyd-B fluid , 2009 .

[5]  T. Hayat,et al.  On the MHD flow of fractional generalized Burgers’ fluid with modified Darcy’s law , 2007 .

[6]  Tan Wen-chang,et al.  A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates , 2003 .

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

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

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

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

[11]  Changfeng Xue,et al.  Exact solutions of Stokes’ first problem for heated generalized Burgers’ fluid in a porous half-space , 2008 .

[12]  Masood Khan,et al.  Partial Slip Effects on the Oscillatory Flows of a Fractional Jeffrey Fluid in a Porous Medium , 2007 .

[13]  Xu Mingyu,et al.  Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model , 2002 .

[14]  Constantin Fetecau,et al.  Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate , 2009, Comput. Math. Appl..

[15]  Constantin Fetecau,et al.  Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate , 2008, Appl. Math. Comput..

[16]  Haitao Qi,et al.  Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model , 2007 .

[17]  I. Podlubny.  Fractional differential equations , 1998 .

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

[19]  Dengke Tong,et al.  Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe , 2005 .

[20]  Daniel D. Joseph,et al.  Fluid Dynamics Of Viscoelastic Liquids , 1990 .

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