D. Vieru

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.

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 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 oscillating motion of an Oldroyd-B fluid between two infinite circular cylinders

Exact solutions for some oscillating motions of Oldroyd-B fluids, between two infinite coaxial circular cylinders, are established by means of the Laplace transform. These solutions, presented as sum of the steady-state and transient solutions describe the motion of the fluid at small and large times and reduce to the similar solutions for Maxwell, second grade and Newtonian fluids as limiting cases. After some time, when the transients disappear, the starting solutions tend to the steady-state solutions which are periodic in time and independent of the initial conditions. The required time to obtain the steady-state for the cosine and the sine oscillations of the boundary is determined by graphical illustrations. This time decreases if the frequency of the velocity of the boundary increases.

Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

The velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.

General Solutions for Magnetohydrodynamic Natural Convection Flow with Radiative Heat Transfer and Slip Condition over a Moving Plate

General solutions for the magnetohydrodynamic (MHD) natural convection flow of an incompressible viscous fluid over a moving plate are established when thermal radiation, porous effects, and slip condition are taken into consideration. These solutions, obtained in closed-form by Laplace transform technique, depend on the slip coefficient and the three essential parameters Gr, Preff, and Keff. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different fluid motions with technical relevance. For illustration, two special cases are considered and some interesting results from the literature are recovered as limiting cases. The influence of pertinent parameters on the fluid motion is graphically underlined.

New exact solutions corresponding to the first problem of Stokes for Oldroyd-B fluids

The velocity field and the tangential stress corresponding to the flow of an Oldroyd-B fluid over a suddenly moved flat plate are determined by means of the Laplace transform. The solutions that have been obtained, all in agreement with those established using the Fourier transform, reduce to the solutions for a Newtonian fluid as a limiting case. Furthermore, the similar tangential stress for a Maxwell fluid can be also obtained as a limiting case of our solution while the associated velocity field is then determined by a simple integration. Finally, some graphical representations confirm the above assertions.