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

2012 ◽  
Author(s):  
Dumitru Vieru ◽  
Corina Fetecau ◽  
Mehwish Rana
Keyword(s):  
Shear Stress ◽  
Rectangular Channel ◽  
Second Grade ◽  
Oscillating Shear Stress ◽  
Starting Solutions ◽  
Second Grade Fluids

Two‐layer flows of generalized immiscible second grade fluids in a rectangular channel

2019 ◽  
Vol 43 (3) ◽  
pp. 1337-1348
Author(s):  
Liang Luo ◽  
Nehad Ali Shah ◽  
Ibrahim M. Alarifi ◽  
Dumitru Vieru
Keyword(s):  
Rectangular Channel ◽  
Second Grade ◽  
Second Grade Fluids

Starting solutions for the motion of second grade fluids due to oscillating shear stresses

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Analytic Solutions ◽  
Second Grade ◽  
Shear Stresses ◽  
Exact Analytic Solutions ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Starting Solutions ◽  
Second Grade Fluids ◽  
Graphical Illustration ◽  
Special Case

AbstractExact analytic solutions for the motion of second grade fluid between two infinite coaxial cylinders are established. The motion is produced by the inner cylinder that at time t = 0+ applies torsional and longitudinal oscillating shear stresses to the fluid. The exact analytic solutions, obtained with the help of Laplace and finite Hankel transforms, and presented as a sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case when a1 to 0 they reduce to those for a Newtonian fluid. Finally, the effect of various parameters of interest on transient parts of velocity components, velocity profiles as well as comparison between second grade and Newtonian fluids is discussed through graphical illustration.

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 Starting solutions for some simple oscillating motions of second-grade fluids

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
C. Fetecau ◽  
Corina Fetecau
Keyword(s):  
Rectangular Cross Section ◽  
Navier Stokes ◽  
Second Grade ◽  
Governing Equations ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Stokes Fluid ◽  
Starting Solutions ◽  
Second Grade Fluids ◽  
Special Case

The exact starting solutions corresponding to the motions of a second-grade fluid, due to the cosine and sine oscillations of an infinite edge and of an infinite duct of rectangular cross-section as well as those induced by an oscillating pressure gradient in such a duct, are determined by means of the double Fourier sine transforms. These solutions, presented as sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case whenα1→0, they reduce to those for a Navier-Stokes fluid.

scholarly journals Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

2011 ◽  
Vol 16 (1) ◽  
pp. 47-58 ◽  
Author(s):  
M. Imran ◽  
M. Kamran ◽  
M. Athar ◽  
A. A. Zafar
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Exact Solutions ◽  
Unit Length ◽  
Time Dependent ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Coaxial Cylinders ◽  
Grade Fluid ◽  
Second Grade Fluids

Exact solutions for the velocity field and the associated shear stress, corresponding to the flow of a fractional second grade fluid between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a time-dependent torque per unit length 2πR1ft2. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1, respectively β → 1 and α1 → 0, the corresponding solutions for ordinary second grade fluids and Newtonian fluids, performing the same motion, are obtained as limiting cases.

scholarly journals Assessing Machine Learning versus a Mathematical Model to Estimate the Transverse Shear Stress Distribution in a Rectangular Channel

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 596
Author(s):  
Babak Lashkar-Ara ◽  
Niloofar Kalantari ◽  
Zohreh Sheikh Khozani ◽  
Amir Mosavi
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Fuzzy Inference ◽  
Rectangular Channel ◽  
Tsallis Entropy ◽  
Shear Stress Distribution ◽  
Data Series ◽  
Shear Stresses ◽  
Inference System ◽  
Aspect Ratios

One of the most important subjects of hydraulic engineering is the reliable estimation of the transverse distribution in the rectangular channel of bed and wall shear stresses. This study makes use of the Tsallis entropy, genetic programming (GP) and adaptive neuro-fuzzy inference system (ANFIS) methods to assess the shear stress distribution (SSD) in the rectangular channel. To evaluate the results of the Tsallis entropy, GP and ANFIS models, laboratory observations were used in which shear stress was measured using an optimized Preston tube. This is then used to measure the SSD in various aspect ratios in the rectangular channel. To investigate the shear stress percentage, 10 data series with a total of 112 different data for were used. The results of the sensitivity analysis show that the most influential parameter for the SSD in smooth rectangular channel is the dimensionless parameter B/H, Where the transverse coordinate is B, and the flow depth is H. With the parameters (b/B), (B/H) for the bed and (z/H), (B/H) for the wall as inputs, the modeling of the GP was better than the other one. Based on the analysis, it can be concluded that the use of GP and ANFIS algorithms is more effective in estimating shear stress in smooth rectangular channels than the Tsallis entropy-based equations.

3-D Simulation for Blood Flow and Artery Compression in Asymmetric Stenotic Arteries With Axial Stretch

2001 ◽  
Author(s):  
Dalin Tang ◽  
Chun Yang ◽  
Shunnichi Kobayashi
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Shear Stress ◽  
Wall Stress ◽  
Small Strain ◽  
Rigid Wall ◽  
Severe Stenosis ◽  
Physiological Conditions ◽  
Oscillating Shear Stress ◽  
Stenotic Arteries

Abstract There has been increasing evidence that severe stenosis may cause artery compression and plaque cap rupture leading to heart attack and stroke. The physiological conditions under which that may occur and mechanisms involved are not well understood. It has been known that severe stenosis causes critical flow and wall mechanical conditions such as flow limitation, flow separation, low and oscillating shear stress distal to the stenosis, high shear stress and low or even negative flow pressure at the throat of stenosis, artery compression or even collapse. Those conditions are related to limitation of blood supply, intimal thickening and thrombosis formation, endothelism damage, platelet activation and aggregation, plaque cap rupture (for review, see [1,2]). Due to the complexity of the problem and lack of experimental data for mechanical properties of arteries under both expansion and compression, previous models were limited primarily to flow behaviors and with various limitations (axisymmetry, rigid wall, small strain, small pressure gradient). In this paper, experimental data for artery mechanical properties under physiological conditions were measured and a 3-d computational model is introduced to investigate flow behaviors and wall stress and strain distributions with fluid-structure interactions to better understand the mechanism involved in artery compression and plaque cap rupture.

scholarly journals Effects of Caveolin-1-ERK1/2 pathway on endothelial cells and smooth muscle cells under shear stress

2019 ◽  
Vol 245 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Lan Jia ◽  
Lihua Wang ◽  
Fang Wei ◽  
Chen Li ◽  
Zhe Wang ◽  
...  
Keyword(s):  
Endothelial Cells ◽  
Shear Stress ◽  
Smooth Muscle ◽  
Growth Factor ◽  
Caveolin 1 ◽  
Low Shear Stress ◽  
And Migration ◽  
Oscillating Shear Stress ◽  
Low Shear ◽  
Proliferation And Migration

Hemodynamic forces have an important role in venous intimal hyperplasia, which is the main cause of arteriovenous fistula dysfunction. Endothelial cells (ECs) constantly exposed to the shear stress of blood flow, converted the mechanical stimuli into intracellular signals, and interacted with the underlying vascular smooth muscle cells (VSMCs). Caveolin-1 is one of the important mechanoreceptors on cytomembrane, which is related to vascular abnormalities. Extracellular signal-regulated kinase1/2 (ERK1/2) pathway is involved in the process of VSMCs proliferation and migration. In the present study, we explore the effects of Caveolin-1-ERK1/2 pathway and uremia toxins on the endothelial cells and VSMCs following shear stress application. Different shear stress was simulated with a ECs/VSMCs cocultured parallel-plate flow chamber system. Low shear stress and oscillating shear stress up-regulated the expression of fibroblast growth factor-4, platelet-derived growth factor-BB, vascular endothelial growth factor-A, ERK1/2 phosphorylation in endothelial cells, and proliferation and migration of VSMCs but down-regulated the Caveolin-1 expression in endothelial cells. Uremia toxin induces the proliferation and migration of VSMCs but not in a Caveolin-1-dependent manner in the static environment. Low shear stress-induced proliferation and migration of VSMCs is inhibited by Caveolin-1 overexpression and ERK1/2 suppression. Shear stress-regulated VSMC proliferation and migration is an endothelial cells-dependent process. Low shear stress and oscillating shear stress exert atherosclerotic influences on endothelial cells and VSMCs. Low shear stress modulated proliferation and migration of VSMCs through Caveolin-1-ERK1/2 pathway, which suggested that Caveolin-1 and ERK1/2 can be used as a new therapeutic target for the treatment of arteriovenous fistula dysfunction. Impact statement Venous intimal hyperplasia is the leading cause of arteriovenous fistula (AVF) dysfunction. This article reports that shear stress-regulated vascular smooth muscle cells (VSMCs) proliferation and migration is an endothelial cell (EC)-dependent process. Low shear stress (LSS) and oscillating shear stress (OSS) exert atherosclerotic influences on the ECs and VSMCs. LSS-induced proliferation and migration of VSMCs is inhibited by Caveolin-1 overexpression and extracellular signal-regulated kinase1/2 (ERK1/2) suppression, which suggested that Caveolin-1 and ERK1/2 can be used as a new therapeutic target for the treatment of AVF dysfunction.

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