Permanent solutions for some oscillatory motions of fluids with power-law dependence of viscosity on the pressure and shear stress on the boundary

2020 ◽  
Vol 75 (8) ◽  
pp. 757-769
Author(s):  
Constantin Fetecau ◽  
Abdul Rauf ◽  
Tahir Mushtaq Qureshi ◽  
Masood Khan
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Fluid Motion ◽  
Viscosity Coefficient ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Constant Shear Stress ◽  
Starting Solutions ◽  
Similar Solutions ◽  
Oscillatory Shear Stress

AbstractIn this paper, we provide simple expressions for the permanent solutions corresponding to some oscillatory motions of two classes of Newtonian fluids with power-law dependence of viscosity on the pressure between two infinite horizontal parallel plates. The fluid motion is generated by the lower plate that applies an oscillatory shear stress to the fluid. Such solutions, which are lack in the existing literature, can be useful both for those who want to eliminate the transients from their experiments and as tests to verify numerical schemes that are developed to study complex unsteady flow problems of these fluids. The similar solutions corresponding to the motion due to a constant shear stress on the boundary are also determined and, contrary to our expectations, the shear stresses are constant on the whole flow domain although the associated velocity fields depend both of the spatial variable and the dimensionless pressure-viscosity coefficient. Finally, for validation, some comparative graphical illustrations are included and the convergence of starting solutions to the permanent solutions is graphically proved. Spatial profiles of starting solutions are also provided.

scholarly journals "Permanent solutions for some motions of UCM fluids with power-law dependence of viscosity on the pressure"

2021 ◽  
Vol 66 (1) ◽  
pp. 197-209
Author(s):  
Constantin Fetecau ◽  
Abdul Rauf
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Fluid Motion ◽  
Steady Motion ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Maxwell Fluids ◽  
Gravity Effects ◽  
Starting Solutions ◽  
Similar Solutions

Steady motion of two types of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure is analytically studied between infinite horizontal parallel plates when the gravity effects are taken into consideration. Simple and exact expressions are established for the permanent components of starting solutions corresponding to two oscillatory motions induced by the lower plate that oscillates in its plane. Such solutions are very important for the experimentalists who want to eliminate the transients from their experiments. The similar solutions for the simple Couette flow of the same fluids, as well as the permanent solutions corresponding to ordinary incompressible Maxwell fluids performing the same motions, are obtained as limiting cases of general solutions. The convergence of starting solutions to their permanent components as well as the influence of physical parameters on the fluid motion is graphically underlined and discussed.

scholarly journals Analytical Solutions for a General Mixed Boundary Value Problem Associated with Motions of Fluids with Linear Dependence of Viscosity on the Pressure

2020 ◽  
Vol 25 (3) ◽  
pp. 181-197
Author(s):  
D. Vieru ◽  
C. Fetecau ◽  
C. Bridges
Keyword(s):  
Shear Stress ◽  
Linear Dependence ◽  
Mixed Boundary ◽  
Fluid Motion ◽  
Hankel Transform ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Special Cases ◽  
Independent Variable ◽  
Suitable Change

AbstractAn unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finite Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.

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 Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Measuring the onset of mine tailings erosion

2007 ◽  
Vol 44 (4) ◽  
pp. 473-489 ◽  
Author(s):  
M Haneef-Mian ◽  
Ernest K Yanful ◽  
Robert Martinuzzi
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Mine Tailings ◽  
Laser Doppler Anemometry ◽  
Critical Shear Stress ◽  
Laser Doppler ◽  
Shear Stresses ◽  
Cohesive Sediments ◽  
Fine Grained ◽  
Power Law Equation

The present study gives details of a methodology for estimating the critical shear stress for erosion of mine tailings and other naturally occurring cohesive sediments. Erosion of a cohesive sediments bed occurs when the critical shear stress is exceeded to break the interparticle bond. Experiments were conducted in a 30 cm diameter laboratory column and calibrated using laser Doppler anemometry. The results showed that the erosion pattern of mine tailings particles was similar to those of fine-grained cohesive sediments. A power-law relation of the form E = α[(τ – τcr)/τcr]n is suggested for mine tailings, where E is the erosion rate, α is a coefficient, τ is the shear stress, τcr is the critical shear stress, and n is an exponent. The computed values of α, n, and τcr in the power-law equation were found to be comparable to values derived from experiments in a rotating circular flume. The derived expression for rate of erosion may be incorporated in resuspension and transport models for fine mine tailings of a similar nature.Key words: mine tailings, laser Doppler velocimetry, wall shear stresses, critical shear stress for erosion, erosion – shear stress relationship.

scholarly journals Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Ahmed Zeeshan
Keyword(s):  
Steady State ◽  
Porous Plate ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Newtonian Fluids ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Fourier Cosine ◽  
Maxwell Fluids

Two unsteady motions of incompressible Maxwell fluids between infinite horizontal parallel plates embedded in a porous medium are analytically studied to get exact solutions using the finite Fourier cosine transform. The motion is induced by the lower plate that applies time-dependent shear stresses to the fluid. The solutions that have been obtained satisfy all imposed initial and boundary conditions. They can be easily reduced as limiting cases to known solutions for the incompressible Newtonian fluids. For a check of their correctness, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The effects of physical parameters on the fluid motion are graphically emphasized and discussed. Required time to reach the steady-state is also determined. It is found that the steady-state is rather obtained for Newtonian fluids as compared with Maxwell fluids. Furthermore, the effect of the side walls on the fluid motion is more effective in the case of Newtonian fluids.

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.

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.

scholarly journals Compressions of magnetorheological fluids under instantaneous magnetic field and constant area

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hongyun Wang ◽  
Cheng Bi ◽  
Yongju Zhang ◽  
Li Zhang ◽  
Fenfen Zhou
Keyword(s):  
Magnetic Field ◽  
Shear Stress ◽  
Magnetic Fields ◽  
Power Law ◽  
Chain Structure ◽  
Influential Factors ◽  
Shear Stresses ◽  
Mr Fluid ◽  
Aggregation Effect ◽  
Yield Shear Stress

AbstractCompressions of magnetorheological (MR) fluids have been carried out under instantaneous magnetic fields. The yield strength of the MR fluid in compressive mode has been derived by assuming that it was a transformed shear flow in Bi-visous model. The compressive stresses have experimentally studied under different magnetic fields, different initial gap distances and different compressive velocities. The nominal yield shear stresses of the compressed MR fluid under different influential factors have been calculated. The compressive stress increased in a power law as the applied magnetic field increased, while it decreased as the initial gap distance and the compressive velocity increased. With the increase of magnetic field, the difference between the nominal yield shear stress curves increased, and the exponents of the power law increased with the increase of the magnetic field strengths. A larger initial gap distance and a lower compressive velocity resulted in a higher nominal yield shear stress under the same instantaneous magnetic field. The achieved results of the nominal yield shear stress with magnetic field seemed to deviate from the prediction of dipole model, and the chain structure aggregation effect, the sealing effect and the friction effect by compression should be considered.

An Apparatus to Study the Response of Cultured Endothelium to Shear Stress

1986 ◽  
Vol 108 (4) ◽  
pp. 332-337 ◽  
Author(s):  
R. F. Viggers ◽  
A. R. Wechezak ◽  
L. R. Sauvage
Keyword(s):  
Finite Element ◽  
Endothelial Cells ◽  
Shear Stress ◽  
Laminar Flow ◽  
Fluid Shear Stress ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Dimensional Flow ◽  
Wide Range ◽  
Wall Shear

An apparatus which has been developed to study the response of cultured endothelial cells to a wide range of shear stress levels is described. Controlled laminar flow through a rectangular tube was used to generate fluid shear stress over a cell-lined coverslip comprising part of one wall of the tube. A finite element method was used to calculate shear stresses corresponding to cell position on the coverslip. Validity of the finite element analysis was demonstrated first by its ability to generate correctly velocity profiles and wall shear stresses for laminar flow in the entrance region between infinitely wide parallel plates (two-dimensional flow). The computer analysis also correctly predicted values for pressure difference between two points in the test region of the apparatus for the range of flow rates used in these experiments. These predictions thus supported the use of such an analysis for three-dimensional flow. This apparatus has been used in a series of experiments to confirm its utility for testing applications. In these studies, endothelial cells were exposed to shear stresses of 60 and 128 dynes/cm2. After 12 hr at 60 dynes/cm2, cells became aligned with their longitudinal axes parallel to the direction of flow. In contrast, cells exposed to 128 dynes/cm2 required 36 hr to achieve a similar reorientation. Interestingly, after 6 hr at 128 dynes/cm2, specimens passed through an intermediate phase in which cells were aligned perpendicular to flow direction. Because of its ease and use and the provided documentation of wall shear stress, this flow chamber should prove to be a valuable tool in endothelial research related to atherosclerosis.

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