Mehwish Rana

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.

Radiative and Porous Effects on Free Convection Flow near a Vertical Plate that Applies Shear Stress to the Fluid

General solutions for the unsteady free convection flow of an incompressible viscous fluid due to an infinite vertical plate that applies a shear stress f (t) to the fluid are established when thermal radiation and porous effects are taken into consideration. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different motions with technical relevance. The velocity is presented as a sum of thermal and mechanical components. Finally, some special cases are brought to light, and effects of pertinent parameters on the fluid motion are graphically underlined.

Exact solution for motion of an Oldroyd-B fluid over an infinite flat plate that applies an oscillating shear stress to the fluid

The unsteady motion of an Oldroyd-B fluid over an infinite flat plate is studied by means of the Laplace and Fourier transforms. After time t = 0, the plate applies cosine/sine oscillating shear stress to the fluid. The solutions that have been obtained are presented as a sum of steady-state and transient solutions and can be easily reduced to the similar solutions corresponding to Newtonian or Maxwell fluids. They describe the motion of the fluid some time after its initiation. After that time when the transients disappear, the motion is described by the steady-state solutions that are periodic in time and independent of the initial conditions. Finally, the required time to reach the steady-state is established by graphical illustrations. It is lower for cosine oscillations in comparison with sine oscillations of the shear, decreases with respect to ω and λ and increases with regard to λr.Mathematical Subject Classification (2010): 76A05; 76A10.PACS: 47.50.-d; 47.85.-g.

First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid

Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.

Unsteady flow of a Maxwell fluid with fractional derivatives in a circular cylinder moving with a nonlinear velocity

Abstract In this paper we determine the velocity field and the shear stress corresponding to the unsteady flow of a Maxwell fluid with fractional derivatives driven by an infinite circular cylinder that slides along its axes with a velocity Ata. The general solutions, obtained by means of integral transforms, satisfy all imposed initial and boundary conditions. They can be easily particularized to give the similar solutions for ordinary Maxwell and Newtonian fluids. Finally, the influence of the parameters α and β on the fluid motion as well as a comparison between models is underlined by graphical illustrations.

Starting solutions for the flow of second grade fluids in a rectangular channel due to an oscillating shear stress

The unsteady motion of a second grade fluid between two parallel side walls perpendicular to a plate is studied by means of the Fourier sine and cosine transforms. Initially, the fluid is at rest and at time t = 0+, the plate applies an oscillating shear to the fluid. The solutions that have been obtained, presented under integral and series form and written as a sum between steady time-periodic and transient solutions can be easily reduced to the similar solutions for Newtonian fluids performing the same motion. They describe the motion of the fluid some time after its initiation. After that time, when the transient solutions disappear, the motion of the fluid is described by the steady time-periodic solutions that are independent of the initial conditions. In the absence of side walls, more exactly when the distance between walls tends to infinity, all solutions reduce to those corresponding to the motion over an infinite plate. As it was to be expected, the steady time-periodic solutions corresponding to sine and cosine oscillations of the shear stress on the boundary differ by a phase shift. Finally, the influence of side walls on the fluid motion, the required time to reach the steady periodic flow, as well as the distance between walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence are established by numerical calculus and graphical illustrations. As expected, the time needed to reach the steady periodic flows is lower in the presence of side walls. It is lower for Newtonian fluids in comparison with second grade fluids and greater for sine oscillations in comparison to the cosine oscillations of the boundary shear.The unsteady motion of a second grade fluid between two parallel side walls perpendicular to a plate is studied by means of the Fourier sine and cosine transforms. Initially, the fluid is at rest and at time t = 0+, the plate applies an oscillating shear to the fluid. The solutions that have been obtained, presented under integral and series form and written as a sum between steady time-periodic and transient solutions can be easily reduced to the similar solutions for Newtonian fluids performing the same motion. They describe the motion of the fluid some time after its initiation. After that time, when the transient solutions disappear, the motion of the fluid is described by the steady time-periodic solutions that are independent of the initial conditions. In the absence of side walls, more exactly when the distance between walls tends to infinity, all solutions reduce to those corresponding to the motion over an infinite plate. As it was to be expected, the steady time-periodic solutions corresponding ...

Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid

Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

THE INFLUENCE OF DEBORAH NUMBER ON SOME COUETTE FLOWS OF A MAXWELL FLUID

Some Couette flows of a Maxwell fluid caused by the bottom plate applying shear rate on the fluid, are studied. Exact expressions for velocity and shear stress corresponding to the fluid motion are determined using Laplace transform. Two particular cases of constant shear rate on the bottom plate and sinusoidal oscillations of the wall shear rate are discussed. Some important characteristics of fluid motion are highlighted through graphs.