Carreau-Yasuda Research Articles

Integrated artificial intelligence and non‐similar analysis for forced convection of radially magnetized ternary hybrid nanofluid of Carreau‐Yasuda fluid model over a curved stretching surface

AbstractThe current study investigates the boundary layer flow of Carreau‐Yasuda (C‐Y) ternary hybrid nanofluid model in a porous medium across curved surface stretching at linear rate under the influence of applied radial magnetic field. , and are nanoparticles and ethylene glycol is considered as base fluid. The effects of viscous dissipation and ohmic heating are present in the energy equation. The governing partial differential equation (PDEs) is nondimensionalized using non‐similarity transformations. They can be treated as ordinary differential equations (ODEs) using local non‐similarity method and solutions are obtained via bvp4c MATLAB tools. The results are evaluated by introducing computational intelligence approach utilizing the AI‐based Levenberg–Marquardt scheme with a backpropagation neural network (LMS‐BPNN) to investigate flow stability. The authors intend to use AI‐based LMS‐BPNN is to optimize the behavior of the hybrid nanofluid (HNF) flow of Carreau‐Yasuda fluid across a stretching curved sheet. Initial/reference solutions are obtained through bvp4c function (an embedded MATLAB function designed to solve systems of ODEs) by systematically adjusting input parameters as demonstrated in Scenarios 1–5. There are three options to divide the numerical data: 80% for training, 10% for testing, and an additional 10% for validation. The LMS‐BPNN is used for approximate solutions of Scenario 1–5. The efficiency and reliability of LMS‐BPNN are validated through fitness curves based on correlation index (R), error, and regression analysis. The velocity and temperature profiles asymptotically satisfy boundary conditions of Scenario 1–5 with LMS‐BPNN.

Viscous dissipation and Joule heating in case of variable electrical conductivity Carreau–Yasuda nanofluid flow in a complex wavy asymmetric channel through porous media

This paper focuses on flow structures and thermal fields of the Carreau–Yasuda (CY) nanofluid model through a two-dimensional, wavy, complicated vertical asymmetrical conduit filled with porous elements. Formulations of the viscous dissipation in the case of CY nanofluids are derived and nonlinear radiation flux as well as joule heating are examined. Buongiorno’s nanofluid approach, which involves Brownian motion and thermophoresis aspects is considered. The electrical conductivity of the suspension is considered as a variable where it depends upon the ambient temperature and concentration distributions and the Joule heating impacts are not neglected. The approach of solving the problem is contingent upon converting the system to dimensionless form then the lubrication approach with low magnetic Reynold numbers is applied. Numerical solutions are found for the resultant system, and wide ranges are considered for Weissenberg number We, non-Newtonian parameter n and Darcy number [Formula: see text], namely, [Formula: see text], [Formula: see text] and [Formula: see text], respectively. The major results indicated that gradients of the pressure are higher in case of shear thickening [Formula: see text] comparing to in the instance of shear thinning [Formula: see text]. Also, the velocity is enhanced, close to the channel’s lowest portion, as the Weissenberg number is growing. The variable electrical conductivity gives a higher mass transfer rate compared to the constant property.

Scrutiny of MHD impact on Carreau Yasuda (CY) fluid flow over a heated wall of the uniform micro-channel

The Carreau-Yasuda model is a useful rheological tool for describing complex fluid flow behavior, especially those involving non-Newtonian fluids. This is significant because it allows for a more accurate depiction of fluids with non-linear connections between shear stress and shear rate. This research aimed to examine the effects of slip on the peristaltic transport of a magnetized Carreau–Yasuda (CY) fluid in a uniform channel where the fluid characteristics change at a heated wall. Non-dimensionalization of the governing equations was achieved by assuming a large wavelength and a low Reynolds number and then solving the resulting coupled equations with appropriate boundary conditions and mathematical "ND Solve" methods. This research looked into the two extremes of shear rate-dependent fluid behavior: shear-thinning (a decrease in viscosity with increasing shear rate) and shear-thickening (an increase in viscosity with increasing shear rate). The model can also predict Newtonian and Carreau fluid behaviors. Critical parameters such as velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number were displayed visually and tabulated in the study's results. In addition, the study used the stream function method to investigate the peristaltic motion of the bolus, uncovering that magnetic effects can decrease bolus size due to their substantial influence on apparent viscosity, with shear-thinning behavior proving more influential than shear-thickening behavior. The study further clarifies the dynamic fluctuations in fluid viscosity in response to increasing shear stress, which sheds light on the viscoelastic nature of shear-dependent behavior in a uniform microchannel using the Carreau–Yasuda fluid.

Effect of Cattaneo-Christov heat and mass flux in Carreau-Yasuda tri-nanofluid

The Cattaneo-Christov heat and mass flux theory extends classic models to provide more accurate predictions in situations with instantaneous heat and mass transfer. Herein, an enhancement of heat and mass transfer in Carreau-Yasuda (CY) tri-nanofluid (TNF) over a stretched surface is modeled and studied via generalized conservation laws subjected to Cattaneo-Christov heat and mass flux theory. Silicon carbide (SiC), Aluminum Oxide (Al2O3), and Silver (Ag) are recruited as active nanoparticles in ethylene glycol (C2H6O2), and hired as CY fluid. Based on Finite Element Method (FEM), the code is created and validated for the formulated problems by comparing the current results to the published benchmarks. The computational findings showed that the thickness of the thermal and diffusion boundary layer decreases by increasing the thermal (δ) and diffusion relaxation (δc) parameters. The numerical analysis showed that CY-TNF exerts the largest shear stress on the wall compared to CY mono nanofluid (NF), and CY hybrid nanofluid (HNF). If CY-TNF has to flow over the specific surface, then adequate surface strength must be ensured. Moreover, comparing enhancement in thermal properties of CY-NF, CY-HNF, and CY-TNF revealed that the CY-TNF performs better than CY-HNF and CY-NF. Owing to the highest heat and mass flux, CY-TNF has an optimized ability to transport heat and mass, thus proving to be an efficient fluid for all processes requiring optimized heat and mass flux.

Nonsimilar modeling analysis of Carreau–Yasuda mixed convective flow in a porous medium subjected to Soret and Dufour influences

AbstractThis nonsimilar convection study is about the flow of Carreau–Yasuda (CY) nanofluid model above a vertically extendible surface. Convection in a fluid‐filled permeable medium has given due consideration because of its relevance in a variety of applications, including insulation, relocation of water from geothermal reservoirs, storage of nuclear waste, renewable energy, mechanical engineering, and enhanced oil reservoir recovery. By virtue of linear stretching and buoyancy effects, flow in a stationary fluid is induced along a vertical porous surface. In x‐momentum equation, linear buoyancy in the context of temperature and concentration is taken into consideration. Modeling of energy expression is done in the presence of Dufour and Soret influences. Governing differential system describing convection equations is changed into nonlinear partial differential system (PDE) by implementing applicable nonsimilar transformations. By making use of analytical local nonsimilarity (LNS) technique and bvp4c (numerical finite difference‐based algorithm), the transformed dimensionless nonsimilar structure is simulated numerically. At the end, the alteration of important nondimensional numbers is studied on transport quantities such as temperature, concentration and velocity field. The repercussions of relevant parameters on drag coefficient, Nusselt number and Sherwood number have been tabulated. Numerical simulations of nonsimilar model suggests that the velocity profile reduces due to rise in the values of Weissenberg number, porosity and suction parameter. The temperature profile is increased in comparison with the higher estimates, Eckert, and Dufour numbers. Because of larger values of Soret and Prandtl number, an increase in concentration profile is seen. Friction coefficient and Nusselt number increases with respect to higher estimations of porosity parameter, Weissenberg number and Prandtl number respectively, whereas they decrease against Dufour and Eckert variations.

Rheological Modeling of 7075 Aluminum Alloy Semi-Solid Slurry and its Application in the Simulation of SEED Rheocasting Process

Rheocasting technology has been successfully applied to produce aluminum alloy parts of automobile and communication equipment. However, its application scope is still limited. One reason is that the strength of the applied alloys is limited. In recent years, lots of researchers have tried to use 7075 aluminum alloy in the rheocasting process because this alloy has excellent mechanical properties. In this work, the rheological behavior of 7075 aluminum alloy semi-solid slurry is studied through shear stress-controlled test and shear rate-controlled test. Then the constitutive parameters in Power-Law (PL) model or Carreau-Yasuda (CY) model of non-Newtonian fluid are determined. The models are used to simulate the flow behavior of 7075 aluminum alloy semi-solid slurry in Swirled Enthalpy Equilibration Device (SEED) rheocasting process. The simulation results indicate that the CY model derived from the shear rate sweep test is more suitable for simulating the flow behavior of 7075 aluminum alloy semi-solid slurry during rheocasting than the other models.

Numerical study of Cattaneo‐Christov heat transfer in MHD Carreau‐Yasuda hybrid nanofluid subjected to Buoyancy force

AbstractHybrid nanofluids (HNFs) have potentials applications in automotive industry, heating and cooling systems, biomedical and other fields due to their ability to introduce higher thermal conductivity than standard nanofluids. The purpose of this study is to investigate and compare the thermal transport performance (in the presence of buoyancy force) of two sets of HNFs. The hybrid nanoparticles which is the combination of titanium carbide and aluminium oxide, and the combination of titanium carbide‐copper oxide are taken into account. Both types of hybrid nanoparticles are dispersed in as a subjective fluid over a vertical nonlinear stretching sheet embedded in a porous medium. This will be the first study on the MXene base material , making it possible for MXene‐based materials to enter the fluid dynamics field. Further, MXene material as heat transporting material is studied less and much more is needed for explore its various aspect. The specific combination of , and is considered because of their promising thermophysical and thermal transport properties. Moreover, considered combination of nanoparticles and the base fluid form a mixture which has thermal relaxation characteristics due to which its deviates from classical Fourier law of heat conduction. Therefore, instead of conventional Fourier's law of heat conduction, the non‐Fourier law of heat conduction is used to formulate the energy equation. It is first time that fhe finite element of method (FEM) is used for such a coupled and nonlinear complex problems of computational fluid dynamics (CFD). The numerical and graphical impacts of magnetic fields, Grashof number, permeable parameter, and thermal relaxation time parameter on velocity, and heat transport are investigated by applying FEM on formulated boundary value problems. In each studied system, increasing the Hartmann number causes an increase the skin friction coefficient and a decrease in the Nusselt number. Moreover, by increasing the thermal relaxation parameter, the temperature of the fluid decreases significantly. The velocity of the modified nanofluids is directly proportional to the Grashof number. The thermal boundary layer thickness (TBLT) and momentum boundary layer thickness (MBLT) of Carreau‐Yasuda (CY)‐HNF (Set II) is greater than CY hybrid nanofluid (CY‐HNF) (Set I) and CY‐Nanofluid (NF), respectively. We believe that the current research work provides new insights to improve the heat transport of nanofluid using appropriate combination of hybrid nanoparticles for practical application.

Double diffusion Forchheimer flow of Carreau-Yasuda nanofluid with bioconvection and entropy generation: Thermal optimized analysis via non-Fourier model

The entropy generation phenomenon is important in thermodynamic systems, chemical engineering, industrial systems, reducing the energy consumptions and optimizing the resource utilization. Owing to such motivated applications, aim of current research is to present the applications entropy generation phenomenon in double diffusion flow Carreau-Yasuda nanofluid due to bidirectional stretched surface. The rheology of non-Newtonian fluid is observed by using the Carreau-Yasuda (CY) nonlinear model. The analysis is further supported with suspension of microorganisms with Carreau-Yasuda nanofluid. The formulated model is extended by entertaining the viscous dissipation, thermal radiation and activation energy consequences. The inertial effects are supported with Darcy Forchheimer approach. Additionally, non-Fourier and Fick theories are implanted to observe the thermal phenomenon. The equations resulted from the given model are analytically entertained via homotopy analysis scheme. The physical insight of thermal model is graphically presented. Moreover, the streamlines are plotted for flow model. An enhancing outcomes for entropy generation phenomenon are noted due to diffusion parameter and magnetic parameter. Moreover, the optimized phenomenon also increases due to Brinkman number.

Interaction of variable diffusion coefficients with electrokinetically regulated peristalsis of Carreau-Yasuda nanofluid

In this analysis, the interaction of variable diffusion coefficients with electrokinetically modulated peristaltic motion of a radiative Carreau-Yasuda (CY) nanofluid is communicated. Here, ethylene glycol is used as the base fluid, and graphene nanoplatelets are considered nanoparticles. Unlike many existing studies, the thermophoretic diffusion term appearing in the equation of temperature and concentration is considered a variable term instead of manipulating their average values to obtain a more precise estimation of the conduct of the nanofluid. The Carreau-Yasuda (CY) model is considered to represent the non-Newtonian features of nanofluids. A mathematical model is developed under the effects of Joule heating, variable thermal conductivity, mixed convection, thermal radiation, electric field, Brownian motion, viscous dissipation, magnetic field, and thermophoresis assumptions. The entropy equation involving a variable diffusion coefficient and thermal conductivity is constructed using the second law of thermodynamics. The acquired dimensionless equations are numerically resolved with the help of built-in function. The graphical results indicate that due to Joule heating characteristics, the temperature profile increases. Manipulation of radiation and thermal conductivity parameters can improve the thermal efficiency and productivity of the system. An electroosmotic parameter causes an augmentation in the Bejan number. The nanofluid flow decreases at a higher electroosmotic velocity. The nanofluid chosen makes it possible to envisage industrial applications, for example in the field of heat extraction, without compromising mechanical performance.

Energy transmission through carreau yasuda fluid influenced by ethylene glycol with activation energy and ternary hybrid nanocomposites by using a mathematical model

The current study aims to assess the augmentation of energy transmission in the presence of magnetic dipole through trihybrid Carreau Yasuda nanofluid flow across a vertical sheet. The rheological properties and thermal conductivity of the based fluids are improved by framing an accurate combination of nanoparticles (NPs). The trihybrid nanofluid (Thnf) has been synthesized by the addition of ternary nanocomposites (MWCNTs, Zn, Cu) to the ethylene glycol. The energy and velocity conveyance has been observed in the context of the Darcy Forchhemier effect, chemical reaction, heat source/sink, and activation energy. The trihybrid nanofluid flow across a vertical sheet has been accurately calculated for velocity, concentration, and thermal energy in the form of a system of nonlinear PDEs. The set of PDEs is reduced to dimensionless ODEs by using suitable similarity replacements. The obtained set of non-dimensional differential equations is numerically computed through the Matlab package bvp4c. It has been perceived that the energy curve enhances by the influence of heat generation factor and viscous dissipation. It is also noted that the magnetic dipole has a momentous contribution to raising the transmission of thermal energy of trihybrid nanofluid and declines the velocity curve. The inclusion of multi-wall carbon nanotubes (MWCNTs), zinc (Zn), and copper (Cu) nano particulates to the base fluid “ethylene glycol”, augments the energy and velocity outlines.

Thermodynamic analysis for peristaltic flow of Carreau-Yasuda magneto nanofluid through a porous medium

Thermodynamic analysis for mixed convective peristaltic transportation of Carreau–Yasuda (CY) magneto nanofluid is presented. The assumed nanofluid is a mixture of graphene nano-powder and ethylene glycol. The Carreau–Yasuda model is considered to represent the non-Newtonian features of nanofluids. A mathematical model is developed under the effects of a porous medium, variable thermal conductivity, Brownian motion, viscous dissipation, magnetic field, thermophoresis, and Ohmic heating assumptions. Mass and heat transfer aspects are also considered. The flow and heat/mass transfer equations were made using Buongiorno’s model of nanofluids. No-slip and zero mass flux boundary conditions are entertained for velocity, thermal, and concentration profiles. A numerical solution via built-in technique is obtained for a coupled system of equations. Graphical outcomes predict that due to Ohmic heating characteristics temperature profile increases. The heat transfer rate at the wall decreases for higher thermal conductivity parameter. The irreversible rate can be controlled by maintaining Darcy’s number. The concentration of nanomaterials increases when the thermophoresis parameter is improved. Fluid velocity is slowed down by enhancing the Hartman number and it improves by enhancing the thermal Grashof number.

Numerical study on the dispersion of hybrid nanoparticles complex rheological liquid media subjected to thermal transport using Carreau-Yasuda model

This study explores the impact of various factors on entropy generation (EG) in non-Newtonian rheological fluid characterized by the Carreau-Yasuda (CY) constitutive model. Methanol is taken as base fluid with shear rate-dependent viscosity. Two types of nanoparticles (NPs) GO and are considered to disperse in methanol. The flow of the mixture over a heated circular pipe is subjected to a radial magnetic field. Mathematical equations are formulated and solved numerically using the finite element method (FEM). The computed solutions are utilized to explore the impact of single-type (), two types of NP (GO and ), magnetic field, Joule heating, and shear rate dependent viscosity on the EG. It is noticed from calculations that in methanol with GO and generates less entropy relative to that generated by methanol with single type NPs (). However, monotonic behavior in the EG in both fluids (GO/methanol and GO–/methanol) versus curvature parameter is noted. Power law index in the constitutive model plays a remarkable role in controling the viscous region in the flow near the vicinity of the pipe.

Numerical investigation of shear-thinning and viscoelastic binary droplet collision

In this work we present a 2D numerical study of the binary collision of viscoelastic drops under surface tension effects. The governing equations for incompressible fluids with free surface are completed with constitutive equations that represent three models for non-Newtonian fluids. We analyze a viscous shear-thinning Carreau–Yasuda (CY) equation and the viscoelastic constitutive models of Oldroyd-B and Phan–Thien–Tanner (PTT). From a computational point of view, the 2D free surface dynamic is handled using the Front-Tracking representation with marker particles, combined with the Marker-And-Cell (MAC) method. In order to discretize the equations, we employ a finite differences scheme. We provide maps of outcomes associated with the categories of Bouncing , Coalescence , and Separation as functions of the dimensionless numbers that govern the problem. In addition to the traditional space defined by the Weber and the impact factor, associated with the collision angle, commonly adopted in Newtonian studies, we explore the power-law index of the CY model, the Weissenberg number in the viscoelastic models, and the extensibility parameter in the PTT model. The transient interface dynamics of the problem is illustrated in a variety of cases. For non-bouncing scenarios, the results show that surface tension and elasticity act to maintain the integrity of the merged drop and avoid Separation . On the other hand, shear-thinning effects induce the Separation outcome. Hence, in the PTT model there are opposite trends associated with elasticity and shear-thinning, what can lead to non-monotonic responses. • Numerical simulations of binary droplets undergoing off-center collisions. • Viscoelastic effects on different post-impact outcomes. • Maps of outcomes associated with the categories of Bouncing, Coalescence , and Separation .

Peristaltic transportation of Carreau–Yasuda magneto nanofluid embedded in a porous medium with heat and mass transfer

Magnetohydrodynamic rheological pumping systems based on biological sources are finding new applications in modern energy systems. These systems combine the electrically conductive properties of flowing fluids with rheological behavior, biological geometry, and propulsion mechanisms. Further improvement of transport characteristics can be achieved with the use of nanofluids. In this study, all these aspects are combined to analyze the heat and mass transfer in mixed convective peristaltic conveyance of Carreau-Yasuda (CY) magneto nanofluid with mixture of ethylene glycol and graphene nano-powder. The Carreau-Yasuda model is utilized for nanofluid rheology and the Buongiorno's model for nanoscale effects. The deemed flow situation is modelled via temperature dependent heat generation/absorption, variable thermal conductivity, porous medium, activation energy, mixed convection, Brownian diffusion, magnetic field, thermophoresis diffusion, Ohmic heating and viscous dissipation assumptions. Fluid saturated porous medium is simulated by employing a modified Darcy's law. Zero mass flux and no-slip boundary conditions are taken for concentration, heat and velocity fields. Using the lubrication assumption, the governing system of equations for the fluid transfer problem is abridged and resolved employing built-in command NDSolve in Mathematica. Effects of different pertinent parameters are shown via graphs.

Non-Newtonian pulsatile flow through an artery with two stenosis

The purpose of this work is to simulate and analyse the movement of blood passing from stenosis of an artery of a person with atherosclerosis artery disease. We used three-dimensional modelling and simulation of blood flow through two arteries consisting of two stenosis each, one with the same radius for both the cases and the other with different radii for each case. The type of blood flow was considered to be simple pulsatile in order to mimic the rhythmic pulses of the human heart. The carreau yasuda model was used for the hemodynamic modeling viscosity of fluid and sst (shear-stress-transport) was used as the numerical model. This study considered blood flow models which is non-newtonian and solved the 3D laminar and unsteady NS Equations to extracted velocity profiles at 6 different locations in a blood vessel and shear strain rate for both cases.

Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids

The Prandtl model is certainly the simplest and most generic microscopic model describing solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past a sinusoidal potential representing the surface energy corrugation of a counterface. While it was primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities, Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which, converted to a dependence of effective (excess) viscosity on shear rate η ( γ ˙ ) , is strikingly similar to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two dimensionless parameters in the CY relation are found to span a broad range of values. When thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ ˙ 2 corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes friction to the regime, where η obeys approximately a sublinear power law of 1 / γ ˙ .

A New Model and Analysis for Peristalsis of Carreau–Yasuda (CY) Nanofluid Subject to Wall Properties

Peristaltic movement of non-Newtonian nanofluid obeying Carreau–Yasuda (CY) model across a complaint wall channel is formulated through a different approach. Unlike past researches, we consider the well-known Buongiorno’s model without relying on conventional assumption of constant diffusion coefficients. However, the considered model assumes long wavelength of channel walls compared with the channel width. Lower channel wall is heated by providing convection from hot fluid at temperature Tf. The developed system is coupled and nonlinear which seems difficult to be solved exactly. Hence, numerical computations are made by adopting shooting method-based package NDSolve of MATHEMATICA. A considerable effect of wall slip and rheology on the solution profiles is apparent from the computational results. Moreover, the computed results are aimed at predicting the role of Brownian diffusion and thermophoresis in peristalsis especially when wall elastic effects are present.

Theoretical study of the flow in a fluid damper containing high viscosity silicone oil: Effects of shear-thinning and viscoelasticity

The flow inside a fluid damper where a piston reciprocates sinusoidally inside an outer casing containing high-viscosity silicone oil is simulated using a Finite Volume method, at various excitation frequencies. The oil is modelled by the Carreau-Yasuda (CY) and Phan-Thien \& Tanner (PTT) constitutive equations. Both models account for shear-thinning but only the PTT model accounts for elasticity. The CY and other generalised Newtonian models have been previously used in theoretical studies of fluid dampers, but the present study is the first to perform full two-dimensional (axisymmetric) simulations employing a viscoelastic constitutive equation. It is found that the CY and PTT predictions are similar when the excitation frequency is low, but at medium and higher frequencies the CY model fails to describe important phenomena that are predicted by the PTT model and observed in experimental studies found in the literature, such as the hysteresis of the force-displacement and force-velocity loops. Elastic effects are quantified by applying a decomposition of the damper force into elastic and viscous components, inspired from LAOS (Large Amplitude Oscillatory Shear) theory. The CY model also overestimates the damper force relative to the PTT, because it underpredicts the flow development length inside the piston-cylinder gap. It is thus concluded that (a) fluid elasticity must be accounted for and (b) theoretical approaches that rely on the assumption of one-dimensional flow in the piston-cylinder gap are of limited accuracy, even if they account for fluid viscoelasticity. The consequences of using lower-viscosity silicone oil are also briefly examined.

Heat transfer analysis for peristaltic flow of Carreau-Yasuda fluid through a curved channel with radial magnetic field

Peristalsis of fluids through curved geometries is widely encountered in several industrial and domestic pumping devices. Keeping this fact in mind, effects of variable magnetic field on peristalsis of Carreau-Yasuda (C-Y) fluid through a curved channel with velocity and thermal slip boundary conditions are studied. Heat transfer analysis has been carried out by considering the Joule heating and viscous dissipation effects. The long wavelength and small Reynolds number assumptions are adopted in mathematical modeling of the problem. Resulting non-linear system of differential equations has been solved numerically. Graphical results for axial velocity, temperature, heat transfer rate and stresses at the walls for the different flow parameters are discussed. It is reported that the radially varying magnetic field decreases velocity and increases the temperature of the fluid. Such magnetic field also enhances the heat transfer rate and stresses at the boundaries.

Investigating the causes of shear-thinning in non-colloidal suspensions: Experiments and simulations

Experiments and computations were carried out to explore the origins of shear-thinning in non-colloidal suspensions. Two grades of polydimethylsiloxane (silicone oil) and a glycerine/water mixture were used as matrices for the suspensions. The particles were 40 μm diameter polystyrene (PS) and polymethyl methacrylate (PMMA) spheres. We concentrated on 40% volume fraction suspensions where shear-thinning was clear. The silicone oil matrices were nearly Newtonian: at 24 °C the viscosity of the 1.15 Pa s sample showed a 2% drop in viscosity a shear rate of about 3000 s−1, the 13.2 Pa s sample showed a drop of 2% at a shear rate of approximately 100 s−1, and the glycerine/water sample appeared to be Newtonian at least up to 104 s−1. Mild shear-thinning was seen with all suspensions, beginning at shear rates of order 0.1–1 s−1, followed by a rapid reduction of torque in the parallel-plate system at shear rates of 14, 150 and 1000 s−1 respectively with the three matrices. These rapid reductions are ascribed to edge effects.Matching smoothed particle hydrodynamics (SPH) simulations were made. The silicone matrix viscosities were modelled by a Carreau–Yasuda (CY) fit up to shear rates of order 107 s−1. The agreement between computations and experiments is generally good for 40% volume fraction suspensions up to the shear rate where edge effects intervene in the experiments- there are no edge effects in the simulations. This confirms the suggestion by Vázquez-Quesada et al. [1] that ‘hidden’ high shear rates between particles, where the non-Newtonian matrix viscosity comes into play, can result in shear-thinning at the macroscopic level. For the glycerine/water matrix at low shear rates this mechanism does not apply and a separate mechanism based on variable interparticle friction is suggested; the two mechanisms can co-exist.