Maxwell Parameter Research Articles

New V control chart for the Maxwell distribution

ABSTRACTControl charts have been popularly used as a user-friendly yet technically sophisticated tool to monitor whether a process is in statistical control or not. These charts are basically constructed under the normality assumption. But in many practical situations in real life this normality assumption may be violated. One such non-normal situation is to monitor the process variability from a skewed parent distribution where we propose the use of a Maxwell control chart. We introduce a pivotal quantity for the scale parameter of the Maxwell distribution which follows a gamma distribution. Probability limits and L-sigma limits are studied along with performance measure based on average run length and power curve. To avoid the complexity of future calculations for practitioners, factors for constructing control chart for monitoring the Maxwell parameter are given for different sample sizes and for different false alarm rate. We also provide simulated data to illustrate the Maxwell control chart. Finally, a real life example has been given to show the importance of such a control chart.

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

The present study examines the effect of induced magnetic field and convective boundary condition on magnetohydrodynamic (MHD) stagnation point flow and heat transfer due to upper-convected Maxwell fluid over a stretching sheet in the presence of nanoparticles. Boundary layer theory is used to simplify the equation of motion, induced magnetic field, energy and concentration which results in four coupled non-linear ordinary differential equations. The study takes into account the effect of Brownian motion and thermophoresis parameters. The governing equations and their associated boundary conditions are initially cast into dimensionless form by similarity variables. The resulting system of equations is then solved numerically using fourth order Runge-Kutta-Fehlberg method along with shooting technique. The solution for the governing equations depends on parameters such as, magnetic, velocity ratio parameter B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, reciprocal of magnetic Prandtl number A, the thermophoresis parameter Nt, and Maxwell parameter β.The numerical results are obtained for velocity, temperature, induced magnetic field and concentration profiles as well as skin friction coefficient, the local Nusselt number and Sherwood number. The results indicate that the skin friction coefficient, the local Nusselt number and Sherwood number decrease with an increase in B and M parameters. Moreover, local Sherwood number -ϕ′(0) decreases with an increase in convective parameter Bi, but the local Nusselt number -θ′(0) increases with an increase in Bi. The results are displayed both in graphical and tabular form to illustrate the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.

Stagnation point flow of Maxwell fluid towards a permeable surface in the presence of nanoparticles

Analysis has been carried out to study the stagnation point flow of Maxwell fluid towards a permeable stretching sheet in the presence of nanoparticles. Using suitable transformations, the governing partial differential equations are first converted to ordinary one and then solved numerically by fourth–fifth order Runge–Kutta–Fehlberg method with MAPLE. The flow and heat transfer characteristics are analyzed and discussed for different values of the parameters. Present work reveals that the velocity increases whereas the temperature and concentration decrease with the increase of Maxwell parameter. The thermal and concentration boundary layer thickness decreases with velocity ratio, Lewis number, Prandtl number suction, Brownian motion and thermophoresis parameters. Comparison with known results for Newtonian fluid flow is found an excellent agreement.

Interfacial Micromechanics Assessment of Classical Rheological Models. I: Single Interface Size and Viscosity

AbstractCreep functions are often represented by “rheological models” consisting of springs and dashpots, while the actual microscopic origins of creep, such as micro-sliding along interfaces, has only recently been explicitly considered in a continuum mechanics framework. The question arises whether formal analogies between the former and the latter can be derived: This question is answered here for the rheological models of the Kelvin-Voigt and Maxwell type. Thereby, it appears a full analogy between shear stresses and strains acting on the rheological models, and those acting on a micromechanical representative volume element consisting of an elastic solid matrix with embedded viscous interfaces, whereby the respective viscosity arises from layered polar fluids absorbed at these interfaces. The corresponding Kelvin-Voigt parameters are much simpler and more intuitively related to the micromechanical quantities, when compared to the Maxwell parameters. More specifically, rheological spring parameters ar...

In-situ measurement of viscoelastic properties of fresh cement paste by a microrheology analyzer

A microrheology analyzer was adapted to in-situ follow the development of viscoelastic properties of fresh cement pastes (FCPs) for the first time. It enables a non-disturbing measurement on the FCPs through monitoring the mean square displacement of cement particles, which gives an insight into the elastic and viscous properties of materials from a microstructural point of view. Various parameters including elastic index, macroscopic viscosity index, storage modulus, loss modulus and Maxwell parameters were obtained to quantitatively analyze the viscoelastic properties of FCPs. Results indicate that these parameters show a progressive increase with time at first and then stay stable. The incorporation of superplasticizer significantly decreases these parameters and their growth rates. Moreover, superplasticizer could evidently weaken the elastic feature of the FCP due to its effects of improving the dispersion of cement grains and retarding cement hydration. The effects of superplasticizer are more pronounced at lower water to cement ratio.

Interfacial Micromechanics Assessment of Classical Rheological Models. II: Multiple Interface Sizes and Viscosities

AbstractCreep functions are often represented by “rheological models” consisting of springs and dashpots, while the actual microscopic origins of creep, such as micro-sliding along interfaces, has only recently been explicitly considered in a continuum mechanics framework. The question arises whether formal analogies between the former and the latter can be derived: This question is answered here for the rheological models of the Kelvin-Voigt and Maxwell type. Thereby, it appears a full analogy between shear stresses and strains acting on the rheological models, and those acting on a micromechanical representative volume element consisting of an elastic solid matrix with embedded viscous interfaces, whereby the respective viscosity arises from layered polar fluids absorbed at these interfaces. The corresponding Kelvin-Voigt parameters are much simpler and more intuitively related to the micromechanical quantities, when compared to the Maxwell parameters. More specifically, rheological spring parameters ar...

An approach for dynamic stiffness evaluation in asphalt concrete

Stiffness modulus is a fundamental parameter for fatigue evaluation in asphalt concrete (AC). It is evaluated with different considerations like static or dynamic loading, elastic or visco-elastic material etc. Asphalt being visco-elastic and fatigue being due to dynamic loading, the modulus parameter happens to be time dependent complex variable. This is named as complex modulus (E∗) and the absolute value of E∗ is known as dynamic stiffness modulus (|E∗|). The present paper focuses on the development of a theoretical approach for E∗ and |E∗| based on principles of linear visco-elasticity. The expression of |E∗| and phase angle (ψ) for generalized Maxwell model under constant strain amplitude sinusoidal loading has been derived. It is seen that both |E∗| and ψ as function of time (t) follow cyclic variation with exponential decay due to viscous effect. Numerical analysis has been performed using Maxwell parameters (under relaxation condition) of AC at 10°C and -20°C. It is observed that |E∗| and ψ variations with time are significantly different at different temperatures. Their rate of decay depends upon the relaxation time of mix. The present work also explores the evaluation of dynamic modulus, while considering decay due to material damage.

Dynamic finite element simulations of composite stiffened panels with a transverse-isotropic viscoelastic energy dissipation model

This paper presents a methodology for predicting the damped response and energy dissipation of laminated composite structures, subjected to dynamic loads. Starting from simple coupon tests to characterize the material, the numerical simulation of damping properties is made possible by a novel linear viscoelastic model that has been developed and implemented in the finite element code B2000++. A nonlinear optimization procedure is adopted to fit experimental data and define the exponential Maxwell parameter model. To illustrate the potentialities of the method, the post-buckling analysis of a relatively complex aeronautical panel is presented, accounting not only for geometric nonlinearities, but also for viscoelastic effects. The results illustrate the effects due to material dissipation, their relation to the effects of inertia, and the influence of geometric imperfections on the response of the panel.

Unsteady flow of Maxwell fluid in the presence of nanoparticles toward a permeable shrinking surface with Navier slip

A detailed study on the problem of unsteady boundary layer flow and heat transfer of an upper-convected Maxwell fluid in the presence of nanoparticles over a permeable shrinking sheet with wall mass transfer is presented. In contrast to the conventional no-slip condition at the surface, Navier’s slip condition is applied at the surface. By use of a similarity transformation, the partial differential equations are reduced to a system of ordinary differential equations which is then solved numerically with shooting technique. The numerical results pertaining to the present study indicate that dual solutions exist for negative values of the unsteadiness parameter (A). It results in from the stability analysis that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically realizable. It is also found that as the Maxwell parameter (β) and velocity slip parameter (δ) increase, the range of the unsteadiness parameter (A) for which the solution exists gradually increases. The local Nusselt number and the local Sherwood number increase with the increase in the values of Maxwell parameter (β) and velocity slip parameter (δ). Furthermore, the effects of different physical parameters on the flow, temperature and concentration profiles are shown graphically and discussed in details.

Physicochemical and textural properties of corn starch gels: Effect of mixing speed and time

The influence of mixing speed (15, 150 and 350 rpm) and heating time (10, 30 and 45 min) at 95 °C on physicochemical and textural properties of corn starch gels was investigated. The gels prepared at 15 rpm and 10 min had the highest hardness, cohesiveness and gumminess values whilst the gels prepared at 350 rpm had the lowest values for these parameters. Maxwell parameters showed that with increasing mixing speed and heating time, starch gels became smoother due to the depolymererisation of starch biopolymers as confirmed by intrinsic viscosity results. SEM images indicated that with increasing time and speed of mixing, air cells of sponge-like structures became larger. The results showed that the mixing speed and time determine the final textural properties of corn starch gels and therefore, to achieve optimum product consistency, it is required to control these two factors during starch pasting.

Large amplitude oscillatory shear and Fourier transform rheology analysis of branched polymer melts

In this paper, the predictions of the Pompom constitutive model in medium and large amplitude oscillatory shear (LAOS) are examined using Fourier transform rheology (FTR). FTR is commonly used in combination with small amplitude oscillatory shear to fit linear Maxwell parameters to dynamic moduli, and in this paper, this process is expanded to larger strain amplitudes and to further terms in the Fourier series. For both small and large amplitudes, these higher harmonics are dependent on the nonlinear Pompom parameters and the Pompom parameter space is explored to see how experimental oscillatory shear data can infer molecular detail. In the regime of small and medium strain amplitude, there exists an asymptotic solution to the Pompom equations which depends only on the ratio of the orientation and stretch relaxation times, τb and τs. This asymptotic solution is found to be accurate up to strains of order unity and the branching priority, q, only affects the stress response at larger strains. The Pompom parameters fitted to extensional data are compared to LAOS data for three materials; two lightly branched metallocene catalyzed high density polyethylenes and a densely branched low density polyethylenes. In general, the Pompom model performs well in LAOS but tends to over predict experimental results at high strain amplitudes.

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell (UCM) model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration (suction) and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration (suction) and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.

Heat transfer characteristics for the Maxwell fluid flow past an unsteady stretching permeable surface embedded in a porous medium with thermal radiation

An unsteady boundary layer flow of a non-Newtonian fluid over a continuously stretching permeable surface in the presence of thermal radiation is investigated. The Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained. The transformed boundary layer equations are then solved numerically by the shooting method. The flow features and heat transfer characteristics for different values of the governing parameters (unsteadiness parameter, Maxwell parameter, permeability parameter, suction/blowing parameter, thermal radiation parameter, and Prandtl number) are analyzed and discussed in detail.

Influence of Internal Heat Generation/Absorption, Thermal Radiation, Magnetic Field, Variable Fluid Property and Viscous Dissipation on Heat Transfer Characteristics of a Maxwell Fluid over a Stretching Sheet

The present study investigates the effects of internal heat generation/absorption, thermal radiation, magnetic field, and temperature-dependent thermal conductivity on the flow and heat transfer characteristics of a Non-Newtonian Maxwell fluid over a stretching sheet. The upper convected Maxwell fluid model is used to characterize the nonNewtonian fluid behavior. Similarity solutions for the governing equations are obtained with prescribed surface temperature (PST) and/or with prescribed surface heat flux (PHF). Numerical solutions for the governing equations subject to the appropriate boundary conditions are obtained by a finite difference scheme known as Keller-Box method. The numerical results thus obtained are analyzed for the effects of the several pertinent parameters namely, the Maxwell parameter, the magnetic parameter, the temperature-dependent thermal conductivity parameter, the heat source/sink parameter, the Prandtl number, the Eckert number, and the thermal radiation parameter on the flow and heat transfer fields. Results for the velocity and temperature fields, skin friction, and Nusselt number are shown through graphs. It is observed that the thermal boundary layer thickness increases with increasing values of the elasticity parameter and the magnetic parameter; however it decreases with the Prandtl number.

Numerical Solution for the Effect of Variable Fluid Properties on the Flow and Heat Transfer in a Non-Newtonian Maxwell Fluid over an Unsteady Stretching Sheet with Internal Heat Generation

This article looks at the flow and heat transfer in the unsteady two-dimensional boundary layer of a non-Newtonian Maxwell fluid over a stretching sheet in the presence of variable fluid properties and internal heat generation. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved numerically, by using the appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary-value problem is based on applying the Chebyshev spectral method over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, heat generation parameter, Maxwell parameter, and Prandtl number on the flow and temperature profiles, as well as on the local skin-friction coefficient and the local Nusselt number, are presented and discussed. Comparison of numerical results is made with the earlier published results in limiting cases. A special attention is given to the effect of the viscosity parameter, thermal conductivity parameter, and heat generation parameter on the velocity and temperature fields above the sheet.

Unsteady MHD boundary layer flow of an upper convected Maxwell fluid past a stretching sheet with first order constructive/destructive chemical reaction

The mass transfer of unsteady two-dimensional flow of MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of first order constructive/destructive chemical reaction is presented. Upper convected Maxwell (UCM) fluid model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions the governing partial differential equations are transformed to ordinary differential equations and are then solved numerically by shooting method. The flow field and mass transfer are significantly influenced by the governing parameters. The results show that fluid velocity initially decreases with increasing unsteadiness parameter (0 to 0.3) and concentration decreases significantly due to unsteadiness. The effect of increasing values of the Maxwell parameter (0 to 0.4) is to suppress the velocity field. The concentration is enhanced with increasing Maxwell parameter. The fluid velocity decreases with increasing magnetic parameter (0 to 0.3). DOI: http://dx.doi.org/10.3329/jname.v9i2.12541 Journal of Naval Architecture and Marine Engineering 9(2012) 123-133

Upper-Convected Maxwell Fluid Flow over an Unsteady Stretching Surface Embedded in Porous Medium Subjected to Suction/Blowing

Unsteady two-dimensional flow of a Maxwell fluid over a stretching surface in a porous medium subjected to suction/blowing is investigated. The upper-convected Maxwell fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of similarity transformations, the boundary layer equation corresponding to the momentum equation is transformed to an ordinary one and then solved numerically by the shooting method. The flow characteristics for different values of the governing parameters are analyzed and discussed in detail. The fluid velocity initially decreases with increasing unsteadiness parameter. Also, it is found that the fluid velocity decreases with increasing permeability parameter. The effect of increasing values of the Maxwell parameter is to suppress the velocity field. Due to suction, the fluid velocity is found to decrease in the boundary layer region.

Unsteady flow of a Maxwell fluid over a stretching surface in presence of chemical reaction

An analysis is presented for unsteady two-dimensional flow of a Maxwell fluid over a stretching surface in presence of a first order constructive/destructive chemical reaction. Using suitable transformations, the governing partial differential equations are converted to ordinary one and are then solved numerically by shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. Fluid velocity initially decreases with increasing unsteadiness parameter and concentration decreases significantly due to unsteadiness. The effect of increasing values of the Maxwell parameter is to suppress the velocity field. But the concentration is enhanced with increasing Maxwell parameter.

A Numerical Study of Oscillating Peristaltic Flow of Generalized Maxwell Viscoelastic Fluids Through a Porous Medium

This article presents a numerical study on oscillating peristaltic flow of generalized Maxwell fluids through a porous medium. A sinusoidal model is employed for the oscillating flow regime. A modified Darcy-Brinkman model is utilized to simulate the flow of a generalized Maxwell fluid in a homogenous, isotropic porous medium. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. The numerical and approximate analytical solutions of the problem are obtained by a semi-numerical technique, namely the homotopy perturbation method. The influence of the dominating physical parameters such as fractional Maxwell parameter, relaxation time, amplitude ratio, and permeability parameter on the flow characteristics are depicted graphically. The size of the trapped bolus is slightly enhanced by increasing the magnitude of permeability parameter whereas it is decreased with increasing amplitude ratio. Furthermore, it is shown that in the entire pumping region and the free pumping region, both volumetric flow rate and pressure decrease with increasing relaxation time, whereas in the co-pumping region, the volumetric flow rate is elevated with rising magnitude of relaxation time.

Effects of Transpiration and Internal Heat Generation/Absorption on the Unsteady Flow of a Maxwell Fluid at a Stretching Surface

The effect of transpiration on unsteady two-dimensional flow of an MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of a heat source/sink is investigated. The upper convected Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Using a similarity transformation the governing partial differential equations of the problem are reduced to a system of ordinary differential equations (ODEs), and the ODEs are solved numerically by a shooting method. The flow features and the heat transfer characteristics are analyzed and discussed in detail for several sets of values of the governing parameters. Though the velocity of the fluid initially decreases with increasing unsteady parameter but it increases finally. Quite the opposite is true with the temperature. Furthermore, the velocity of the fluid decreases with an increasing magnetic or Maxwell parameter. But the temperature is enhanced with an increasing Maxwell parameter. It is observed that the effect of the transpiration is to decrease the fluid velocity as well as the temperature. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.