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

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Corina Fetecau
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Viscous Fluid ◽  
Fourier Transforms ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Side Walls ◽  
Oscillating Shear Stress ◽  
Similar Solutions

AbstractThe 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.

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

2013 ◽  
Vol 68 (12) ◽  
pp. 725-734 ◽  
Author(s):  
Mehwish Rana ◽  
Nazish Shahid ◽  
Azhar Ali Zafar
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Integral Transforms ◽  
Second Grade ◽  
Shear Stresses ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions

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.

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

2011 ◽  
Vol 66 (12) ◽  
pp. 753-759 ◽  
Author(s):  
Constantin Fetecau ◽  
Corina Fetecau ◽  
Mehwish Rana
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Newtonian Fluids ◽  
Second Grade ◽  
Moving Plate ◽  
General Solutions ◽  
Similar Solutions ◽  
Second Grade Fluids

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.

scholarly journals General solutions for the mixed boundary value problem associated to hydromagnetic flows of a viscous fluid between symmetrically heated parallel plates

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1389-1405 ◽  
Author(s):  
Maria Javaid ◽  
Muhammad Imran ◽  
Constantin Fetecau ◽  
Dumitru Vieru
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Viscous Fluid ◽  
Mixed Boundary ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Shear Stresses ◽  
Parallel Plates ◽  
General Solutions ◽  
Special Cases

Exact general solutions for hydromagnetic flows of an incompressible viscous fluid between two horizontal infinite parallel plates are established when the upper plate is fixed and the inferior one applies a time-dependent shear stress to the fluid. Porous effects are taken into consideration and the problem in discussion is completely solved for moderate values of the Hartman number. It is found that the fluid velocity and the non-trivial shear stress satisfy PDE of the same form and the motion characteristics do not depend of magnetic and porous parameters independently but only by a combination of them that is called the effective permeability. For illustration, as well as to bring to light some physical insight of results that have been obtained, three special cases are considered and the influence of Reynolds number as well as combined porous and magnetic effects on the fluid motion are graphically underlined and discussed for motions due to constant or ramped-type shear stresses on the boundary. The starting solutions corresponding to motions induced by the lower plate that applies constant or oscillatory shear stresses to the fluid are presented as sum of steady-state and transient solutions and the required time to reach the steady-state is graphically determined. This time is greater for motions due to sine as compared to cosine oscillating shear stresses on the boundary. The steady-state is rather obtained in the presence of a magnetic field or porous medium.

scholarly journals Exact solutions for unsteady axial Couette flow of a fractional Maxwell fluid due to an accelerated shear

2011 ◽  
Vol 16 (2) ◽  
pp. 135-151 ◽  
Author(s):  
Muhammad Athar ◽  
Corina Fetecau ◽  
Muhammad Kamran ◽  
Ahmad Sohail ◽  
Muhammad Imran
Keyword(s):  
Shear Stress ◽  
Positive Real Number ◽  
Fractional Integration ◽  
Maxwell Fluid ◽  
Unsteady Motion ◽  
Positive Real ◽  
Special Cases ◽  
Multiple Integrals ◽  
Similar Solutions ◽  
R Functions

The velocity field and the adequate shear stress corresponding to the flow of a fractional Maxwell fluid (FMF) between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The motion is produced by the inner cylinder that at time t = 0+ applies a shear stress fta (a ≥ 0) to the fluid. The solutions that have been obtained, presented under series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as special cases of general solutions. The unsteady solutions corresponding to a = 1, 2, 3, ... can be written as simple or multiple integrals of similar solutions for a = 0 and we extend this for any positive real number a expressing in fractional integration. Furthermore, for a = 0, 1 and 2, the solutions corresponding to Maxwell fluid compared graphically with the solutions obtained in [1–3], earlier by a different technique. For a = 0 and 1 the unsteady motion of a Maxwell fluid, as well as that of a Newtonian fluid ultimately becomes steady and the required time to reach the steady-state is graphically established. Finally a comparison between the motions of FMF and Maxwell fluid is underlined by graphical illustrations.

Some Unsteady Flows of a Jeffrey Fluid between Two Side Walls over a Plane Wall

2011 ◽  
Vol 66 (12) ◽  
pp. 745-752 ◽  
Author(s):  
Masood Khan ◽  
Faiza Iftikhar ◽  
Asia Anjum
Keyword(s):  
Infinite Plate ◽  
Unsteady Flows ◽  
Integral Transforms ◽  
Plane Wall ◽  
Second Grade ◽  
Jeffrey Fluid ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions ◽  
Oscillating Plate

In this paper, some time-dependent flows of a non-Newtonian fluid between two side walls over a plane wall are investigated. The following three problems have been studied: (i) flow due to an oscillating plate, (ii) flow due to an accelerating plate, and (iii) flow due to applied constant stress. The explicit expressions for the velocity field are determined by using the integral transforms. The solutions that have been obtained, depending on the initial and boundary conditions, are written as sum of the steady state and transient solutions. The similar solutions for second-grade and Newtonian fluids can be deduced as limiting cases of our solutions. Furthermore, in absence of the side walls they reduce to the similar solutions over an infinite plate. The effects of some important parameters due to side walls on the flow field are investigated.

EXACT SOLUTIONS FOR THE POISEUILLE FLOW OF A GENERALIZED MAXWELL FLUID INDUCED BY TIME-DEPENDENT SHEAR STRESS

2010 ◽  
Vol 51 (4) ◽  
pp. 416-429 ◽  
Author(s):  
W. AKHTAR ◽  
CORINA FETECAU ◽  
A. U. AWAN
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Poiseuille Flow ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Similar Solutions ◽  
Generalized Maxwell Fluid

AbstractThe Poiseuille flow of a generalized Maxwell fluid is discussed. The velocity field and shear stress corresponding to the flow in an infinite circular cylinder are obtained by means of the Laplace and Hankel transforms. The motion is caused by the infinite cylinder which is under the action of a longitudinal time-dependent shear stress. Both solutions are obtained in the form of infinite series. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases. Finally, the influence of the material and fractional parameters on the fluid motion is brought to light.

Flow of Second Grade Fluid between two Walls Induced by Rectified Sine Pulses Shear Stress

2015 ◽  
Vol 31 (5) ◽  
pp. 573-582
Author(s):  
Q. Sultan ◽  
M. Nazar ◽  
I. Ahmad ◽  
U. Ali
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Fourier Cosine ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Grade Fluid

AbstractThis paper concerns with the unsteady MHD flow of a second grade fluid between two parallel walls through porous media induced by rectified sine pulses shear stress. The analytical expressions for the velocity field and the adequate shear stress are determined by means of the Laplace transform technique and Fourier cosine and sine transforms and are written as a sum of steady state and transient solutions. The influence of side walls on the fluid motion, the distance between walls for which the velocity of the fluid in the middle of the channel is negligible, and the required time to reach the steady state are presented by graphical illustrations. As the second grade fluid parameter → 0 the problem reduces to the Newtonian fluids performing the same motion.

scholarly journals First Problem of Stokes for Generalized Burgers' Fluids

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Velocity Field ◽  
Integral Transforms ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Second Grade ◽  
Material Parameters ◽  
Transient Solutions ◽  
Similar Solutions

The velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers’ fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.

Unsteady flow of a generalized Oldroyd-B fluid due to an infinite plate subject to a time-dependent shear stress

2010 ◽  
Vol 88 (9) ◽  
pp. 675-687 ◽  
Author(s):  
D. Vieru ◽  
Corina Fetecau ◽  
C. Fetecau
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Unsteady Flow ◽  
Infinite Plate ◽  
Time Dependent ◽  
Fourier Cosine ◽  
Series Form ◽  
Maxwell Fluids ◽  
Similar Solutions

The unsteady flow of an incompressible generalized Oldroyd-B fluid induced by an infinite plate subject to a time-dependent shear-stress is studied by means of the Fourier cosine and Laplace transforms. The solutions that have been obtained, written under integral and series form in terms of the generalized Ga,b,c(·,t) functions, are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. They satisfy all imposed initial and boundary conditions, and for λ and λr → 0 reduce to the Newtonian solutions. Furthermore, the similar solutions for generalized Maxwell fluids as well as those for ordinary fluids are also obtained as limiting cases of general solutions. Finally, to reveal some relevant physical aspects of the obtained results, the diagrams of the velocity field v(y, t) have been depicted against y for different values of t and of the material and fractional parameters.

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

2013 ◽  
Vol 68 (1-2) ◽  
pp. 130-138 ◽  
Author(s):  
Corina Fetecau ◽  
Mehwish Rana ◽  
Constantin Fetecau
Keyword(s):  
Shear Stress ◽  
Free Convection ◽  
Viscous Fluid ◽  
Thermal Radiation ◽  
Vertical Plate ◽  
Fluid Motion ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Special Cases ◽  
Infinite Vertical Plate

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.

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