Rheological Analysis of CNT Suspended Nanofluid with Variable Viscosity: Numerical Solution

In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transformations are used to simplify the governing boundary layer equations for nanofluid. This is the first article on the stagnation point flow of CNTs over a stretching sheet with variable viscosity. A well known Reynold's model of viscosity is used. Single wall CNTs are used with water as a base fluid. The resulting nonlinear coupled equations with the relevant boundary conditions are solved numerically using shooting method. The influence of the flow parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are explored and presented in forms of graphs and interpreted physically.     

Temperature dependences of kinematic viscosity of bismuth,lead, and their mutual solutions

Measurement results for temperature dependences of kinematic viscosity in Bi-Pb melts are presented. Measurements were carried out in the temperature range between liquidus and 1400 K. The distinctive feature of experiments was their performance at heating after sample melting and further cooling. On the experimental temperature dependences of kinematic viscosity the values of viscosity at fixed temperature and activation energy of viscous flow have been calculated. Special attention was paid to non-coincidence of the curves obtained at heating and cooling. The specified anomaly is explained by the concept of metastable microcoherence of the studied melts.     

Further results on the variable viscosity with magnetic field on flow and heat transfer to a continuous moving flat plate

The steady, laminar-boundary-layer flow along an isothermal, continuously moving, flat plate is studied taking into account the variation of viscosity with temperature in the presence of a magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. The resulting, governing equations are non-dimensionalized and are transformed using a similarity transformation and then solved numerically by the shooting method. Comparison with previously published work is performed and full agreement is obtained. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter and the Nusselt number is illustrated graphically to show typical trends of the solutions. It is worth pointing out that, when the variation of viscosity with temperature is strong in the presence of the effect of a magnetic field, the results of the present work are completely different from those that studied the same problem in the absence of magnetic field.     

Peristaltic Flow of Shear Thinning Fluid via Temperature-Dependent Viscosity and Thermal Conductivity

In this paper Williamson fluid is taken into account to study its peristaltic flow with heat effects. The study is carried out in a wave frame of reference for symmetric channel. Analysis of heat transfer is accomplished by accounting the effects of non-constant thermal conductivity and viscosity and viscous dissipation. Modeling of fundamental equations is followed by the construction of closed form solutions for pressure gradient, stream function and temperature while assuming Reynold's number to be very low and wavelength to be very long. Double perturbation technique is employed, considering Weissenberg number and variable fluid property parameter to be very small. The effects of emerging parameters on pumping, trapping, axial pressure gradient, heat transfer coefficient, pressure rise, velocity profile and temperature are analyzed through the graphical representation. A direct relation is observed between temperature and thermal conductivity whereas the indirect proportionality with viscosity. The heat transfer coefficient is lower for a fluid with variable thermal conductivity and variable viscosity as compared to the fluid with constant thermal conductivity and constant viscosity.     

Temperature-Dependent Viscosity Effects on Non-Darcy Hydrodynamic Free Convection Heat Transfer from a Vertical Wedge in Porous Media

An analysis is presented to investigate the effect of temperature-dependent viscosity on free convection flow along a vertical wedge adjacent to a porous medium in the presence of heat generation or absorption. The governing fundamental equations are transformed into the system of ordinary differential equations using scaling group of transformations and are solved numerically by using the fifth-order Rung-Kutta method with shooting technique for various values of the physical parameters. The effects of variable viscosity parameter on the velocity, temperature and concentration are discussed. Numerical results for the problem considered are given and illustrated graphically.     

Order parameter dependence of the viscosity coefficients of a biaxial nematic liquid crystal

We derive expressions for the order parameter dependence of the viscosity coefficients of a biaxial nematic liquid crystal by comparing its dissipation function expressed in terms of directors with that expressed in terms of order tensors. The results enable us to identify the dominant flow viscosity coefficients and to compare their temperature variation according to their dependence on the dominant scalar order parameters. By considering different orientations of an external field, we identify three characteristic switching times corresponding to three rotational viscosities, and we estimate the ratio of the switching times of the primary and the secondary directors.     

An elastic,plastic, viscous model for slow shear of a liquid foam

We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material-specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called “quasi-static”) limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.     

Modified Single-Mode Leonov Rheological Equations for Polymer Melts and Solutions

The shear viscosity and the normal stress coefficients are important parameters in the flow of polymer melts and polymer solutions. Based on the Leonov model, modified single-mode rheological equations are presented by introducing relaxation time and temperature functions, and the shear viscosity and the normal stress coefficients are predicted. Without a complex statistical simulation, the experimental data of a low-density polyethylene melt, a poly(ethylene oxide) solution and a mixed decalin/polybutene oil solution were compared to verify the modified equations in very wide range of deformation rates. Furthermore, based on the equations, the relationship between the stress overshoot and the temperature is discussed. In addition, the predicted shear thinning behavior for the modified equations is also compared with other single-mode models.     

Effect of slip boundary condition on flow and heat transfer of a double fractional Maxwell fluid

The purpose of the present paper is to investigate the flow and heat transfer of a double fractional Maxwell fluid with a second order slip model. The fractional governing equations are solved numerically by using the finite difference method. By comparing the analytical solutions of special boundary conditions, the validity of the present numerical method is examined. The effects of the two slip parameters and the fractional parameters on the velocity and temperature distribution are presented graphically and discussed. The results reveal that the fractional Maxwell fluid exhibits a stronger viscosity or elasticity for different fractional parameters, and the oscillation phenomenon will gradually decrease as expected with an increase in slip parameters.     

Structural relaxation and viscous flow in amorphous ZrAlCu

The ternary metallic glass Zr₆₅Al_7.5Cu_27.5 offers a wide temperature range between glass transition temperature and crystallization temperature and is therefore well suited for investigation of the glass transition and the state of the super cooled liquid. The non-linear viscosity change caused by structural relaxation has been measured caused by structural relaxation has been measured using tensile creep experiments on as quenched samples. The increase of viscosity can be described by bimolecular annihilation kinetics of flow defects. The Arrhenius plot of equilibrium viscosity shows a kink at a temperature which seems to be the glass transition temperature. The activation energies of viscous flow below and above that glass transition temperature differ by nearly a factor two. Different microscopic processes responsible for viscous flow in the two regimes of temperature are therefore conceivable. This view is also encouraged by Dynamic-Mechanical-Analysis on relaxed samples, a method to examine the viscoelastic behaviour of glassy materials on different time scales and by recent diffusion measurements on a different system.     

Impact of Internal Heat Source on Mixed Convective Transverse Transport of Viscoplastic Material under Viscosity Variation

This communication addresses the impact of heat source/sink along with mixed convection on oblique flow of Casson fluid having variable viscosity. Similarity analysis has been utilized to model governing equations, which are simplified to set of nonlinear differential equations. Computational procedure of shooting algorithm along with 4 th order Range-Kutta-Fehlberg scheme is opted to attain the velocity and temperature distributions. Impact of imperative parameters on Casson fluid flow, temperature, significant physical quantities such as skin friction, local heat flux and streamlines are displayed via graphs.     

Impact of Internal Heat Source on Mixed Convective Transverse Transport of Viscoplastic Material under Viscosity Variation

This communication addresses the impact of heat source/sink along with mixed convection on oblique flow of Casson fluid having variable viscosity. Similarity analysis has been utilized to model governing equations, which are simplified to set of nonlinear differential equations. Computational procedure of shooting algorithm along with 4th order Range-Kutta-Fehlberg scheme is opted to attain the velocity and temperature distributions. Impact of imperative parameters on Casson fluid flow, temperature, significant physical quantities such as skin friction, local heat flux and streamlines are displayed via graphs.     

Melt Elongation Properties of Linear Low-Density Polyethylene

The melt extensional properties of a linear low-density polyethylene (LLDPE) were measured using melt spinning techniques in a range of temperature varying from 150 to 200°C, and the entry flow method in the capillary extrusion at 170°C was used to investigate the effects of elongation strain rate, temperature, and extrusion velocity in the capillary on the melt elongation stress and viscosity. The melt stretching force at break decreased nonlinearly with a rise of temperature. A low melt elongation viscosity might be beneficial to improve the melt drawability. With the increase of elongation strain rate, the melt elongation stress increased while the melt elongation viscosity decreased nonlinearly. Both melt elongation stress and viscosity decreased with a rise of temperature. Under the experimental conditions, the melt elongation stress and viscosity decreased with an increase of extrusion velocity in the capillary. Moreover, the relationship between the elongation viscosity determined from the entry flow and strain rate was similar to that from the melt spinning flow.     

Review of viscosity prediction models of liquid pure metals and alloys

Viscosity is an important property which could determine the flow liquid metal characteristics and reflect the liquidus structure. Therefore, the existence of an accurate model is necessary to calibrate the experimental measurement value of viscosity. At present, many models have been proposed to estimate the viscosity of pure liquid metal, the temperature dependence of viscosity and the viscosity of multicomponent alloy systems. In this paper, a number of the familiar models are given, and their fundamental modelling theory, model characteristics and applicability are adequately discussed. The general semi-empirical models which have been very successful in predicting the viscosity of pure liquid metal are divided into Andrade and Eyring two branches. The common multivariate melt viscosity prediction models are mostly based on the fundamental molecular theory method, which combines the thermodynamic parameters and achieves good validity. It is expected in the final that the corresponding viscosity prediction model of phase diagram might be more likely to replace the independent general prediction equation in the future.     

Viscosity and activation parameters of viscous flow of sodium cholate aqueous solution

Viscosity, density and electrical conductance of sodium cholate aqueous solution in dilute concentrations are reported. Concentration and temperature effects on the viscosity are discussed. Molar conductance of the salt at infinite dilution is obtained by fitting experimental conductivity in Quint–Viallard equation. Viscosity data is analyzed by Jones–Dole equation, and viscous B-coefficient and activation parameters are evaluated, which shows a strong effect of sodium cholate aggregation on viscosity flow. Our result shows that salt diffusion is characterized by molecular aggregation, and is enhanced progressively as the concentration of bile salt monomer increases.     

Structural relaxation and viscous flow in amorphous ZrAlCu

The ternary metallic glass Zr₆₅Al_7.5Cu_27.5 offers a wide temperature range between glass transition temperature and crystallization temperature and is therefore well suited for investigation of the glass transition and the state of the super cooled liquid. The non-linear viscosity change caused by structural relaxation has been measured caused by structural relaxation has been measured using tensile creep experiments on as quenched samples. The increase of viscosity can be described by bimolecular annihilation kinetics of flow defects. The Arrhenius plot of equilibrium viscosity shows a kink at a temperature which seems to be the glass transition temperature. The activation energies of viscous flow below and above that glass transition temperature differ by nearly a factor two. Different microscopic processes responsible for viscous flow in the two regimes of temperature are therefore conceivable. This view is also encouraged by Dynamic-Mechanical-Analysis on relaxed samples, a method to examine the viscoelastic behaviour of glassy materials on different time scales and by recent diffusion measurements on a different system.     

The Melting Temperature of 99.97 wt.% Al Estimated from Activation Energy for Viscous Flow

The viscous flow phenomenon in molten aluminium and the viscosity, in the vicinity of its melting temperature, was analyzed. When the temperature decreases, both the viscosity and the activation energy for viscous flow increase. This is explained on the basis of the atomic rearrangement due to interatomic interactions prior to the separation of the solid phase. The latter was found to be nonlinear as the temperature is decreased wherein the solid phase is separated from the liquid. The second derivative of the activation energy for viscous flow with respect to temperature was found to show discontinuity in the vicinity of the melting temperature. Thus, the second derivative offers a way of estimating the melting temperature of metals. Our estimations indicate that the break of the second derivative vs. temperature could be observed at 938 K.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the 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 under limiting cases.     

Kinetics of sonic coagulation and precipatation of high disperse aerosols

An equation describing the kinetic process of sonic coagulation is presented which accounts for changes in particule concentration, resulting from changing conditions in the sonic field and dust gas flow. Also the effects of other parameters such as temperature, viscosity and density of the medium were analysed practically to ascertain the optimum and limiting conditions of the analytical equations. The results indicate the ideal economic and practicable operating frequency of the sonic coagulation process.     

The Effect of Melt Vibration on Polystyrene Melt Flowing Behavior During Extrusion

Vibration extrusion (VE) is achieved by superimposing a mechanical vibration on the flowing melt during extrusion. The effect of melt vibration on the melt flow behavior of polystyrene (PS) was studied. The melt flow behavior during conventional extrusion (CE) was studied for comparison. With the application of the melt vibration technology, the melt flow behavior of PS was greatly improved. The melt viscosity during the VE strongly depends on the vibration frequency and vibration amplitude. Extruded at constant vibration amplitude, the melt viscosity decreases sharply with increasing vibration frequency and also does so for increasing vibration amplitude when extruded at a constant vibration frequency. The improved melt flow property is explained in terms of shear-thinning criteria. The effect of melt vibration on the melt flow behavior is also related to the melt temperature and extrusion pressure; the greatest decease in viscosity is obtained at low temperature and low extrusion pressure.