Carreau-Yasuda Model Research Articles

Magnetized peristaltic transportation of Boron-Nitride and Ethylene-Glycol nanofluid through a curved channel

The present investigation explores the heat transfer impact on magneto-hydrodynamic peristalsis of Boron Nitride-Ethylene Glycol nanofluid past a curved channel. Experimental study revealed that the nanofluid formed by suspending Boron Nitride particles in Ethylene Glycol mixture exhibits the non-Newtonian behavior. Further, Carreau-Yasuda model is utilized to characterize the shear thinning features of nanofluid. The obtained non-linear differential expressions are solved numerically using built in solver NDSolve. The temperature and the velocity of nanofluid drop as the volume fraction of Boron Nitride nanomaterial increases. Further, it is discovered that temperature decreases, and fluid momentum/velocity is assisted with increasing curvature parameter.

Rheological and Microstructural Properties of Acidified Milk Drink Stabilized with Butternut Squash Pulp Hydrocolloids (BSPHs)

In this study, hydrocolloids from butternut squash pulp (BSPH) have been employed as stabilizers for the development of acidified milk drinks to evaluate their physicochemical, rheological, and microstructural properties. BSPH was obtained in the alkaline medium (yield of 630 mg of hydrocolloids/100 g of pulp), presenting 79.97 ± 0.240% carbohydrate and non-Newtonian-type shear thinning. Four acidified milk drinks (AMDs) were obtained with 0.25, 0.50, and 1.00% BSPHs and a control sample without BSPHs. The addition of BSPHs did not alter the proximal composition of AMDs with similar proximal values; also, the samples present typical behavior of non-Newtonian-fluid-type shear thinning adjusted to the Carreau–Yasuda model. Storage (G′) and loss (G″) moduli values were slightly dependent on the frequency in most of the studied systems. Then, the addition of BSPHs retained their uniform internal structure and contributed to the stabilization of the products.

Melting process of PCM with Carreau – Yasuda non-Newtonian behavior in a shell and tube heat exchanger occupied by anisotropic porous medium

Purpose This study aims to evaluate the melting process of the phase-change RT-35 material in a shell and tube heat exchanger saturated with a porous medium. Titanium porous media with isotropic and inhomogeneous structures are studied. The considered tubes in the shell and tube exchanger are made of copper with specific thicknesses. The phase-change material has a non-Newtonian behavior and follows the endorsed Carreau–Yasuda Model. Design/methodology/approach The enthalpy–porosity method is used for modeling of the melting process. The governing equations were transferred to their dimensionless forms. Finally, the equations are solved by applying the Galerkin finite element method. Findings The findings for different values of the relative permeability (K*) and permeability deviation angle (λ) are represented in the forms of charts, streamlines and constant temperature contours. The considerable effects of the relative permeability (K*) and deviation angle (λ) on the flow line patterns of the melting phase-change material are some of the significant achievements of this works. Originality/value This study was conducted using data from relevant research articles provided by reputable academic sources. The data included in this manuscript have not been published previously and are not under consideration by any other journal.

Thermo-Solutal Convection of Carreau-Yasuda Non-Newtonian Fluids in Inclined Square Cavities Under Dufour and Soret Impacts

The thermosolutal convection of non-Newtonian fluids under Soret and Dufour influences within an inclined square enclosure is explored. The active walls are subject to constant and uniform concentrations and temperatures. On the other hand, they are impermeable and adiabatic. A Carreau-Yasuda model is utilized to determine the fluid behavior. A special attention is paid to the impact of rheological parameters (, , and ), the thermal Rayleigh number , Dufour number, , Soret number, , Lewis number, , buoyancy ratio, , and the inclination angel, . The numerical findings are represented in terms thermal fields, iso-concentration, and viscosity apparent contours, and the influence of certain parameters on the variation of stream function, Nusselt and Sherwood numbers, and apparent viscosity is also inspected. The findings suggest that the rise of the time constant parameter, , causes an increase in thermal and mass exchange for various power-law indices, . The decrease of the of ratio of infinite-to zero-shear-rate viscosities, , and parameter, , enhances the both thermal and mass transfers. The rise of the orientation angel from 0° to 90°yields an increase in thermal and mass transfer, but without a specific pattern in the different parameters studied.

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 .

A numerical study on pulsatile non-Newtonian hemodynamics in double-fusiform abdominal aortic aneurysms

Abdominal Aortic Aneurysm (AAA) is a multi-factorial pathological event that occurs in the human body. In the present work, the hemodynamics pertaining to AAA are numerically analyzed. To comprehend the blood flow phenomenon in a double-fusiform aneurysm, axisymmetric simulations of pulsatile non-Newtonian blood flow are performed using OpenFOAM. The Carreau–Yasuda model is used to evaluate the non-Newtonian behavior of blood. The Reynolds number and Womersley number are altered as per the physiologically applicable range to characterize the hemodynamics. The Dilatation Index is also varied to quantify the consequence of different enlargements of the abdominal aorta on the blood flow. Four hemodynamic indicators—time-averaged wall shear stress, Oscillatory Shear Index (OSI), Relative Residence Time (RRT), and vascular impedance—are used to identify several complications such as atherosclerosis, vascular inflammation, endothelial dysfunction, and hyperplasia. As the pulse rate increases, the chances of particle stagnation inside the aneurysm decrease due to lower RRT. Our results suggest that patients with hypoxia or bradycardia (low Womersley number) are more susceptible to atherosclerosis due to the high value of RRT. Thus, we recommend mild exercise for patients with AAA. After analyzing the hemodynamic indicators, % of area with RRT > 0.5 is identified as the critical parameter to propose a regime map. Low pulse rates are found to be critical at low flow rates, whereas high pulse rates are found to be critical with high flow rates. Furthermore, it is found that the severity increases as the size of the aneurysm increases.

Comparison and Evaluation of Different Test Methods and Models for Determining Zero Shear Viscosity of Asphalt Binder

Abstract Zero shear viscosity (ZSV) has been proven to be a reasonable indicator for characterizing the high-temperature performance of asphalt binders. Various test methods and models have been used in the literature to determine the ZSV, while no consistent result can be obtained. In addition, the differences and similarities among these methods are not yet clear, which can often bring difficulties and confusion to researchers when trying to implement the ZSV methods. This paper aims to evaluate the applicability of different test methods and rheological models in determining the ZSVs of asphalts. The shear rate sweep test, frequency sweep test, and creep test were performed on 60/80 and 80/100 pen grade base asphalts and styrene-butadiene-styrene (SBS) modified asphalt, and ZSVs were determined using Carreau’s model, Carreau-Yasuda model, Cross/Sybilski’s model, Cross/Williamson’s model, Burger’s model, the threshold method, and the ratio method. The test results showed that the shear rate sweep test and the creep test have lower variability and better applicability than the frequency sweep test, and the four rheological models and the threshold method used in the shear rate sweep test could determine the ZSV well. In the frequency sweep test, the Cross/Sybilski’s model failed to determine the ZSVs of all asphalts, and the ZSV of SBS asphalt could only be calculated by the ratio method. Under different test methods and models, the ZSVs of each base asphalt were similar, while that of SBS asphalt were significantly different. Considering the time consumption and applicability of the test, the shear rate sweep test seems to be the most promising test method for determining ZSVs.

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.

Data-Driven Modelling of Polyethylene Recycling under High-Temperature Extrusion.

Two main problems are studied in this article. The first one is the use of the extrusion process for controlled thermo-mechanical degradation of polyethylene for recycling applications. The second is the data-based modelling of such reactive extrusion processes. Polyethylenes (high density polyethylene (HDPE) and ultra-high molecular weight polyethylene (UHMWPE)) were extruded in a corotating twin-screw extruder under high temperatures (350 °C < T < 420 °C) for various process conditions (flow rate and screw rotation speed). These process conditions involved a decrease in the molecular weight due to degradation reactions. A numerical method based on the Carreau-Yasuda model was developed to predict the rheological behaviour (variation of the viscosity versus shear rate) from the in-line measurement of the die pressure. The results were successfully compared to the viscosity measured from offline measurement assuming the Cox-Merz law. Weight average molecular weights were estimated from the resulting zero-shear rate viscosity. Furthermore, the linear viscoelastic behaviours (Frequency dependence of the complex shear modulus) were also used to predict the molecular weight distributions of final products by an inverse rheological method. Size exclusion chromatography (SEC) was performed on five samples, and the resulting molecular weight distributions were compared to the values obtained with the two aforementioned techniques. The values of weight average molecular weights were similar for the three techniques. The complete molecular weight distributions obtained by inverse rheology were similar to the SEC ones for extruded HDPE samples, but some inaccuracies were observed for extruded UHMWPE samples. The Ludovic® (SC-Consultants, Saint-Etienne, France) corotating twin-screw extrusion simulation software was used as a classical process simulation. However, as the rheo-kinetic laws of this process were unknown, the software could not predict all the flow characteristics successfully. Finally, machine learning techniques, able to operate in the low-data limit, were tested to build predicting models of the process outputs and material characteristics. Support Vector Machine Regression (SVR) and sparsed Proper Generalized Decomposition (sPGD) techniques were chosen to predict the process outputs successfully. These methods were also applied to material characteristics data, and both were found to be effective in predicting molecular weights. More precisely, the sPGD gave better results than the SVR for the zero-shear viscosity prediction. Stochastic methods were also tested on some of the data and showed promising results.

Bubble's rise characteristics in shear-thinning xanthan gum solution: a numerical analysis

The rise of gaseous bubbles in shear-thinning liquid is a fundamental issue in fluid physics, particularly the bubbles rise dynamics in water-soluble xanthan gum concentration have a strong link for enhancing the stability of foams that have been encountered extensively in oil recovery, methane hydrate formation processing, froth flotation, and food and beverage industries. Here, air bubble rise behavior in xanthan gum solution (XGs) was investigated by using a coupled volume of fluid with the level set approach in CFD (computational fluid dynamics) modelling. The Carreau-Yasuda rheological model was adopted to define the viscous properties of the XGs and the continuum surface force model was used to track the interface between bubble and XGs. Additionally, ANN (artificial neural network) modeling was demonstrated for estimating the outputs of CFD. Our estimated CFD results for different bubble terminal velocities in water and experimental data obtained from the literature showed that there was a maximum relative error of 4.51%. Then, the CFD setup was utilized to investigate the effect of different concentrations of XGs and liquid flow index (N) on bubble rise dynamics within the bubble Reynolds number (Reb) range up to 10.05 and Eotvos number (Eo) range up to 3.47. For a fixed bubble size, the dimensionless bubble terminal velocity decreased in increased flow index and concentration of XGs, which led to decrease Reb and increase Eo. For a given XGs, the dimensionless bubble terminal velocity significantly depends on Reb and Eo. It was found that XGs and flow index significantly affect the distribution of dimensionless liquid viscosity than that of the dimensionless liquid velocity close to the bubble's underneath region. In a comparison with the rheological power-law model, the Carreau-Yasuda model showed to predict more accurate results. The estimated drag coefficient showed a deviation from the empirical equation reported in the literature, in contrast, a more accurate estimation in drag coefficient was obtained based on modified Reynolds number and Archimedes number. ANN modelling outputs agreed with CFD results and indicated that the training and testing of ANN have great efficiency to predict unknown values.

Steady and dynamic shear rheology of Indian Jujube (Ziziphus mauritiana Lam.) fruit pulp with physiochemical, textural and thermal properties of the fruit

Indian jujube (Ziziphus mauritiana Lam.) is a globally underutilized fruit and is well-known for being a good source of total phenolics and a rich source of ascorbic acid with essential minerals such as calcium, phosphorus and iron. A rheometer was used to investigate the rheological characterization of Indian jujube pulp. It was found that Indian jujube pulp exhibit a shear thinning behaviour as viscosity (η) and shear stress (σ) of pulp significantly (p < 0.05) decreased as the shear rate (γ̇̇) increased. Pulp's behaviour was characterized efficiently by correlating Power-law, Carreau-Yasuda, and Cross models with flow curve. The Cross model was found more efficient (R2:0.99775) than the Power-law (R2:0.85995) and Carreau-Yasuda model (R2:0.97291). Dynamic shear rheology test of the Indian jujube pulp presented weak gel behaviour as storage modulus (G') surpassed loss modulus (G") value. The frequency dependency of both the storage G′ and loss G′′ moduli was evaluated using a power Law model with a determination coefficient (R2) greater than 0.9. The tan(δ) values (0.020 to 0.535) suggested that the Indian jujube pulp is elastic in nature. Textural properties of Indian jujube fruit like hardness, percentage deformation at the hardness and peak stress of Indian jujube fruit were 32.76 ± 5.00 N, 7.15 ± 1.06% and 17780.80 ± 3185.47 N/m2. DSC curve showed glass transition phase of unprocessed Indian jujube fruit flesh at (98.29°C), and specific heat (Delta Cp) was found 193.96 J/g. The findings of this study will aid in the development of handling and processing machinery for the commercial manufacture of Indian jujube pulp.

Fit and Evaluate the Viscous Models Used for ABS

Viscous models such as Bird-Carreau, Cross, modified Cross, Carreau-Yasuda and Power are often used in commercial software. In order to get the most suitable model, a series of rheological tests were carried out in this study, and a model fitting method based on least square approach was proposed. Combined with the WLF equation related to temperature, these five viscous models were fitted by the fitting method proposed in this paper. The calculated results of the fitted models are compared with the experimental data. The results show that, of the investigated five models, the Carreau-Yasuda and Cross type models can better describe the rheological characteristics of ABS, the Bird-Carreau model is the second, and the Power model is the poorest one. The fitted models are in good agreement with that by Polymat. Some models such as Cross and Power models fitted by the proposed method are even better than that by Polymat.

Preparation and rheological Evaluation of a thixotropic polymer gel for water shutoff in fractured tight reservoirs

In this study, a thixotropic and high-strength gel system (THSG) is developed, which is experimentally proven to be feasible for conformance control in fractured reservoirs. The THSG is based on in-situ polymerization of the acrylamide monomer, incorporating a weak gel system. It is found that the superior rheological properties of THSG are beneficial for injection and placement of gelant into the fractures. The viscosity of THSG at varying shear rates can be well fit by the Carreau–Yasuda model, and its shear thinning behavior contributes to low injection pressure during the gelant injection. Moreover, this THSG system exhibits much better thixotropy than the traditional Cr(Ⅲ)-acetate-HPAM gel system (HPAM/Cr(Ⅲ) gel), which would enable the THSG an easier access to the small apertures. It is also found that the injection pressure is greatly increased with decreasing of the diameter of aperture during injection of the HPAM/Cr(Ⅲ) gel, while little effect of the aperture size on injection pressure was observed during THSG injection. Additionally, the yield stress of the thixotropic gelant is noticeably high, which would greatly mitigate the adverse effect of gravity segregation in fractures during well shut-off. This would be also beneficial for plugging the whole fractures. To better understand the properties of THSG, the gelation performance, the microstructure of the gel and the blocking ability of gel in the tubes were investigated. The results show that the clay particles strengthened gel exhibits a large storage modulus and excellent thermal stability. Scanning electron microscopy (SEM) results show that the clay particles were readily distributed on the polymer chains, and the clay particles could facilitate the gel to form a firm and uniform network. Consequently, the clay particles strengthened THSG gels have relatively high rupture pressure, which would be exceedingly favorable for efficient gel treatments in fractured reservoirs. • Rheology behaviors of the THSG have been studied. • The flow curve of the THEG can be well described by the Carreau–Yasuda model. • The THSG has a typical thixotropic behavior, which can effectively plug the entire fractures. • The injection pressure of the THSG is almost irrelevant to the apertures.

Designing an interpenetrating network of silane-functionalized nanocomposites for enhanced particle dispersity and interfacial bonding strength

We design an interpenetrating network of silane-functionalized nanocomposites to enhance particle dispersity and interfacial bonding strength in nanocomposites. To qualitatively measure the enhanced particle dispersity in the nanocomposites, we carry out rheological characterizations and suggest a simple particle dispersity index from the viscoelastic responses. Yield stresses of the nanocomposites are obtained by fitting with the Carreau-Yasuda model. After comparing the yield stresses and elastic moduli of the nanocomposites during photo-polymerization, we confirm that interphase regions significantly affect the interfacial bonding and mechanical strengths. Prediction of elastic moduli of the nanocomposites by the Mori-Tanaka micromechanics model agrees well with the experimental data, verifying that a good interpenetrating network exists between the nanoparticles and matrix.

Analytical modelling of complex stiffness modulus tests in direct tension-compression on asphalt concrete and nonlinearity effect due to strain amplitude

A new analytical model is designed to reproduce the complex modulus of asphalt concrete in cyclic dynamic tests. Instead of multiplying rheological elements with fixed parameters, only two elements with variable parameters are connected in parallel: the stiffness component related to the strain and the viscosity component related to the strain rate. They compose the VENoL (NOnLinear ViscoElastic) model. Their variations as a function of pulsation are calibrated with the Carreau–Yasuda model at a reference temperature and strain amplitude. The conversion from one temperature to another is done using the Time-Temperature Superposition Principle defined by its shift factor . For the conversion from one strain amplitude to another (nonlinearity), the Time-Amplitude Semi-Superposition Principle is newly created, defined by two shift factors and . The model is calibrated with experimental data from the literature based on direct tension-compression tests. The results obtained corroborate the experiments accurately.

An Iterative Approach for the Parameter Estimation of Shear-Rate and Temperature-Dependent Rheological Models for Polymeric Liquids.

Numerical flow simulations play an important role in polymer processing. One of the essential prerequisites for accurate and precise flow simulations is to obtain accurate materials functions. In the framework of the generalized Newtonian fluid model, one needs to obtain shear viscosity as a function of the rate-of-shear and temperature—as determined by rheometry—and then fitted to a mathematical model. Often, many subjectively perform the fitting without paying attention to the relative quality of the estimated parameters. This paper proposes a unique iterative algorithm for fitting the rate-of-shear and temperature-dependent viscosity model under the time–temperature superposition (TTS) principle. Proof-of-concept demonstrations are shown using the five-parameter Carreau–Yasuda model and experimental data from small-amplitude oscillatory shear (SAOS) measurements. It is shown that the newly proposed iterative algorithm leads to a more accurate representation of the experimental data compared to the traditional approach. We compare their performance in studies of the steady isothermal flow of a Carreau–Yasuda model fluid in a straight, circular tube. The two sets of parameters, one from the traditional approach and the other from the newly proposed iterative approach, show considerable differences in flow simulation. The percentage difference between the two predictions can be as large as 10% or more. Furthermore, even in cases where prior knowledge of the TTS shifting factors is not available, the newly proposed iterative approach can still yield a good fit to the experimental data, resulting in both the shifting factors and parameters for the non-Newtonian fluid model.

Study on rheological behaviors of media and material removal mechanism for abrasive flow machining (AFM) micro structures and corresponding simulations

The abrasive flow machining (AFM) technique has great potentials for machining micro and complicated structures, when the specific media with both favorable fluidity and machinability are essential. In the present study, components, structures and rheological behaviors of a typical type of media were analyzed, based on with the material removal mechanism was firstly discussed. The Carreau-Yasuda model was applied for simulating the AFM process, in which the shear viscosity and relative parameters were precisely determined by analyzing the rheological behaviors of the media. The wall slipping behavior was analyzed and defined by the Generalized Navier slipping model. It was showed that the polymer melt and plasticizer oil presented similar compositions and structures, containing linear chains with few side groups, contributing to the fluidity of the media. The intense peak value in the creep curve (3.55 Pa−1) demonstrated a higher value of the viscous component than that of the elastic component, while the occurrence of saltatory regression further verified the linear structure of polymer chains. Owing to the retraction of streamlines from larger chambers into micro structures, and the combined effects of the shear stress and first normal stress difference, the polymer chains remained in stretched states, leading to uniform indentation depths and machining effects all over the machined surfaces. The flow velocity in the micro holes, which was obtained by the new simulation method, was roughly 1.5 m/s, proving that the retention time (2 × 10−3 s) was much shorter than the relaxation time of the media (230 s), indicating long-standing stretched states. The homogenous and a certain degree of shear stress, storage and loss moduli close to the inner hole surface further verified the favorable and uniform machining effects. This research is valuable for guiding the design of the media and abrasive flow machining procedures for micro structures, from aspects of either experiments or simulations.

FORCED CONVECTION IN A LID-DRIVEN NON-NEWTONIAN BLOOD FLOW THROUGH A STENOTIC ARTERY

Cardiovascular diseases are one of the major health concerns globally, mainly caused by inadequate blood flow in different body parts. The lack of blood flow is often due to abnormal narrowing of blood vessels, and a systematic technique to boost blood flow in these areas can help cure the disease. One such method uses elevated temperatures to influence blood flow in the concerned areas. This paper investigates this process, i.e. the forced convection, through blood flow in a stenotic region of a human artery. A part of the stenotic region is considered a porous medium and the top wall is subjected to a higher temperature with a lid moving from left to right. Blood is considered as a non-Newtonian fluid with the power law index varying from 0.5 to 1.5. The geometric properties are considered to match the problem of blood flow in the artery affected by stenosis. The Carreau-Yasuda model is used to represent the non-Newtonian fluid flow in porous media and the numerical analysis is carried out using the Lattice Boltzmann method. This problem is investigated to study the influence of the moving lid and other geometric properties on convection and flow properties such as velocity profiles, streamlines, isotherms and heat transfer.

Finite element computation of magneto-hemodynamic flow and heat transfer in a bifurcated artery with saccular aneurysm using the Carreau-Yasuda biorheological model.

"Existing computational fluid dynamics studies of blood flows have demonstrated that the lower wall stress and higher oscillatory shear index might be the cause of acceleration in atherogenesis of vascular walls in hemodynamics. To prevent the chances of aneurysm wall rupture in the saccular aneurysm at distal aortic bifurcation, clinical biomagnetic studies have shown that extra-corporeal magnetic fields can be deployed to regulate the blood flow. Motivated by these developments, in the current study a finite element computational fluid dynamics simulation has been conducted of unsteady two-dimensional non-Newtonian magneto-hemodynamic heat transfer in electrically conducting blood flow in a bifurcated artery featuring a saccular aneurysm. The fluid flow is assumed to be pulsatile, non-Newtonian and incompressible. The Carreau-Yasuda model is adopted for blood to mimic non-Newtonian characteristics. The transformed equations with appropriate boundary conditions are solved numerically by employing the finite element method with the variational approach in the FreeFEM++ code. Hydrodynamic and thermal characteristics are elucidated in detail for the effects of key non-dimensional parameters i.e. Reynolds number (Re = 14, 21, 100, 200), Prandtl number (Pr = 14, 21) and magnetic body force parameter (Hartmann number) (M = 0.6, 1.2, 1.5) at the aneurysm and throughout the arterial domain. The influence of vessel geometry on blood flow characteristics i.e. velocity, pressure and temperature fields are also visualized through instantaneous contour patterns. It is found that an increase in the magnetic parameter reduces the pressure but increases the skin-friction coefficient in the domain. The temperature decreases at the parent artery (inlet) and both the distant and prior artery with the increment in the Prandtl number. A higher Reynolds number also causes a reduction in velocity as well as in pressure. The blood flow shows different characteristic contours with time variation at the aneurysm as well as in the arterial segment. The novelty of the current research is therefore to present a combined approach amalgamating the Carreau-Yasuda model, heat transfer and magnetohydrodynamics with complex geometric features in realistic arterial hemodynamics with extensive visualization and interpretation, in order to generalize and extend previous studies. In previous studies these features have been considered separately and not simultaneously as in the current study. The present simulations reveal some novel features of biomagnetic hemodynamics in bifurcated arterial transport featuring a saccular aneurysm which are envisaged to be of relevance in furnishing improved characterization of the rheological biomagnetic hemodynamics of realistic aneurysmic bifurcations in clinical assessment, diagnosis and magnetic-assisted treatment of cardiovascular disease."

Effect of foam insertion in aneurysm sac on flow structures in parent lumen: relating vortex structures with disturbed shear.

Numerous studies suggest that disturbed shear, causing endothelium dysfunction, can be related to neighboring vortex structures. With this motivation, this study presents a methodology to characterize the vortex structures. Precisely, we use mapping and characterization of vortex structures' changes to relate it with the hemodynamic indicators of disturbed shear. Topological features of vortex core lines (VCLs) are used to quantify the changes in vortex structures. We use the Sujudi-Haimes algorithm to extract the VCLs from the flow simulation results. The idea of relating vortex structures with disturbed shear is demonstrated for cerebral arteries with aneurysms virtually treated by inserting foam in the sac. To get physiologically realistic flow fields, we simulate blood flow in two patient-specific geometries before and after foam insertion, with realistic velocity waveform imposed at the inlet, using the Carreau-Yasuda model to mimic the shear-thinning behavior. With homogenous porous medium assumption, flow through the foam is modeled using the Forchheimer-Brinkman extended Darcy model. Results show that foam insertion increases the number of VCLs in the parent lumen. The average length of VCL increases by 168.9% and 55.6% in both geometries. For both geometries under consideration, results demonstrate that the region with increased disturbed shear lies in the same arterial segment exhibiting an increase in the number of oblique VCLs. Based on the findings, we conjecture that an increase in oblique VCLs is related to increased disturbed shear at the neighboring portion of the arterial wall.