Time-dependent Shear Stress Research Articles

Investigating Magnetohydrodynamic Motions of Oldroyd-B Fluids through a Circular Cylinder Filled with Porous Medium

We analytically investigated the magnetohydrodynamic motions of electrically conductive, incompressible Oldroyd-B fluids through an infinite circular cylinder filled with a porous medium. A general expression was established for the dimensionless velocity of fluid as a cylinder moves along its symmetry axis with an arbitrary velocity; the expression can generate exact solutions for any motion of this fluid type, solving the discussed problem. Special cases were considered and validated through graphical investigation to illustrate important characteristics of fluid behavior. In application, this is the first presentation of an exact general expression for non-trivial shear stress related to the magnetohydrodynamic motions of Oldroyd-B fluids when a longitudinal time-dependent shear stress is applied to the fluid by a cylinder. Solutions for the motions of rate-type fluids are lacking. The graphical representations show that in the presence of a magnetic field or porous medium, fluids flow more slowly and the steady state is reached earlier.

Multilayered Inhomogeneous Beams under Torsion and Bending: An Analytical Study of Energy Dissipation

The present theoretical paper is devoted to the problem of energy dissipation in multilayered inhomogeneous beam structures of visoelastic behaviour. In particular, our attention is concentrated on studying the energy dissipation for the case of a beam that is loaded simultaneously in torsion and bending. Both torsion and bending moments which are applied on the beam change with time so that the angles of twist and rotation of the beam end vary continuously with time. The viscoelastic mechanical behaviour of the beam under torsion is treated by a viscoelastic model that has two linear springs and a linear dashpot. The model is under time-dependent shear stress. The viscoelastic behaviour of the beam under bending is modelled in a similar way. An analytical approach of deriving the energy dissipation is applied. The approach treats a multilayered beam that has an arbitrary number of layers of different thicknesses and material properties. The layers are longitudinally inhomogeneous. An investigation of the energy dissipation is carried-out to clarify the effect of the parameters of the time-dependent bending and torsion moments, the material inhomogeneity and the beam size on the energy dissipation.

Dynamical behavior and transport coefficients of the pseudo hard-sphere fluid

In this work, we employ a recent approach to characterize the hard-sphere (HS) fluid by means of a continuous interaction potential, commonly referred to as pseudo hard-sphere potential, in order to determine HS transport coefficients as a function of the volume fraction for the three-dimensional mono disperse fluid. Using equilibrium molecular dynamics simulations, we determine time-dependent velocity, shear stress, and energy flux autocorrelation functions in order to use them within the Green–Kubo framework to compute the self-diffusion, shear viscosity, and thermal conductivity coefficients, respectively. Results are discussed as a function of the volume fraction and were compared to theoretical and simulations results previously reported by other authors. The main purpose of this work is twofold: first, testing the continuous approach of the HS fluid for the computation of dynamic properties and second, performing a systematic determination of aforementioned transport coefficients to analyze them as a function of fluid volume fraction. Furthermore, our results are used to provide a practical correction to the Chapman–Enskog equations for the HS self-diffusion, shear viscosity, and thermal conductivity predictions in a wide range of volume fractions.

Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate

The main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an infinite flat plate are analytically investigated when porous effects are taken into consideration. The fluid motion is due to the plate moving in its plane with an arbitrary time-dependent velocity or applying a time-dependent shear stress to the fluid. Closed-form expressions are established both for the dimensionless velocity and shear stress fields and the Darcy’s resistance corresponding to the first motion. The dimensionless shear stress corresponding to the second motion has been immediately obtained using a perfect symmetry between the governing equations of velocity and the non-trivial shear stress. Furthermore, the obtained results provide the first exact general solutions for MHD motions of second grade fluids through porous media. Finally, for illustration, as well as for their use in engineering applications, the starting and/or steady state solutions of some problems with technical relevance are provided, and the validation of the results is graphically proved. The influence of magnetic field and porous medium on the steady state and the flow resistance of fluid are graphically underlined and discussed. It was found that the flow resistance of the fluid declines or increases in the presence of a magnetic field or porous medium, respectively. In addition, the steady state is obtained earlier in the presence of a magnetic field or porous medium.

General Solutions for Some MHD Motions of Second-Grade Fluids between Parallel Plates Embedded in a Porous Medium

General solutions are established for an initial boundary value problem by means of the integral transforms. They correspond to the isothermal MHD unidirectional motion of incompressible second-grade fluids between infinite horizontal parallel plates embedded in a porous medium. The fluid motion, which in some situations becomes symmetric with respect to the median plane, is generated by the two plates that apply time-dependent arbitrary shear stresses to the fluid. Closed-form expressions are established both for the fluid velocity and the corresponding non-trivial shear stress. Using an important remark regarding the governing equations of velocity and shear stress, exact general solutions are developed for similar motions of the same fluids when both plates move in their planes with arbitrary time-dependent velocities. The results that have been obtained here can generate exact solutions for any motion with the technical relevance of this type of incompressible second-grade fluids and their correctness being proved by comparing them with the numerical solution or with known results from the existing literature. Consequently, both motion problems of these fluids with shear stress or velocity on the boundary are completely solved.

Steady-State Solutions for Two Mixed Initial-Boundary Value Problems Which Describe Isothermal Motions of Burgers’ Fluids: Application

Steady-state solutions of two mixed initial-boundary value problems are presented in equivalent forms. They describe isothermal permanent motions of incompressible Burgers’ fluids over an infinite flat plate that applies time-dependent shear stresses to the fluid. More exactly, they are the first exact solutions for motions of Burgers’ fluids with differential expressions of the shear stress or velocity on the boundary. The obtained results are designed to make equivalent solutions for motions caused by an infinite plate moving in its plane at velocities that seem to be similar to previous shear stresses. It is simple to limit all results for the purpose of providing efficient results for incompressible Oldroyd-B, Maxwell, second grade and Newtonian fluids undergoing comparable motions. They may also be used to estimate how long it will take to get to a steady or permanent state.

Long-time solutions for some mixed boundary value problems depicting motions of a class of Maxwell fluids with pressure dependent viscosity

Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

The first solution for the helical flows of generalized Maxwell fluid with longitudinal time dependent shear stresses on the boundary

Helical flows of generalized Maxwell fluid is researched between two infinite co-axial circular cylinders. The velocity field and the adequate shear stress corresponding to the flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The first solutions that have been obtained, presented under integral and series form in terms of the generalized G- and R-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Maxwell and Newtonian fluid can be also obtained as the limit of the solution of generalized Maxwell fluid.

Influence of Hartmann Number on Convective Flow of Maxwell Fluid between Two Hot Parallel Plates through Porous Medium Subject to Arbitrary Shear Stress at the Boundary

Natural convection flow of unsteady Maxwell fluid with the effects of constant magnetic force in the course of a porous media is investigated in this research work. Fluid motion between a channel of parallel plates is tempted by time dependent shear stress applied on one plate. The governing partial differential equations of a model under consideration are transformed into ordinary differential equations by Laplace transform method and then solved for temperature and velocity fields. The obtained results for temperature fields are expressed in terms of complementary error function. The influences of involved parameters likes Hartmann number, Grashf number, Prandlt number and porosity parameter, on temperature and velocity profiles are shown graphically. There is no such result regarding Maxwell fluid in the existing literature.

On intermittency in sheared granular systems.

We consider a system of granular particles, modeled by two dimensional frictional soft elastic disks, that is exposed to externally applied time-dependent shear stress in a planar Couette geometry. We concentrate on the external forcing that produces intermittent dynamics of stick-slip type. In this regime, the top wall remains almost at rest until the applied stress becomes sufficiently large, and then it slips. We focus on the evolution of the system as it approaches a slip event. Our main finding is that there are two distinct groups of measures describing system behavior before a slip event. The first group consists of global measures defined as system-wide averages at a fixed time. Typical examples of measures in this group are averages of the normal or tangent forces acting between the particles, system size and number of contacts between the particles. These measures do not seem to be sensitive to an approaching slip event. On average, they tend to increase linearly with the force pulling the spring. The second group consists of the time-dependent measures that quantify the evolution of the system on a micro (particle) or mesoscale. Measures in this group first quantify the temporal differences between two states and only then aggregate them to a single number. For example, Wasserstein distance quantitatively measures the changes of the force network as it evolves in time while the number of broken contacts quantifies the evolution of the contact network. The behavior of the measures in the second group changes dramatically before a slip event starts. They increase rapidly as a slip event approaches, indicating a significant increase in fluctuations of the system before a slip event is triggered.

English

Two isothermal motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are investigated when gravity effects are taken into account. The fluid motion, between two infinite horizontal parallel plates, is generated by the lower plate that applies a time-dependent shear stress to the fluid. Exact expressions are established for the steady-state components of the dimensionless start-up velocity, shear stress, and normal stress. They are used to find the needed time to touch the steady-state and to provide corresponding solutions for the motion of the same fluids induced by an exponential shear stress on the boundary. This time is useful for experimentalists who want to eliminate transients from their experiments. It is higher for motions of ordinary fluids as compared to fluids with pressure-dependent viscosity. The variation of starting solutions (numerical solutions) in time and space is graphically represented and some characteristics of the fluid motion are brought to light.

The Association Between Time-Varying Wall Shear Stress and the Development of Plaque Ulcerations in Carotid Arteries From the Plaque at Risk Study.

Background and Purpose: Shear stress (WSS) is involved in the pathophysiology of atherosclerotic disease and might affect plaque ulceration. In this case-control study, we compared carotid plaques that developed a new ulcer during follow-up and plaques that remained silent for their exposure to time-dependent oscillatory shear stress parameters at baseline.Materials and Methods: Eighteen patients who underwent CTA and MRI of their carotid arteries at baseline and 2 years follow-up were included. These 18 patients consisted of six patients who demonstrated a new ulcer and 12 control patients selected from a larger cohort with similar MRI-based plaque characteristics as the ulcer group. (Oscillatory) WSS parameters [time average WSS, oscillatory shear index (OSI), and relative residence time (RRT)] were calculated using computational fluid dynamics applying the MRI-based geometry of the carotid arteries and compared among plaques (wall thickness>2 mm) with and without ulceration (Mann–Whitney U test) and ulcer-site vs. non-ulcer-site within the plaque (Wilcoxon signed rank test). More detailed analysis on ulcer cases was performed and the predictive value of oscillatory WSS parameters was calculated using linear and logistic mixed-effect regression models.Results: The ulcer group demonstrated no difference in maximum WSS [9.9 (6.6–18.5) vs. 13.6 (9.7–17.7) Pa, p = 0.349], a lower maximum OSI [0.04 (0.01–0.10) vs. 0.12 (0.06–0.20) p = 0.019] and lower maximum RRT [1.25 (0.78–2.03) Pa−1 vs. 2.93 (2.03–5.28) Pa−1, p = 0.011] compared to controls. The location of the ulcer (ulcer-site) within the plaque was not always at the maximal WSS, but demonstrated higher average WSS, lower average RRT and OSI at the ulcer-site compared to the non-ulcer-sites. High WSS (WSS>4.3 Pa) and low RRT (RRT < 0.25 Pa) were associated with ulceration with an odds ratio of 3.6 [CI 2.1–6.3] and 2.6 [CI 1.54–4.44] respectively, which remained significant after adjustment for wall thickness.Conclusion: In this explorative study, ulcers were not exclusively located at plaque regions exposed to the highest WSS, OSI, or RRT, but high WSS and low RRT regions had a significantly higher odds to present ulceration within the plaque even after adjustment for wall thickness.

Mixed initial-boundary value problems describing motions of Maxwell fluids with linear dependence of viscosity on the pressure

Abstract Some mixed initial-boundary value problems are analytically studied. They correspond to unsteady motions of the incompressible upper-convected Maxwell (IUCM) fluids with linear dependence of viscosity on the pressure between infinite horizontal parallel plates. The fluid motion is generated by the upper plate that applies time-dependent shear stresses to the fluid. Exact solutions are established for the dimensionless velocity and nontrivial shear stress fields using a suitable change of the spatial variable and the Laplace transform technique. They are presented as sum of the steady-state and transient components and are used to determine the required time to reach the permanent state. Comparisons between exact and numerical solutions indicate an excellent agreement. Analytical solutions for the unsteady motion of the same fluids induced by an exponential shear stress on the boundary are obtained as limiting cases of the general solutions. Moreover, the steady-state solutions corresponding to the ordinary IUCM fluids performing the initial motions are provided by means of asymptotic approximations of standard Bessel functions. Finally, spatial variation of starting solutions and the influence of physical parameters on the fluid motion are graphically underlined and discussed.

A Review on the Effect of Temporal Geometric Variations of the Coronary Arteries on the Wall Shear Stress and Pressure Drop.

Temporal variations of the coronary arteries during a cardiac cycle are defined as the superposition of the changes in the position, curvature, and torsion of the coronary artery axis markers and the variations in the lumen cross-sectional shape due to the distensible wall motion induced by the pulse pressure and contraction of the myocardium in a cardiac cycle. This review discusses whether modeling of the temporal variations of the coronary arteries is needed for the investigation of hemodynamics specifically in time-critical applications such as a clinical environment. The numerical modelings in the literature that model or disregard the temporal variations of the coronary arteries on the hemodynamic parameters are discussed. The results in the literature show that neglecting the effects of temporal geometric variations is expected to result in about 5% deviation of the time-averaged pressure drop and wall shear stress values and also about 20% deviation of the temporal variations of hemodynamic parameters, such as time-dependent wall shear stress and oscillatory shear index. This review study can be considered as a guide for future studies to outline the conditions in which temporal variations of the coronary arteries can be neglected while providing a reliable estimation of hemodynamic parameters.

A Numerical Study of Sheet Flow Driven by Skewed-Asymmetric Shoaling Waves Using SedWaveFoam

SedWaveFoam, an OpenFOAM-based two-phase model that concurrently resolves the free surface wave field, and the bottom boundary layer is used to investigate sediment transport throughout the entire water column. The numerical model was validated with large-scale wave flume data for sheet flow driven by shoaling skewed-asymmetric waves with two different grain sizes. Newly obtained model results were combined with previous nonbreaking and near-breaking wave cases to develop parameterization methods for time-dependent bed shear stress and sediment transport rate under various sediment sizes and wave conditions. Gonzalez-Rodriguez and Madsen (GRM07) and quasi-steady approaches were compared for intra-wave bed shear stress. The results show that in strongly asymmetric flows, considering the separated boundary layer development processes at each half wave-cycle (i.e., GRM07) is essential to accurately estimating bed shear stress and highlights the impact of phase-lag effects on sediment transport rates. The quasi-steady approach underpredicts (∼60%) sediment transport rates, especially for fine grains under large velocity asymmetry. A modified phase-lag parameter, incorporating velocity asymmetry, sediment stirring, and settling processes is proposed to extend the Meyer-Peter and Mueller type power law formula. The extended formula accurately estimated the enhanced net onshore sediment transport rate observed under skewed-asymmetric wave conditions.

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

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.

Convection heat mass transfer and MHD flow over a vertical plate with chemical reaction, arbitrary shear stress and exponential heating

The present research article is directed to study the heat and mass transference analysis of an incompressible Newtonian viscous fluid. The unsteady MHD natural convection flow over an infinite vertical plate with time dependent arbitrary shear stresses has been investigated. In heat and mass transfer analysis the chemical molecular diffusivity effects have been studied. Moreover, the infinite vertical plate is subjected to the phenomenon of exponential heating. For this study, we formulated the problem into three governing equations along with their corresponding initial and boundary conditions. The Laplace transform method has been used to gain the exact analytical solutions to the problem. Special cases of the obtained solutions are investigated. It is noticed that some well-known results from the published literature are achieved from these special cases. Finally, different physical parameters’ responses are investigated graphically through Mathcad software.

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

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.

The effect of fluid shear stress in hydrogen sulphide production and cystathionine γ-lyase expression in human early endothelial progenitor cells.

BackgroundPhysiological fluid shear stress has been shown to have a beneficial impact on vascular homeostasis. Endothelial progenitor cells (EPCs) make a significant contribution to maintaining endothelial integrity. Therefore, we hypothesised that shear stress-induced endothelium protection plays a role in hydrogen sulphide (H2S) production and up-regulation of cystathionine γ-lyase (CSE) expression in EPCs.MethodsHuman EPC-derived CSE activity was detected by colorimetric assay, and H2S production was evaluated by membrane adsorption method. Cell proliferation, migration, and adhesion were assessed by MTT, Transwell, and endothelial cell-mediated adhesion assays, respectively. Real-time polymerase chain reaction (RT-PCR) was carried out to analyse gene expression. Protein expression was analysed by western blot.ResultsHuman EPCs were treated with shear stress levels of 5–25 dyn/cm2 for up to 3 h, and 25 dyn/cm2 for up to 24 h. H2S production and CSE mRNA expression in the EPCs were increased by shear stress in a dose-dependent manner in vitro. Likewise, time-dependent shear stress also significantly enhanced CSE protein expression. Compared to static condition, shear stress improved EPCs proliferation, migration and adhesion capacity. Knockdown of CSE expression by small interfering RNA substantially eliminated the shear stress-induced above functions of human EPCs in vitro.ConclusionsThis study gives new insight into the regulatory effect of physiological shear stress on the CSE/H2S system in human EPCs. Our findings may contribute to the development of vascular protective research, although the relevant evidence is admittedly indirect.

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

An 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.