Constantin Fetecau

A new exact solution for the flow of a Maxwell fluid past an infinite plate

Abstract A new exact solution corresponding to the flow of a Maxwell fluid over a suddenly moved flat plate is determined. This solution is in all accordance with a previous one and for λ→0 it goes to the well-known solution for Navier–Stokes fluids.

The first problem of stokes for an Oldroyd-B fluid

Abstract The velocity field and the associated tangential tension corresponding to the flow of an Oldroyd-B fluid over a suddenly moved flat plate are determined. The well-known solutions for a Navier–Stokes fluid, as well as those corresponding to a Maxwell fluid and a second-grade one, appear as limiting cases of our solutions. Finally, some comparative diagrams concerning the velocity and tension profiles are presented for different values of the material constants.

Analytical solutions for non-Newtonian fluid flows in pipe-like domains

Abstract This paper deals with some unsteady unidirectional transient flows of an Oldroyd-B fluid in unbounded domains which geometrically are axisymmetric pipe-like. An expansion theorem of Steklov is used to obtain exact solutions for flows satisfying no-slip boundary conditions. The well known solutions for a Navier–Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limiting cases of our solutions. The steady state solutions are also obtained for t→∞.

Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate

The unsteady flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate is investigated. Exact solutions for the velocity field are established by means of the Fourier and Laplace transforms. The similar solutions for Maxwell and Newtonian fluids can be obtained as limiting cases of our results. In the absence of side walls, all solutions that have been determined reduce to those corresponding to the motion over an infinite plate.

Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate

The velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized Maxwell fluid are determined using Fourier sine and Laplace transforms. They are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. The similar solutions for Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general results. Graphical illustrations show that the velocity profiles corresponding to a generalized Maxwell fluid are going to that for an ordinary Maxwell fluid if @a->1.

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.

Decay of a potential vortex in a Maxwell fluid

Abstract The velocity field and the associated tangential tension corresponding to a potential vortex in a Maxwell fluid are determined by means of the Hankel transform. The similar solutions for a Newtonian fluid appear as a limiting case of our solutions.

Decay of a potential vortex in a generalized Oldroyd-B fluid

The velocity field and the adequate shear stress corresponding to the decay of a potential vortex in a generalized Oldroyd-B fluid are determined by means of Hankel and Laplace transforms. The exact solutions, written in terms of the generalized G and R functions, are presented as a sum of the Newtonian solutions and the adequate non-Newtonian contributions. These solutions can be easy specialized to give the solutions for generalized Maxwell fluids and ordinary Oldroyd-B or Maxwell fluids performing the same motion. The influence of the fractional parameters as well as that of the material parameters on the decay of the vortex is emphasized by graphical illustrations.

On the energetic balance for the flow of an Oldroyd-B fluid due to a flat plate subject to a time-dependent shear stress

Exact and approximate expressions for the power due to the shear stress at the wall L, the dissipation @F and the boundary layer thickness @d are established for the unsteady flow of an Oldroyd-B fluid driven by the transverse motion of an infinite plate subject to a time-dependent shear stress. The change of the kinetic energy with time is also obtained from the energetic balance. Similar expressions for Newtonian, Maxwell and second-grade fluids are obtained as limiting cases of general results. Series solutions for the velocity and shear stress are also obtained for small values of the dimensionless relaxations and retardation times. Graphical illustrations corresponding to the exact expressions for L, @F and @d agree with the associated asymptotic approximations. Usually for many industrial applications the velocity of the wall is given and what is required is the energy that is necessary to keep the wall running with the prescribed value. The problem discussed by us now is that where, on the contrary, the wall shear stress is given but the velocity and the energy of the medium are required.

General Solutions for the Unsteady Flow of Second-Grade Fluids over an Infinite Plate that Applies Arbitrary Shear to the Fluid

General solutions corresponding to the unsteady motion of second-grade fluids induced by an infinite plate that applies a shear stress ƒ (t) to the fluid are established. These solutions can immediately be reduced to the similar solutions for Newtonian fluids. They can be used to obtain known solutions from the literature or any other solution of this type by specifying the function ƒ (.). Furthermore, in view of a simple remark, general solutions for the flow due to a moving plate can be developed.