Carreau Fluid Model Research Articles

New Insight into AuNP Applications in Tumour Treatment and Cosmetics through Wavy Annuli at the Nanoscale

The purpose of this study is to probe the peristaltic propulsion of a non-Newtonian fluid model with suspended gold nanoparticles. The base fluid is considered to simulate blood using the Carreau fluid model. We model a small annulus as a tube with a peristaltic wave containing a clot propagating towards the tube wall. An external variable magnetic field is also considered in the governing flow. An approximation for long wavelengths and small Reynolds numbers is employed to formulate the governing flow problem. The resulting nonlinear equations are solved using a perturbation scheme. Series solutions are obtained for the velocity profile, temperature profile, pressure rise and streamlines. The results indicate an enhancement in the temperature profile that can be utilized in eradicating tumour cells.

Numerical investigations on magnetic field modeling for Carreau non-Newtonian fluid flow past an isothermal sphere

In the current study, the effects of radial magnetic field, slip and jump conditions on the steady two-dimensional free convective boundary layer flow over an external surface of an isothermal sphere for an electro-conductive polymer are numerically studied. It is assumed that the studied fluid has a non-Newtonian rheological behavior and follows the Carreau fluid model. In this investigation, the formulation of the Carreau fluid model has been used first time for describing the present boundary layer problem, and then the resulting partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller-Box method. The finding results show that a weak elevation in temperature is accompanied with the increase in the Carreau fluid parameter, whereas a significant acceleration in the flow is computed near the sphere surface. It is shown also that an increase in the thermal slip parameter allows to strongly decrease both the skin friction coefficient and the local Nusselt number. The skin friction coefficient is also depressed with increasing magnetic body force parameter. Moreover, it is observed that an increase in the momentum slip parameter allows to decrease the skin friction coefficient, whereas the local Nusselt number is reduced with the increase in the Carreau fluid parameter. It is found also that the skin friction coefficient is increased with greater stream-wise coordinate, whereas the local Nusselt number is reduced with the increase in this parameter.

Modeling of unsteady non-Newtonian blood flow through a stenosed artery: with nanoparticles

Literature survey related to the nanoparticles reveals that nanofluids are getting popularity in hematological treatment. Development in this direction motivated us to write a theoretical study on unsteady blood motion in stenosed vessel with nanoparticles. Geometry of a stenosed arterial section is being written mathematically by an appropriate geometric expression. The constitutive equation of Carreau fluid model is used to characterize the dynamical behavior of the blood. The rheology of the blood is formulated mathematically by coupled partial differential equations. Similarly, the effects of nanoparticles are incorporated mathematically into governing equations by using Buonjiornio’s formulation. Mild stenotic condition is employed to reduce the two-dimensional differential equations to simple form. Numerical technique is being used to obtain the numerical solution to the existing problem. The obtained simulation reveals that the magnitude of velocity shows an accelerating behavior for Brownian motion parameter and shows deceleration trend on increasing the thermophoresis parameter. Similarly, the instantaneous behavior of blood flow pattern is shown through streamlines.

Carreau fluid flow in a thermally stratified medium with heat generation/absorption effects

In this article theoretical attempt is carried to inspect the flow field characteristics of Carreau fluid model. The fluid flow is achieved by stretching cylindrical surface with no slip condition that is the relative velocity of Carreau fluid particles and cylindrical surface is zero. The role of both temperature stratification and heat generation/absorption are considered with the source of energy equation. The physical illustration of flow model with both temperature stratification and heat generation/absorption effects is translated in terms of partial differential equations through fundamental laws, namely law of conservation of mass, momentum and energy. The obtained partial differential equations are non-linear in nature and it seems difficult to solve them analytically. Therefore the boundary layer approximation is utilized to retain the active parts of flow narrating differential equations. Then to step down the partial differential equations in terms of ordinary differential equations a set of transformations is introduced. The reduced system is solved by shooting method and self-coded algorithm is executed in this regard. The note down observations are offered with the aid of graphs and tables. It is noticed that the Carreau fluid temperature shows decline nature towards the positive values of thermal stratification parameter and heat absorption parameter but it reflects opposite trend for the case of heat generation parameter.

Impact of heat transfer analysis on Carreau fluid-flow past a static/moving wedge

The foremost aspiration of the present endeavor is to investigate the boundary-layer flow of a generalized Newtonian Carreau fluid model past a static/moving wedge. In addition, the effects of heat transfer on the flow field are also taken into account. The governing equations of the problem based on the boundary-layer approximation are changed into a non-dimensional structure by introducing the local similarity transformations. The subsequent system of ODE has been numerically integrated with fifth-order Runge-Kutta method. Influence of the velocity ratio parameter, the wedge angle parameter, the Weissenberg number, the power law index, and the Prandtl number on the skin friction and Nusselt number are analyzed. The variation of the skin friction as well as other flow characteristics has been presented graphically to capture the influence of these parameters. The results indicate that the increasing value of the wedge angle substantially accelerates the fluid velocity while an opposite behavior is noticed in the temperature field. Moreover, the skin friction coefficient for the growing Weissenberg number significantly enhances for the shear thickening fluid and show the opposite behavior of shear thinning fluid. However, the local Nusselt number has greater values in the case of moving wedge. An excellent comparison with previously published works in various special cases has been made.

Peristaltic Pumping of a Generalized Newtonian Fluid in an Elastic Tube

The paper investigates the peristaltic pumping of an incompressible non-Newtonian fluid in an elastic tube with long wavelengths and low Reynolds number approximations. Carreau fluid model is considered for present study to describe the peristaltic flow characteristics of non- Newtonian fluid in an elastic tube. Carreau fluid is a generalized Newtonian fluid which exhibits Newtonian behaviour for and it resembles as a power-law model at higher shear rates. For it exhibits shear-thinning property, i.e., the apparent viscosity reduces with increasing shear rate. The equations governing the fluid flow are solved with usual perturbation expansion by taking Weissenberg number as a perturbation parameter. The expressions for axial velocity, stream function and volume flow rate as function of pressure difference are derived. The effects of various pertinent parameters on variation of flux for a Carreau fluid flow through an elastic tube along with peristalsis are calculated and interpreted through graphs. The pressure rise per wavelength and shear stress distribution for different values of physical parameters are calculated and presented. Trapping phenomenon is presented graphically to understand the physical behaviour of various parameters. The difference in flux variation is examined by two different models of Rubinow and Keller (1972) and Mazumdar (1992). It is observed that in elastic tubes, the flux of Carreau fluid with peristalsis is more when the tension relation is a fifth degree polynomial as compared to exponential curve. When the power-law index or Weissenberg number and without peristalsis, the present results are similar to the observations of Rubinow and Keller (1972). Further, the relation between the function and radius of the elastic tube for both Newtonian, non-Newtonian cases are discussed graphically and these findings are identical with the investigations of Mazumdar (1992). The results observed for the present flow characteristics reports several interesting behaviours that warrant further study of physiological fluids in elastic tubes with peristalsis.

Lattice Boltzmann simulation of polymer melt flow with a low Reynolds number

The lattice Boltzmann method (LBM) has been used in various fluid flow analyses as an alternative to the traditional method of computational fluid dynamics. In the study reported here, the LBM was used to simulate a simple Hele–Shaw melt flow of polymers considering their actual physical properties, whereas the Carreau fluid model was used to evaluate the polymer melt viscosity. Since the Reynolds number of a polymer melt flow is typically quite low due to its high viscosity, which in turn lowers its convergence rate in the LBM, introducing a new density offset method improved that rate. In this paper, cases of simulations with pressure or velocity inlet boundary conditions are discussed in which the density offset method is applied.

SIMULATION ANALYSIS OF BLOOD FLOW IN ARTERIES OF THE HUMAN ARM.

Arteries in the upper limb play important roles in the circulation system of the human body. In particular, the radial artery has received considerable attention in traditional Chinese medicine for thousands of years. Here, a 3D model for the arm arteries has been created uncomplicated, in a Chinese adult's left hand, from the magnetic resonance imaging data, using professional modeling software to restore the basic structure of the arm artery in human body, before being imported to Ansys software for simulation. Blood model has been only simulated, and using the blood density of constant parameter and viscosity using the Carreau fluid model, and using viscous-laminar model of Fluent to obtain the velocity profile, static pressure and shear stress in the brachial, interosseous, ulnar, radial and palmar arch arteries. In particular, the brachial and bifurcations have the high pressure and velocity profiles. The simulation results obtained here are also validated by those published in the literature and proved the ulnar artery prevails over the radial artery as a blood supplier to the vessels in the wrist and hand.

Linear stability of thermocapillary liquid layers of a shear-thinning fluid

The linear stability analysis has been performed for the thermocapillary liquid layers of a shear-thinning fluid. The Carreau fluid model is applied to describe the rheological property. The critical parameters are determined as a function of Prandtl number (Pr), degree of shear-thinning, and gravity level. For linear flow, the shear-thinning effect is destabilizing for small and moderate Pr but increases the stability slightly for large Pr. For return flow, the perturbation kinetic energy concentrates near the surface, and the flow is stabilized when the surface viscosity is used. The streamwise wave is excited at large Pr, and a new mechanism is found at moderate Pr, where the hot spots appear at the bottom of the layer. In the presence of gravity, the viscosity stratification is enhanced and more kinds of different modes are excited. The preferred mode changes to downstream at large Pr while the gravity becomes an important perturbation energy source at small Pr. The shear-thinning effect for the instability mechanism is discussed and the comparisons are made with channel flows.

Empirical resistive-force theory for slender biological filaments in shear-thinning fluids.

Many cells exploit the bending or rotation of flagellar filaments in order to self-propel in viscous fluids. While appropriate theoretical modeling is available to capture flagella locomotion in simple, Newtonian fluids, formidable computations are required to address theoretically their locomotion in complex, nonlinear fluids, e.g., mucus. Based on experimental measurements for the motion of rigid rods in non-Newtonian fluids and on the classical Carreau fluid model, we propose empirical extensions of the classical Newtonian resistive-force theory to model the waving of slender filaments in non-Newtonian fluids. By assuming the flow near the flagellum to be locally Newtonian, we propose a self-consistent way to estimate the typical shear rate in the fluid, which we then use to construct correction factors to the Newtonian local drag coefficients. The resulting non-Newtonian resistive-force theory, while empirical, is consistent with the Newtonian limit, and with the experiments. We then use our models to address waving locomotion in non-Newtonian fluids and show that the resulting swimming speeds are systematically lowered, a result which we are able to capture asymptotically and to interpret physically. An application of the models to recent experimental results on the locomotion of Caenorhabditis elegans in polymeric solutions shows reasonable agreement and thus captures the main physics of swimming in shear-thinning fluids.

Three-dimensional flow analysis of Carreau fluid model induced by peristaltic wave in the presence of magnetic field

This work investigates the impact of magnetohydrodynamics (MHD) on a non-Newtonian peristaltic flow of Carreau fluid in a uniform duct of rectangular cross section. An applied magnetic field is considered whereas the induced magnetic field is taken to be zero here due to small magnetic Reynolds number. Non-Newtonian fluid model is impossible to describe with the help of single constitutive relationship among strain and stress rate. These kinds of constitutive equations give a very complicated mathematical models and thus, mathematicians, physicist, modelers and computer scientist face multiple kinds of problems during the development of numerical and analytical methods. Generally, non-Newtonian fluids are classified into three categories such as the rate type, differential type, and integral type. Carreau fluid model is one of them. The governing nonlinear equations are studied under the considerations of long wavelength and the inertial forces have been ignored. Flow is examined in a wave frame of reference with the velocity of the wave. Such types of flow with magnetic effect are beneficial in drug delivery systems and also helpful to control the flow. Further in microfluidics, magnetohydrodynamics helps to produce a nonpulsating and stable flow in a design of complex microchannel. Analytical solutions of nonlinear partial differential equations are obtained by employing a perturbation method with the combination of eigenfunction expansion method. Numerical computation has been successfully used in order to analyze the pumping characteristic of the flow. Peristaltic pumping is also an engrossing mechanism in a human body that helps to propagate various kinds of biological fluids in different parts of a human body. Velocity behavior is analyzed and presented in both two and three-dimensional profile. Contours are also drawn with the help of streamlines against various involved parameters. Particularly, the obtained results are presented graphically to explore the impact of all the sundry parameters for velocity, pressure gradient, and pressure rise. An excellent comparison is also presented with previously published data to validate the current methodology and results. This problem has multiple numbers of applications in different fields of biomedical engineering including the three-dimensional fluid flow under the influence of elastic waves, blood flow dynamics in a living body.

Nonlinear 3D flow of Casson-Carreau fluids with homogeneous–heterogeneous reactions: A comparative study

Nonlinear convective flow of magneto-Carreau-Casson liquids past a deformable surface under the aspects of heterogeneous and homogeneous reactions is investigated. The present phenomenon also included the interaction of nonlinear radiation, Ohmic and Joule dissipations. At moderate to high temperature, the nonlinear convection and radiation are significant. The governed nonlinear system is illustrated numerically via Runge-Kutta based shooting scheme in the domain [0,∞). Role of significant parameters on flow fields as well as on the fiction factor, heat and mass transportation rates are determined and discussed in depth. Comparison is done for distinct flow fields of Carreau and Casson fluids. It is evaluated that the velocities of Casson liquid are higher in comparison to Carreau fluid model. However, liquid temperature for Casson fluid model is weaker in comparison to Carreau fluid.

Effects of multiple slip on flow of magneto-Carreau fluid along wedge with chemically reactive species

Of concern in this work is an investigation of the heat and mass transfer mechanisms in the presence of first-order chemical reaction for an incompressible flow of non-Newtonian Carreau fluid model past a wedge. The hydromagnetic effects are also incorporated in the present study alongside the momentum, thermal, and solutal slips on the surface of the wedge. In addition to it, the impact of variable thermal conductivity is taken into account to explore the heat transfer characteristics of the flow field. The principal equations corresponding to the physical situation are transformed over to an arrangement of non-dimensional ordinary differential equations through local similarity variables. The numerical solutions of non-dimensional systems are acquired by enforcing fifth-order Runge–Kutta integration scheme and Newton’s method with the assistance of broadly utilized computer software MATLAB. The curiosity of present investigation is that the shear stress and the fluid velocity are substantially raised by the magnetic parameter, while the temperature and concentration profiles are decelerated. Another interesting result is that the thermal slip parameter prompts the lessening of fluid temperature together with the rate of heat transfer. Furthermore, the present computations reveal that the concentration of the chemical reaction is observed to be a decreasing function of the Schmidt number and solutal slip parameter. Moreover, the suitable validations are presented to confirm the achieved results accuracy.

Numerical analysis for peristaltic transport of Carreau-Yasuda fluid with variable thermal conductivity and convective conditions

Peristalsis of Carreau-Yasuda fluid is investigated. Analysis is carried out in the presence of velocity slip and convective boundary conditions. Thermal conductivity of the fluid is taken to be temperature dependent. Lubrication analysis is used in the formulation of the problem. Resulting nonlinear system of equations is solved numerically. Impact of embedded parameters on the quantities of interest is examined through graphs and tables. Comparison of the behavior of the Carreau-Yasuda, Carreau and Newtonian fluid models is presented. Results show that the heat transfer rate at the wall for the Carreau fluid model is large when compared with the Newtonian or the Carreau-Yasuda fluid model. Also the heat transfer rate at the wall decreases with increase in the velocity slip and variable thermal conductivity parameters. Further, an increase in the Biot number reduces the fluid temperature by a considerable amount.

Effects of MHD and wall properties on the peristaltic transport of a Carreau fluid through porous medium

This work concerns the peristaltic flow of a Carreau fluid model through porous medium under combined effects of MHD and wall properties. The assumptions of Reynolds number and long wavelength is investigated. The flow is investigated in a wave frame of reference moving with velocity of the wave. The perturbation series in terms of the Weissenberg number (We <1) was used to obtain explicit forms for velocity field and stream function. The effects of thermal conductivity, Grashof number, Darcy number, magnet, rigidity, stiffness of the wall and viscous damping force parameters on velocity, temperature and stream function have been studied.

Carreau fluid model for blood flow through a tapered artery with a stenosis

In present article, we have studied the blood flow through tapered artery with stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Carreau fluid. Carreau fluid is a type of generalized Newtonian fluid. At low shear rate Carreau fluids behaves as a Newtonian fluid n=1 and at high shear rate as power law fluid. For n<1 Carreau fluid gives pseudoplastic(non-Newtonian), or shear-thinning fluids have a lower apparent viscosity at higher shear rates and for n>1 Carreau fluid behaves as Dilatant(non-Newtonian), or shear-thickening fluids increase in apparent viscosity at higher shear rates. All three cases are appropriate for blood flow in arteries because the assumption of Newtonian behavior of blood is acceptable for high shear rate flow, i.e. the case of flow through larger arteries. It is not, however, valid when the shear rate is low as is the flow in smaller arteries and in the downstream of the stenosis. It has been pointed out that in some diseased conditions, blood exhibits remarkable non-Newtonian properties. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shear stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Analytical solutions has been evaluated for velocity, resistance impedance, wall shear stress and shear stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: Dual solutions

Present analysis is carried out to study the two-dimensional stagnation-point flow of an in-compressible Carreau fluid toward a shrinking surface. The formulation of the Carreau fluid model has been developed first time for boundary layer problem of shrinking sheet and the governing partial differential equations are rehabilitated into ordinary differential equations using similarity transformations. The simplified nonlinear boundary value problem is solved by Runge-Kutta method after converting into the system of initial value problem using shooting method. Dual solutions are obtained graphically and results are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients are also computed.

Effects of Nanofluid on Peristaltic Flow of a Carreau Fluid Model in an Inclined Magnetic Field

In the present article we talk about the influence of a nanofluid on the peristaltic flow of a Carreau fluid model in the presence of an inclined channel and magnetic field. The mathematical modeling of the proposed problem is given for the two‐ dimensional and directional flow. The governing highly nonlinear coupled equations are simplified by means of the assumptions of long wavelength and low Reynolds number approximation. The solutions of the simplified coupled nonlinear equations are calculated using an analytical approach. At the end, graphical results are displayed to show the effects of various emerging parameters of interest. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 368–383, 2014; Published online 3 October 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21082

A robust simulation of Direct Drive Friction Welding with a modified Carreau fluid constitutive model

The subject of this paper is the presentation of a holistic, fully-temperature-coupled simulation of Direct Drive Friction Welding (DDFW) based on the modified Carreau fluid model. The main motivation therein is the consistent and stable prediction of suitable process parameters, which is still the major problem in adopting Rotary Friction Welding (RFW) processes to new pairs of weld partners at industrial applications.The Carreau type fluid constitutive equation is derived from a Norton–Bailey law wherein the temperature dependency is accounted for by a Johnson–Cook power approach. Its main benefit is the stable and robust simulation of the process and the physical palpability of the utilized material parameters. Using a special element formulation on the general axisymmetric frame in conjunction with an Augmented Lagrange bulk viscosity term, a purely displacement based form of the numerical solution procedure is applicable. A penalty contact approach together with a regularized friction law allow for an efficient determination of the interface pressure and friction forces. The model’s performance is demonstrated by means of a test problem highlighting the potential of adopting it to industrial applications later on.

A Theoretical and Numerical Study of an Additional Viscosity Term in a Modified Elasto-Plastic Friction Model for Wet Friction Clutch Simulations

This paper deals with a theoretical and numerical study of various viscosity terms in the modified elasto-plastic friction model and their influence on the resulting friction force-torque, transmitted through the contact of the friction clutch. Various simple viscous definitions for fluids considering shear rate dependent viscosity were investigated. The Carreau fluid model was chosen as a basis for the research, since it can describe Newtonian, dilatant, and pseudo plastic fluids. In addition to theoretical investigations, numerical simulations under realistic friction clutch operation conditions were carried out. The results were compared to the results of a validation case for a dry friction clutch simulation using the modified elasto-plastic friction model. This research showed significant differences between various viscosity definitions and revealed the drawbacks of such approach, were simple viscous models were used. In addition to viscosity, calculating the heat generated due to friction and its influence on the contact temperatures are discussed briefly. The basic theory and equations are given along with the directions for future work. The requirements for an accurate temperature calculation in the friction contact are outlined.