Relaxation Time Parameter Research Articles

Numerical simulations of Taylor anvil-on-rod impact tests using classical and new approaches

Plastic deformation of samples undergoing Taylor anvil-on-rod impact test is simulated utilising finite element method (FEM). Classical (bilinear plasticity using von Mises stress, Johnson-Cook plasticity model) plasticity models and a new plasticity model based on notion of incubation time of plastic flow initiation are employed to model dynamic deformation of tested samples. In order to verify the obtained solutions, the received predictions are compared to available experimental measurements of deformed sample shapes for two different materials (copper, aluminium) and various initial sample velocities. It is shown that bilinear von Mises plasticity model is not able to provide satisfactory coincidence between the shape of the sample boundary received in numerical simulations and in real experimental conditions. At the same time, models accounting for rate dependency of deformation are providing much more accurate results. Substitution of the concept of "dynamic" yielding stress of a material, depending on the rate of deformation by characteristic time of plastic stress relaxation provides a powerful tool for robust prediction of plastic deformation for a wide range of strain rates. The parameter of the characteristic relaxation time has a clear physical interpretation and theoretically can be evaluated from microstructural studies.

The effect of strain and age on the mechanical properties of rat Achilles tendons.

Achilles tendon (AT) ruptures are common in the middle age population; however, the pathophysiology and influence of age on AT ruptures is not fully understood. This study evaluates the effect and interactions between, strain and age on the in vitro biomechanical properties of ATs. Bilateral ATs were harvested from 17 young (8 months) and 14 middle-aged (24 months) rats and underwent stress-relaxation using Fung's quasilinear viscoelastic (QLV) modeling and load-to-failure testing. The initial viscoelastic response (parameter B) in middle-age animals was dependent on the amount of strain applied to the tendon and was significantly increased in middle-aged animals at higher strain. Higher strain in older animals led to a prolonged relaxation time (parameter tau 2). There was a trend toward an increased magnitude of the relaxation response (parameter C) at higher strain in the middle-aged animals. Middle-aged animals had a significantly lower mean stress at ultimate failure (p=0.01), while Young's modulus was similar in both groups (p=0.46). The passive biomechanical properties of the rat AT change with age and the influence stress-relaxation response of the AT, thereby possibly predisposing the AT of older animals to fail at lower loads compared to younger animals. Not applicable, this is a basic science study.

An improved heat conduction and mass diffusion models for rotating flow of an Oldroyd-B fluid

An analysis is presented to inspect the steady three-dimensional boundary layer flow of an Oldroyd-B fluid over a stretching surface. Heat and mass transfer analysis are scrutinized by utilizing the non-Fourier’s and non-Fick’s models in rotating frame. The expressions of heat and mass fluxes are based upon the Cattaneo-Christov theory. The Cattaneo-Christov heat and mass flux models are used for the development of energy and concentration equations which account the contribution of thermal and concentration relaxation times. Additionally, temperature dependent thermal conductivity is also considered here. Apposite transformations are betrothed to obtain the ordinary differential equations with high nonlinearity. The analytical solutions are established for the resulting ordinary differential system by utilizing the homotopy analysis method (HAM). Our observations reveal that the rotation parameter serves to diminish the primary velocity f′(η) and associated momentum boundary layer thickness and similar trend is observed for the secondary velocity g(η). It is also observed that the thermal and concentration relaxation time parameters reduce the temperature and concentration profiles. For endorsement of the current relation, the attained consequences are eminent with former exploration in precise cases and splendid agreement has been distinguished.

Abstract 13091: Relaxation and Calcium Cycling in Isolated Contracting Myocardium From Patients With Hypertensive Heart Disease and Heart Failure With Preserved Ejection Fraction

Prolonged myocardial relaxation is believed to play an important role in the pathophysiology of heart failure with preserved ejection fraction (HFpEF). An impairment of cellular Ca 2+ extrusion in diastole may contribute to this delay in relaxation. We investigated relaxation characteristics and cellular Ca 2+ - and Na + -handling in intact, contracting myocardial strip preparations dissected from epicardial biopsies obtained from patients with hypertensive heart disease (HHD) with and without HFpEF. Relaxation time parameters (at rates of 60/min and 180/min), cellular Ca 2+ - (Fura-2) and Na + - (ANG-2) cycling were studied in 20 patients with HHD without HFpEF (HHD), 12 with HHD and HFpEF (HHD(+)HFpEF) and 26 without HHD or HFpEF, who served as referent controls (CTR). Expression levels of key ion transporters were also measured. Since Ca 2+ -handling can be pharmacologically modified, we evaluated the therapeutic potential of the Na + -influx inhibitors ranolazine (10μM), furosemide (50μM) and amiloride (50μM) to accelerate relaxation. Compared with controls, the time to half maximal relaxation at 60/min was prolonged in both HHD and HHD(+)HFpEF (CTR: 263±5ms, HHD: 295±12ms, HHD(+)HFpEF: 296±11ms; p=0.01 and p<0.01, respectively). When the stimulation rate was increased to 180/min, this prolongation resulted in incomplete relaxation manifested as increased diastolic force in both HHD (26±3%, p=0.01) and HHD(+)HFpEF (33±9%, p=0.01). This finding was associated with an increase in diastolic Ca 2+ (Fura-2: 28±6%; p<0.01) and a minor increase in Na + (ANG-2: 0.5±0.2%; p=0.05). Expression levels of Ca 2+ - and Na + -handling proteins were not different between the groups. None of the pharmacologic agents accelerated relaxation or improved incomplete relaxation at high heart rates. We conclude that relaxation is prolonged in isolated myocardium from patients with HHD and HHD(+)HFpEF. An impairment of diastolic Ca 2+ removal appears to play a role in incomplete relaxation at higher heart rates. This functional deficit is not due to changes in expression levels of key transporters or regulatory proteins and was not improved by pharmacologic inhibition of Na + -influx.

Stability characteristics of Rayleigh-Taylor instability in a strongly coupled incompressible dust fluid with finite shear flow

The stability characteristics of Rayleigh-Taylor instability (RTI) has been investigated in an unmagnetized, strongly coupled dusty plasma in the presence of velocity shear. The description of the dust has been made through the Generalized Hydrodynamic model, where a strong correlation between the dust grains comes via the Maxwell relaxation time parameter. It has been found that when the correlations become stronger, the shear vortices that are originating from the Rayleigh-Taylor (RT) dynamics tend to propagate through the medium, giving a lesser opportunity to the RT mode to grow. Physically, in the strongly coupled regime, viscosity contributes to the dispersive correction, instead of normal dissipation in the RT mode and reduces the gravitational energy which is the main factor responsible for the RTI. In this process, shear flow also helps to stabilize the RT mode by extracting energy from the gravitational energy. Due to this combined effect, the long wavelength modes grow first and the shorter ones get completely suppressed. The results, first, have been obtained by local approximation and thereafter via nonlocal analysis with numerical techniques. A cut-off value of the wave vector, for the RT mode, has also been obtained analytically, which closely matches with the numerical one in the shorter wavelength regime.

Numerical investigation of generalized Fourier's and Fick's laws for Sisko fluid flow

The principal emphasis of this article is to investigate the characteristics of Cattaneo-Christov heat and mass flux models on steady 2D flow of Sisko fluid over a nonlinear stretching surface. The Cattaneo-Christov heat and mass flux models are the generalization of classical Fourier's and Fick's laws through thermal and concentration relaxation times, respectively. The heat transfer analysis is carried out in the presence of temperature dependent thermal conductivity. The nonlinear ordinary differential equations are first established through the transformation procedure which are then solved numerically by using the bvp4c function in MatLab. The influences of involved parameters on the temperature and concentration distributions are deliberated and physical characteristics of these parameters are examined through graphs and discussed in detail. Results reveal that the temperature and concentration profiles have converse relationship with the nondimensional thermal and concentration relaxation time parameters. Moreover, it is also fascinating to observe that the concentration profile is significantly affected by the power-law index when it escalates from n<1 to n>1

Spectral analysis for stability of bubble steady states of a Keller–Segel's minimal chemotaxis model

A number of techniques, some of which are novel, are introduced to develop a systematic method to study a set of eigenvalue problems arising from the stability analysis of bubble steady states of a Keller–Segel's minimal chemotaxis model. Estimates of the eigenvalue with largest real part of an elliptic system without variational structure and the second eigenvalue of a corresponding subproblem possessing variational structure are obtained. These estimates provide critical information about the stability of the bubble steady state with respect to the time relaxation parameter; in particular, it is shown that the stability decreases to zero as the relaxation parameter goes to infinity.

Composite metric R2 - R1ρ (1/T2 - 1/T1ρ ) as a potential MR imaging biomarker associated with changes in pain after ACL reconstruction: A six-month follow-up.

This study looked to investigate a new quantitative metric, R2 - R1ρ (1/T2 - 1/T1ρ ), using magnetic resonance (MR) images and voxel-based relaxometry (VBR) for detecting early cartilage degeneration and explore the association with patient-reported outcomes measures (PROMs) in patients 6 months after ACL reconstruction. Sixty-four patients from three sites were bilaterally scanned on a 3T MR with a combined T1ρ /T2 protocol to calculate R1ρ (1/T1ρ ) and R2 (1/T2 ) values at baseline and 6 months after reconstructive surgery. Non-rigid registration was applied to align images onto a template, allowing VBR to determine VBR rate differences and explore cross-sectional and longitudinal differences between injured and uninjured knees, generating Statistical Parametric Maps (SPMs). Baseline R2 - R1ρ differences were further correlated with change in PROMs from the Knee Injury and Osteoarthritis Outcome Score (KOOS) from baseline to 6 months. Cross-sectional results demonstrated low relaxation rate differences in the injured patella (baseline: 21%, p = 0.01; 6-months: 18%, p = 0.02), lateral tibia (baseline: 25%, p = 0.01; 6-months: 24%, p = 0.01), and weight-bearing regions of the tibia and femur. The uninjured patella showed significant longitudinal changes (17%, p = 0.02). R2 - R1ρ differences showed significant correlations with KOOS PROMs, particularly in the lateral tibia, patella, and trochlea. R2 - R1ρ difference VBR analyses provide new and highly sensitive parameters for assessing early cartilage degeneration in patients after ACL injury by integrating findings from both T1ρ and T2 , commonly used relaxation time parameters, into a single metric. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:718-729, 2017.

Impact of chemical processes on 3D Burgers fluid utilizing Cattaneo-Christov double-diffusion: Applications of non-Fourier's heat and non-Fick's mass flux models

This article communicates the characteristics of Cattaneo-Christov heat and mass flux models on steady three-dimensional flow of Burgers fluid over a bidirectional stretching surface. These models are the modifications of classical Fourier's and Fick's laws through thermal and concentration relaxation times, respectively. Additionally, characteristics of heterogeneous and homogeneous reactions are further investigated. Transformation procedure is adopted to obtain the highly coupled nonlinear ordinary differential equations. The developed nonlinear problem is then solved analytically by utilizing the homotopy analysis method (HAM). The impact of various physical parameters on the temperature and concentration distributions are deliberated and physical characteristics of these parameters are exhibited through graphs and discussed through the reasonable judgment. Our investigation conveys that the temperature and concentration profiles decay as the nondimensional thermal and concentration relaxation time parameters enhances. On the other hand, it is perceived that concentration boundary layer thickness moderates with the growth of Deborah numbers β1 and β2. Additionally, it is fascinating to find that the concentration profiles decline as the Schmidt number escalates. To sum up, the verdict of the present investigation is that the proficiency of thermal and concentration systems can be enriched by introducing the Cattaneo-Christov heat and mass flux models.

On 2D stratified flow of an Oldroyd-B fluid with chemical reaction: An Application of non-Fourier heat flux theory

This research work explores the double stratified flow of an Oldroyd-B liquid induced by linear stretching surface with first order chemical reaction. Characteristics of heat transfer are investigated by considering non-Fourier heat flux model. Formulation is arranged for variable thermal conductivity. Flux model under consideration is the modified form of Fourier's classical expression which studies the fascinating characteristic of thermal relaxation time. Implementation of appropriate transformations yields ordinary differential systems which are then computed through homotopic procedure. Impacts of various sundry parameters on the non-dimensional velocity, temperature, concentration and Sherwood number are scrutinized. Moreover it is seen that temperature distribution has opposite behavior for thermal relaxation time and variable thermal conductivity parameter.

Poroacoustic waves under a mixture-theoretic based reformulation of the Jordan–Darcy–Cattaneo model

Using mixture theory, we present a reformulation of the Jordan–Darcy–Cattaneo (JDC) poroacoustic model. The one-dimensional (1D) version of the resulting system is then applied to the description of first ‘start-up’ acceleration waves, and then those exhibited under the traveling wave reduction, in a gas that saturates a rigid, porous solid. Results obtained are contrasted with those of the Darcy–Jordan model, the impact of τ, the model’s relaxation time parameter, is assessed, and issues stemming from the acceleration wave analysis performed by Ciarletta et al. (2013), who proposed the original JDC model, are resolved. Also, the weakly-nonlinear Darcy–Jordan model is generalized to include the case τ>0.

A tropical atmosphere model with moisture: global well-posedness and relaxation limit

In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture, which was derived in Frierson et al (2004 Commum. Math. Sci. 2 591–626). We establish the global existence and uniqueness of strong solutions to this system, with initial data in H1, for each fixed convective adjustment relaxation time parameter . Moreover, if the initial data possess slightly more regularity than H1, then the unique strong solution depends continuously on the initial data. Furthermore, by establishing several appropriate ε-independent estimates, we prove that the system converges to a limiting system as the relaxation time parameter ε tends to zero, with a convergence rate of the order . Moreover, the limiting system has a unique global strong solution for any initial data in H1 and such a unique strong solution depends continuously on the initial data if the initial data posses slightly more regularity than H1. Notably, this solves the viscous version of an open problem proposed in the above mentioned paper of Frierson, Majda and Pauluis.

Surface, compressibility and viscometric measurements of binary system containing cationic surfactant with achiral amino acid at different temperatures

In the preset manuscript, we intend to examine the type of solute-solvent interactions present in such system which is valuable to food/pharmaceutical sector. A systematic knowledge of the volumetric properties in conjunction with other thermodynamic properties provides useful information about water-solute interactions. We examine, therefore, surface tension, density, speed of sound and viscosity for binary system contains cationic surfactant cetyltrimetylammonium bromide (CTAB) in aqueous glycine solution (0.2, 0.3 and 0.4) mol/kg at four different temperatures ranging from (298.15 to 313.15) K. The surface tension result indicates the change in critical micelle concentration (CMC) values in the presence of additive. Various thermodynamic and adsorption parameters like surface excess, Γmax, minimum area at air-liquid interface, Amin etc. have been evaluated form surface tension data. The density and speed of sound measurements have been used to calculate the apparent molar volume and adiabatic compression which reveals the kind of interactions present pertaining to hydrophilic-hydrophillic and ion-hydrophillic interactions. In addition, hydrophobic hydration also plays a key role especially at higher surfactant concentration. Viscosity data further strengthen the concept of hydrophobic interactions present in the binary solution taken into consideration the relative viscosity and viscous relaxation time parameters. The effect of temperature and additive for all the calculated parameters has also been discussed in detail.

Modeling the phase change process for a two-phase closed thermosyphon by considering transient mass transfer time relaxation parameter

The method with minimal errors considering transient mass transfer time relaxation parameter for the phase change process is proposed in this study. A model coupled Volume of Fluid (VOF) model, phase change model and continuum surface force model is developed to simulate heat transfer characteristics and phase change process for a two-phase closed thermosyphon. The mass transfer process is implemented by adding User Define Function (UDF) to FLUENT code. The results obtained from this study show that the model with transient mass transfer time relaxation parameter has smaller relative errors (0.27–0.73%) for absolute temperature distributions along the wall of a two-phase closed thermosyphon than the model without transient mass transfer time relaxation parameter (2.01–2.97%). The model with transient mass transfer time relaxation parameter has smaller relative errors for the thermal resistances at evaporation and condensation sections (3.21–4.23% and 2.45–6.78%) than the model without transient mass transfer time relaxation parameter (18.31–21.74% and 15.34–28.25%), respectively. The model developed in this study can also detail the phase change process and therefore can be used to predict heat performance better for different types of heat pipes.

MHD viscoelastic flow and heat transfer over a vertical stretching sheet with Cattaneo-Christov heat flux effects

This paper presents a research for MHD (magnetohydrodynamics) viscoelastic flow and heat transfer over a vertical stretching sheet with velocity slip boundary. The Cattaneo-Christov heat flux model is introduced energy equation, which is used in formulating the relaxation framework of MHD viscoelastic flow. The highly coupled boundary layer governing equations are reduced into local similarity solutions ordinary differential equations by suitable transformation and then solved numerically. The effects of velocity slip number, magnetic number, Prandtl number, mixed convection parameter and relaxation time parameters on velocity and temperature fields are graphically analyzed in detail. Results indicated that the formulated models in this paper can be successfully used to predict the relaxation times transport characteristics of MHD viscoelastic flow and heat transfer.

Squeezed flow subject to Cattaneo–Christov heat flux and rotating frame

This article investigates the unsteady two-dimensional squeezing flow of Jeffrey fluid in a rotating frame. The lower plate of channel is stretched in its own plane while the upper plate squeezed towards the lower plate. Cattaneo–Christov heat flux model is imposed to investigate the characteristics of heat transfer. This model is the modification of classical Fourier's law through thermal relaxation time. Transformation procedure is adopted to obtain the non-linear ordinary differential equations from the fundamental laws of mass, linear momentum and energy. Convergent series solutions are constructed for the resulting problems. Characteristics of various involved parameters on the velocity, temperature and skin friction coefficient are analyzed. It is found that the temperature of fluid decreases for higher thermal relaxation time parameter.

Unsteady MHD Flow of a Dusty Visco-elastic Fluid between Parallel Plates with Exponentially Decaying Pressure Gradient in an Inclined Magnetic Field

The present paper deals with the unsteady laminar flow of an incompressible, electrically conducting dusty visco-elastic fluid between two parallel stationary plates. The flow is caused by an exponentially decaying pressure gradient .A uniform magnetic field is applied on the lower plate at different inclinations. We observe that the motions of the fluid and dust particles are affected by the variation of some significant physical parameters of the visco-elastic fluid. Mass concentration number, time-relaxation parameter, visco-elastic parameter, intensity of the applied magnetic field and time are some of indispensable physical parameters of fluid flow. The governing equations of motion have been solved by analytical method and the results have been discussed with the help of graphs. The velocity is observed to be symmetrical with the centre of the channel of fluid flow as well as of dust particles. The velocity of the fluid particles and that of the dust particles go on decreasing with an increase in the values of mass concentration number, magnetic field intensity, visco-elastic parameter and time whereas the velocity profiles of fluid and dust particles are observed to be increasing with an increase in the time- relaxation parameter.

진동형 히트 파이프에서 튜브의 지름과 개수에 따른 전산 열유동해석

In this paper, heat transfer characteristics of pulsating heat pipes are investigated with the diameter and the number of tubes through the computational analysis of thermal flow. The numerical simulation includes the phase change precess with VOF model using OpenFOAM software. The numerical code is modified for the phase change to occur with saturation temperature. The numerical results are compared with the previous ones to validate the present code. The resonable results have been obtained based on the mass transfer time relaxation parameter considering the density ratio. When the ratio of length to diameter and the number of tubes are on the decrease, the thermal resistances also tends to decrease in the pulsating heat pipes. These numerical results will supply the base line data to design and to manufacture the pulsating heat pipe.

Thermodynamic and Molecular Dielectric Relaxation Studies of Polar–Polar Binary Mixtures Using Time Domain Reflectometry Technique

The complex dielectric spectra of nitrobenzene, 2-butanol and their binary mixtures were measured in the frequency range of 10 MHz–20 GHz at different temperatures using Time Domain Reflectometry. The static permittivities and relaxation times were extracted from the complex dielectric spectra of the pure compounds and binary mixtures by fitting to the Debye model using the least-squares fitting method. The derived static permittivity (e 0) and dielectric relaxation time (τ 0) values were used to calculate various dielectric parameters including the excess dielectric constant, effective Kirkwood correlation factor, excess inverse relaxation time and thermodynamic parameters. Excess dielectric parameters were fitted with the Redlich–Kister type polynomial equation. The result from dielectric analyses confirms the formation of a heterogeneous complex structure by association of unlike molecules. This hetero-molecule interactions produce a electric field in the mixtures and, as a result, the effective dipoles rotate faster. Molecular rotation and dipole reorientation motions in these complex system are discussed in terms of the molar activation entropy and enthalpy. Additionally, the hydrogen bond interaction between solute and solvent were confirmed by FT–IR spectral analysis.

Electron Inertia Effects on the Gravitational Instability under the Influence of FLR Corrections and Suspended Particles

In this paper, we investigate the effects of electron inertia on the gravitational instability of gaseous plasma under the influence of FLR (Finite Larmor Radius) corrections and suspended particles. A general dispersion relation has been derived through relevant linearized perturbation equations. The general dispersion relation is reduced for both longitudinal and transverse mode of propagation. Numerical calculations have been performed to show the effect of various parameters on the growth rate of the gravitational instability. It is found that the simultaneous effect of viscosity, finite conductivity and permeability of the medium does not essentially change the Jeans criterion of instability. From the curves, we find that relaxation time, Stoke drag, viscosity and FLR parameter have a stabilizing effect on the growth rate of instability, but the thermal conductivity and finite electron inertia parameter have a destabilizing effect on the growth rate of instability.