STOKES FIRST PROBLEM FOR AN OLDROYD-B FLUID IN A POROUS HALF SPACE

Based on a modified Darcy’s law for a viscoelastic fluid, Stokes’ first problem was extended to that for an Oldroyd-B fluid in a porous half space. By using Fourier sine transform, an exact solution was obtained. In contrast to the classical Stokes’ first problem for a clear fluid, there is a y-dependent steady state solution for an Oldroyd-B fluid in the porous half space, which is a damping exponential function with respect to the distance from the flat plate. The thickness of the boundary layer, which tends to be a limited value, is also different from that of a clear fluid. The effect of viscoelasticity on the unsteady flow in porous media is investigated. It was found if α>1∕4[(αt∕Re)+Re]2, oscillations in velocity occur obviously and the system exhibits viscoelastic behaviors, where α and αt are nondimensional relaxation and retardation times, respectively, Re is Reynold number in porous media. Some previous solutions of Stokes’ first problem corresponding to Maxwell fluid and Newtonian fluid in por...

[1]  Kambiz Vafai,et al.  The role of porous media in modeling flow and heat transfer in biological tissues , 2003 .

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

[3]  Roger I. Tanner,et al.  Note on the Rayleigh problem for a visco-elastic fluid , 1962 .

[4]  R. Huilgol.  Corrections and extensions to “propagation of a vortex sheet in viscoelastic liquids—the rayleigh problem”,J. non-newtonian fluid mech., 8 (1981) 337–347 , 1983 .

[5]  P. Royer,et al.  Derivation of macroscopic filtration law for transient linear viscoelastic fluid flow in porous media , 2000 .

[6]  C. L. Tien,et al.  Boundary and inertia effects on flow and heat transfer in porous media , 1981 .

[7]  T. Phillips,et al.  Comparison of creeping and inertial flow of an Oldroyd B fluid through planar and axisymmetric contractions , 2002 .

[8]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[9]  Mingyu Xu,et al.  The impulsive motion of flat plate in a generalized second grade fluid , 2002 .

[10]  C. Fetecau,et al.  A new exact solution for the flow of a Maxwell fluid past an infinite plate , 2003 .

[11]  D. Frenkel,et al.  Velocity fluctuations and dispersion in a simple porous medium. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  John C. Slattery,et al.  Advanced transport phenomena , 1999 .

[13]  H. Schlichting.  Boundary Layer Theory , 1955 .

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

[15]  Anis Younes,et al.  On modelling the multidimensional coupled fluid flow and heat or mass transport in porous media , 2003 .

[16]  Turbulence Characteristics in Porous Media , 2002 .

[17]  Min Chan Kim,et al.  Thermal instability of viscoelastic fluids in porous media , 2003 .

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

[19]  A. Lozinski,et al.  An energy estimate for the Oldroyd B model: theory and applications , 2003 .

[20]  P. Luchini,et al.  Linear stability and receptivity analyses of the Stokes layer produced by an impulsively started plate , 2001 .

[21]  F. Pinho,et al.  Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions , 2003 .

[22]  N. Phan-Thien,et al.  On the Rayleigh problem for a viscoelastic fluid , 1988 .

[23]  D. Joseph,et al.  Stokes' first problem for viscoelastic fluids , 1987 .

[24]  P. Jordan,et al.  Stokes’ first problem for a Rivlin–Ericksen fluid of second grade in a porous half-space , 2003 .

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

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

[27]  C. Fetecau,et al.  The Rayleigh–Stokes problem for heated second grade fluids , 2002 .

[28]  Daniel D. Joseph,et al.  Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids , 1998, Journal of Fluid Mechanics.

[29]  I. Teipel,et al.  The impulsive motion of a flat plate in a viscoelastic fluid , 1981 .