Carreau Model Research Articles

Gray correlation entropy analysis of zero shear viscosity and high-temperature rheological parameters of phosphogypsum-modified asphalt

The high-temperature rheological properties of solid waste-modified asphalt are useful indicators for ensuring the effective operation of asphalt pavements, and inhibiting their rutting. However, there are numerous high-temperature rheological indicators, and only a few key indicators of high-temperature properties of solid waste modified asphalt are reported. This leads to a lack of uniformity in the evaluation of high-temperature performance indicators. In this study, the variables that affect the high-temperature parameters of phosphogypsum-modified asphalt were analyzed. Various contents of phosphogypsum (0 %, 4 %, 8 %, 12 %, 16 %, and 20 %) were mixed with 70# asphalt binder to form phosphogypsum-modified asphalt. Penetration, ring and ball tests were applied to describe the conventional high-temperature properties of the phosphogypsum-modified asphalt. Moreover, the rheological properties were determined using temperature sweep, frequency sweep, and multiple stress creep and recovery experiments to determine the complex modulus (G*), phase angle (δ), SHRP rutting (G*/sinδ) and Shenoy rutting (G*/(1−(1/sinδtanδ))) parameters, zero shear viscosity (ZSV), the percent recovery (R), and the nonrecoverable creep compliance (Jnr) of the phosphogypsum-modified asphalt. Further, a gray correlation entropy analysis of ZSV and high-temperature rheological parameters was performed. The penetration of asphalt gradually decreased with adding phosphogypsum while softening point increased. At a constant temperature, the G* of asphalt binders increased with the increase in phosphogypsum content. Additionally, the δ decreased slightly, and the G*/sinδ and G*/(1−(1/sinδtanδ)) increased significantly. The G* increased with the increase in frequency from 0.1 to 100 rad/s. Phosphogypsum improved the R and reduced the Jnr of the asphalt binder. The ZSV fitted by the Carreau and Cross models exhibited a similar trend, indicating that phosphogypsum could improve the ZSV of the base binder. The gray entropy correlation degree between the ZSV and R values at 0.1 and 3.2 kPa, G*/(1−(1/sinδtanδ)), G*/sinδ, and G* were larger than 0.99. In contrast, Jnr exhibited a low correlation was about 0.96. Thus, R and ZSV can be adapted to assess the high-temperature properties of phosphogypsum-modified asphalt.

Effect of Reynolds number and blood viscosity models on the left coronary artery with multiple stenoses

This study aims to identify the significance of different blood viscosity models along with different Reynolds numbers in the simulation of blood flow in a multi-stenosed Left Coronary Artery (LCA) model. Computational fluid dynamics techniques were implemented to derive the hemodynamic outcomes of the diseased three-dimensional Left Coronary Artery (LCA) models comprising of multiple stenoses. The three-dimensional LCA model was reconstructed using the angiographic images of a healthy person, and three viscosity models, i.e., Carreau, Quemada, and Modified Cross, were considered for carrying out blood flow simulation through it. In this work, the behavior of blood velocity was analyzed by increasing the level of blockage in each of the considered blood viscosity model. It is noticed that the increase in velocity is in proportion with the rise in Reynolds number. This study shows that the Quemada model records the maximum velocity magnitude with the other two rheological models for higher Reynolds numbers. In this work, the area-averaged wall shear stress (AAWSS) along the left anterior descending segment between the areas of double stenoses for different Reynolds numbers was also analyzed. Two peaks of AAWSS were seen for all the Reynolds numbers indicating the two sections of constrictions. The obtained highest peak reflects the primary blockage. Also, an emphasis is laid to prefer the Carreau model over the Quemada and Modified Cross model. This work is purely computational based that might be helpful in providing an insightful understanding of blood flow conduct at the diseased stage in the cardiovascular system.

Activation Energy and Inclination Magnetic Dipole Influences on Carreau Nanofluid Flowing via Cylindrical Channel with an Infinite Shearing Rate

Background: The infinite shear viscosity model of Carreau fluid characterizes the attitude of fluid flow at a very high/very low shear rate. This model has the capacity for interpretation of fluid at both extreme levels, and an inclined magnetic dipole in fluid mechanics has its valuable applications such as magnetic drug engineering, cold treatments to destroy tumors, drug targeting, bio preservation, cryosurgery, astrophysics, reaction kinetics, geophysics, machinery efficiency, sensors, material selection and cosmology. Novelty: This study investigates and interprets the infinite shear rate of Carreau nanofluid over the geometry of a cylindrical channel. The velocity is assumed to be investigated through imposing an inclined magnetic field onto cylindrical geometry. Activation energy is utilized because it helps with chemical reactions and mass transport. Furthermore, the effects of thermophoresis, the binary chemical process and the Brownian movement of nanoparticles are included in this attempt. Formulation: The mathematics of the assumed Carreau model is derived from Cauchy stress tensor, and partial differential equations (PDEs) are obtained. Similarity transformation variables converted these PDEs into a system of ordinary differential equations (ODEs). Passing this system under the bvp4c scheme, we reached at numerical results of this research attempt. Findings: Graphical debate and statistical analysis are launched on the basis of the obtained computed numerical results. The infinite shear rate aspect of Carreau nanofluid gives a lower velocity. The inclined magnetic dipole effect shows a lower velocity but high energy. A positive variation in activation energy amplifies the concentration field.

Constitutive models that exceed the fitting capabilities of the Herschel–Bulkley model: A case study for shear magnetorheology

A significant proportion of non-Newtonian fluids exhibits the phenomena of shear-thinning and yield stress. The Herschel-Bulkley model is probably the most widespread equation to describe the rheological behaviour of such systems, although greater attention is being paid to discerning more accurate mathematical models for viscoplastic systems. In this regard, the work presented herein investigates existing, unconventional viscoplastic models and evaluates their fitting and predictive capabilities in relation to collected magnetorheological data. The four-parameter models of modified Carreau, modified Cross (and its variant extended with the Quemada equation), Shulman and Nasiri-Ashrafizadeh were applied to appraise the shear data of the magnetorheological fluids. Their suitability was also statistically evaluated and compared with that attained for the conventional Herschel-Bulkley model and recently employed analogues, such as the Robertson-Stiff and Mizrahi-Berk models. It was found that the performance of all models for describing magnetorheological flow curves was adequate, with relatively high correlation coefficients. Applying the four-parameter models, however, provided higher accuracy, demonstrated by notably reduced statistical coefficients of regression analysis. Both of the modified Carreau and Cross models exhibited superior fitting performance (up to 4-times lower root mean square error), while the Shulman and Nasiri-Ashrafizadeh models proved questionable in application. Although interpreting four-parameter equations is a rather complex matter, they provided more reliable prediction of shear stress data across the entire range of shear rate than the Herschel-Bulkley approximation, especially the modified Carreau and modified Cross models. It is believed that these findings can be extended to describe the rheology of other systems with viscoplastic characteristics.

Application of a multicomponent model of convectional reaction-diffusion to description of glucose gradients in a neurovascular unit.

A supply of glucose to a nervous tissue is fulfilled by a cerebrovascular network, and further diffusion is known to occur at both an arteriolar and a microvascular level. Despite a direct relation, a blood flow dynamic and reaction-diffusion of metabolites are usually considered separately in the mathematical models. In the present study they are coupled in a multiphysical approach which allows to evaluate the effects of capillary blood flow changes on near-vessels nutrient concentration gradients evidently. Cerebral blood flow (CBF) was described by the non-steady-state Navier-Stokes equations for a non-Newtonian fluid whose constitutive law is given by the Carreau model. A three-level organization of blood–brain barrier (BBB) is modelled by the flux dysconnectivity functions including densities and kinetic properties of glucose transporters. The velocity of a fluid flow in brain extracellular space (ECS) was estimated using Darcy’s law. The equations of reaction-diffusion with convection based on a generated flow field for continues and porous media were used to describe spatial-time gradients of glucose in the capillary lumen and brain parenchyma of a neurovascular unit (NVU), respectively. Changes in CBF were directly simulated using smoothing step-like functions altering the difference of intracapillary pressure in time. The changes of CBF cover both the decrease (on 70%) and the increase (on 50%) in a capillary flow velocity. Analyzing the dynamics of glucose gradients, it was shown that a rapid decrease of a capillary blood flow yields an enhanced level of glucose in a near-capillary nervous tissue if the contacts between astrocytes end-feet are not tight. Under the increased CBF velocities the amplitude of glucose concentration gradients is always enhanced. The introduced approach can be used for estimation of blood flow changes influence not only on glucose but also on other nutrients concentration gradients and for the modelling of distributions of their concentrations near blood vessels in other tissues as well.

Pickering emulsion polymerized Fe3O4@graphene oxide-polystyrene composite particles and their electro/magnetorheological responses

In this study, magnetic and semiconducting Fe3O4@graphene oxide (GO)-polystyrene (PS) composite particles were fabricated using the Pickering emulsion polymerization technique. The Fe3O4@GO composite particles were initially synthesized via a co-precipitation method and then used as a Pickering emulsifier. The basic properties, such as the morphology, chemical properties, and the magnetic properties of the Fe3O4@GO-PS composite particles, were characterized using transmission electron microscopy, Fourier-transform infrared spectroscopy, and VSM. The Fe3O4@GO-PS composite particles were then dispersed in silicone oil to obtain electrorheological (ER) and magnetorheological (MR) fluids. The ER and MR properties were tested using a rheometer with two different geometries under electric and magnetic fields. The ER dynamic yield stresses were obtained using the Bingham model fitting method, whereas the MR dynamic yield stresses were obtained using the Casson model fitting method. Furthermore, the yield stress was obtained by fitting the complex viscosity using the Carreau model. All three yield stresses were also fitted with respect to the electric or magnetic field strengths, and a slope of 1.5 was determined.

Novel numerical results for heat transfer along a stretching cylinder immersed in a shear-thinning fluid

Boundary layer formation over a moving or stationary surface has a wide range of applications in aerodynamics, heat transfer enhancement, and prediction of drag or resistance on a surface. Furthermore, viscosity changes with deformation cannot be ignored in almost all industrially vital fluids. Present work describes boundary layer development around a cylinder stretching axially in a shear-thinning fluid obeying Carreau model. Accompanying heat transfer problem is analyzed in the existence of frictional heating and Joule heating terms in the thermal energy equation. Previous studies concerning Carreau fluid flow driven by a stretching cylinder are discussed with a view to point out some errors concerning mathematical modeling. For computational results, a widely employed MATLAB package bvp4c is utilized, which is based on a collocation scheme. New numerical results of the resulting six parameter problem are worked out, which are utilized to assess the contribution of surface curvature on the flow fields in the presence of a shear-thinning effect. The results show that the fluid velocity is considerably enhanced for larger values of flow index behavior . In the presence of a magnetic field, momentum diffusion is significantly reduced while temperature profile is expanded.

An Extended Unified Viscoelastic Model for Predicting Polymer Apparent Viscosity at Different Shear Rates

Summary Polymer flooding is one of the most commonly used chemical enhanced oil recovery (EOR) methods. Conventionally, this technique was believed to improve macroscopic sweep efficiency by sweeping only bypassed oil. Nevertheless, recently it has been found that polymers exhibiting viscoelastic behavior in the porous medium can also improve microscopic displacement efficiency resulting in higher additional oil recovery. Therefore, an accurate prediction of the complex rheological response of polymers in porous media is crucial to obtain a proper estimation of incremental oil to polymer flooding. In this paper, a novel viscoelastic model is proposed to comprehensively analyze the polymer rheological behavior in porous media. This proposed model was developed and validated using 30 coreflooding tests obtained from the literature and further verified against a few existing viscoelastic models. The proposed viscoelastic model is considered an extension of the unified apparent viscosity model provided in the literature and is termed as extended unified viscoelastic model (E-UVM). The main advantage of the proposed model is its ability to capture the polymer mechanical degradation at ultimate shear rates primarily observed near wellbores. Moreover, the fitting parameters used in the model were correlated to rock and polymer properties using machine learning technique, significantly reducing the need for time-consuming coreflooding tests for future polymer screening works. Furthermore, the E-UVM was implemented in MATLAB Reservoir Simulation Toolbox (MRST) and verified against the original shear model existing in the simulator. It is worth mentioning that the irreversible viscosity drop for mechanical degradation regime was captured during implementing our model in the simulator. It was found that implementing the E-UVM in MRST for polymer non-Newtonian behavior might be more practical than the original method. In addition, the comparison between various viscosity models proposed earlier and E-UVM in the reservoir simulator showed that the latter model could yield more reliable oil recovery predictions as the apparent viscosity is modeled properly in the mechanical degradation regime, unlike UVM or Carreau models. This study presents a novel viscoelastic model that is more comprehensive and representative as opposed to other models in the literature. Furthermore, the need to conduct an extensive coreflooding experiment can be reduced by virtue of developed correlations that may be used to estimate model fitting parameters accounting for shear-thickening and mechanical degradation.

Computational fluid dynamics investigation on aortic hemodynamics in double aortic arch before and after ligation surgery

Double aortic arch (DAA) malformation is one of the reasons for symptomatic vascular rings, the hemodynamics of which is still poorly understood. This study aims to investigate the blood flow characteristics in patient-specific double aortic arches using computational fluid dynamics (CFD). Seven cases of infantile patients with DAA were collected and their computed tomography images were used to reconstruct 3D computational models. A modified Carreau model was used to consider the non-Newtonian effect of blood and a three-element Windkessel model taking the effect of the age of patients into account was applied to reproduce physiological pressure waveforms. Numerical results show that blood flow distribution and energy loss of DAA depends on relative sizes of the two aortic arches and their angles with the ascending aorta. Ligation of either aortic arch increases the energy loss of blood in the DAA, leading to the increase in cardiac workload. Generally, the rising rate of energy loss before and after the surgery is almost linear with the area ratio between the aortic arch without ligation and the ascending aorta.

Directional Migration and Distribution of Magnetic Microparticles in Polypropylene-Matrix Magnetic Composites Molded by an Injection Molding Assisted by External Magnetic Field.

Surface-functionalized polymer composites with spherical particles as fillers offer great qualities and have been widely employed in applications of sensors, pharmaceutical industries, anti-icing, and flexible electromagnetic interference shielding. The directional migration and dispersion theory of magnetic microparticles in polypropylene (PP)-matrix magnetic composites must be studied to better acquire the functional surface with remarkable features. In this work, a novel simulation model based on multi-physical field coupling was suggested to analyze the directed migration and distribution of magnetic ferroferric oxide (Fe3O4) particles in injection molding assisted by an external magnetic field using COMSOL Multiphysics® software. To accurately introduce rheological phenomena of polymer melt into the simulation model, the Carreau model was used. Particle size, magnetic field intensity, melt viscosity, and other parameters impacting particle directional motion were discussed in depth. The directional distribution of particles in the simulation model was properly assessed and confirmed by experiment results. This model provides theoretical support for the control, optimization, and investigation of the injection-molding process control of surface-functionalized polymer composites.

The Impact of Different Arrangements of Molecular Chains in Terms of Low and High Shear Rate's Viscosities on Heat and Mass Flow of Nonnewtonian Shear thinning Fluids.

Non-newtonian fluids, especially shear thinning fluids, have several applications in the polymer industry, food industry, and even everyday life. The viscosity of shear thinning fluids is decreased by two or three orders of magnitude due to the alignment of the molecules in order when the shear rate is increased, and it cannot be ignored in the case of polymer processing and lubrication problems. So, the effects of viscosities at the low and high shear rates on the heat and mass boundary layer flow of shear thinning fluid over moving belts are investigated in this study. For this purpose the generalized Carreau model of viscosity relate to shear rate is used in the momentum equation. The Carreau model contains the five parameters: low shear rate viscosity, high shear rate viscosity, viscosity curvature, consistency index, and flow behavior index. For the heat flow, the expression of the thermal conductivity model similar to the viscosity equation due to the non-Newtonian nature of the fluid is used in the energy equation. On the mathematical model of the problem, boundary layer approximations are applied and then simplified by applying the similarity transformations to get the solution. The solution of the simplified equations is obtained by numerical technique RK-shooting method. The results are compared with existing results for limited cases and found good agreement. The results in the form of velocity and temperature profiles under the impact of all the viscosity's parameters are obtained and displayed in graphical form. Moreover, the boundary layer parameters such as the thickness of the regions, momentum thickness, and displacement thickness are calculated to understand the structure of the boundary layer flow of fluid. The velocity and temperature of the fluid are decreased and increased respectively by all viscosity's parameters of the model. So, the results of the boundary layer fluid flow under rheological parameters will not only help engineers to design superior chemical equipment but also help improve the economy and efficiency of the overall process.

Thermal energy and mass transport of shear thinning fluid under effects of low to high shear rate viscosity

The current investigation is deliberated the flow and heat transfer of a shear thinning fluid over a non-linear stretching sheet has variable thickness. All rheological aspects at low to high shear rates are accounted theoretical by using generalized Carreau model of viscosity. Theoretical flow model is formulated for boundary layer phenomena by applying boundary layer approximations and then convert it from partial differential equations to ordinary differential equations with the help of similarity transformations. The solution is obtained by numerical method and the result are displayed in the form of velocity and temperature profiles under impact of rheological and geometrical governing parameters. In addition, the results of skin friction coefficient and Nusselt number are obtained under effects of these parameters. It is found that Nusselt number is significantly decreased when stretching is increased by velocity index parameter.

Accelerating Effects of Flow Behavior Index n on Breakup Dynamics for Droplet Evolution in Non-Newtonian Fluids.

This paper studied the evolution of NaAlg solution micro-droplet in a coaxial microchannel. The Bird–Carreau model was used to characterize the flow properties of NaAlg solution. As the mass fraction decreased, the flow behavior index n also decreased, indicating that the NaAlg solution was increasingly shear-thinning. There were three stages during the micro-droplet evolution, which were the growth stage, the squeezing stage, and the pinch-off stage. This paper led the flow behavior index n to estimate the effects of rheological property on the breakup dynamics of micro-droplet. We proposed two new prediction models of the minimum neck width wm which were affected by |n| in the squeezing and pinch-off stages for the non-Newtonian fluids. In addition, this paper indicated the rate ratio Qd/Qc was another factor on the wm model in the squeezing stage and the H(λ) of Stokes mechanism was a function governed by |n|2 in the pinch-off stage.

Effect of surface stretching on convective instabilities of Kármán flow of non-Newtonian Carreau fluid

Linear convective instability analysis of non-Newtonian fluids has immense practical applications in the field of aerodynamics and engineering mechanics. The paper deals with linear convective instability analysis of laminar Kármán swirling flow of a non-Newtonian Carreau fluid over a radially stretchable rotating disk of infinite radius when the Coriolis force is significant in the boundary layer. In this paper, the velocity profiles for both shear-thinning and shear-thickening fluids the above-mentioned flow of Carreau model have been determined under stretch boundary condition. By using the Chebyshev collocation method, a study of convective instability has been carried out in order to perform a stability analysis of the flow and determine the neutral stability curves. The stability curves reveal that the bottom disk’s surface stretching has a globally stabilizing effect on the fluid exhibiting shear-thinning flow behaviour and a globally destabilizing effect on shear-thickening flow behaviour. To verify the above physical facts, the flow has been subjected to an energy analysis at the same time.

P12: Investigation of Ventricular Assist Device Inflow Configurations Within Single Ventricle Hearts

Study: Ventricular assist devices (VADs) provide cardiac support to failing hearts. A recent study showed that over half of VAD inflow cannulas are malpositioned; this number is estimated to be greater in patients with congenital heart defects. VAD malpositioning can lead to thrombus formation (clotting), pump failure, or even patient death. The relationship between VAD inflow cannula configuration and thrombus formation was explored for a pediatric patient with a single systemic ventricle. Methods: A post-Fontan hypoplastic left heart syndrome pediatric patient was evaluated. Computational fluid dynamics (CFD) was used to investigate the potential for thrombus formation in the apical vs. diaphragmatic inflow cannula configurations. A dynamic, non-Newtonian Carreau model was used and thrombogenic potential was defined by fluid with low velocity, low strain, and long residence times. CFD was validated using particle image velocimetry (PIV) and a mock circulatory loop with a moving ventricular sac. Results: While regions with thrombogenic potential were found in both the diaphragmatic and apical cannula configurations, the apical position exhibited a greater volume of fluid with these characteristics. PIV also confirmed these results. Conclusions: Although low velocity, low strain, long residence time flow may be indicative of thrombogenic potential, many factors actually contribute to thrombus formation and should be taken into account when comparing VAD implant configurations. Furthermore, while PIV validated overall trends observed in CFD, specific numerical values differed, suggesting the need for future refinement of both the CFD and PIV models.

Modeling and simulation of the carbonate reactive-dissolution process by viscoelastic-surfactant-based acid

In carbonate reservoir treatment, uneven distribution of acid may occur due to strong heterogeneity. To avoid the selective flow of fluid into the high permeability zones, viscoelastic surfactant-based self-diverting acids are commonly used in stimulation operations. To better comprehend this phenomenon, this work proposes a mathematical model to describe the dissolution process associated with this problem. The rheology of the acid solution was experimentally obtained for some degrees of neutralization and the flow curves were fitted by a Carreau model with neutralization dependent coefficients. In addition to the usual governing equations of this problem that include mass conservation, momentum balance, and acid concentration conservation, we considered a transport equation for the reaction products. The solid–liquid interaction term at the porous scale is determined by the fractions of acid and products, that in addition to brine compose the total fluid phase. Simulations in plug geometry were performed to validate this model against experimental results in different samples, where good agreement was found.

Quantitative insights into rheology of self-crosslinking dialdehyde carboxymethyl cellulose/collagen solution: A comprehensive experimental and modelling investigation

Rheological behaviors (fluid type, thixotropy, viscoelasticity and deformation resistance) of self-crosslinking dialdehyde carboxymethyl cellulose (DCMC)/collagen solutions were comprehensively investigated and quantitatively modelled. The formation of self-crosslinking bonds gave rise to the enhancement of entanglements among collagen molecules and aggregates, resulting in the improvement of collagen solution's mechanical properties. The collagen solution was typical pseudoplastic fluid with shear-thinning behavior, and DCMC did not alter its flow behavior; therefore, the flow curves for all samples could be well simulated by Ostwald-de Waele and Carreau models. However, the viscosity and pseudoplasticity increased, and the effect of DCMC became more pronounced at higher DCMC/collagen ratios. Similar upward variation was observable for thixotropy, detected by the increased area of hysteresis loops from 20.947 to 219.978 Watts/m3. Additionally, the negative values of apparent yield stress and flow index below 1 from Herschel–Bulkley model confirmed that the DCMC/collagen solutions remained pseudoplasticity without yield stress. The viscoelasticity was examined based on dynamic frequency sweep and creep–recovery measurement and then simulated using Leonov model, Burger model and a semi-empirical model, respectively. The increases in elastic moduli and proportion of recoverable compliance reflected the self-crosslinking DCMC/collagen solutions had stronger elasticity and exhibited more resistance to deformation than the native collagen solution. Nevertheless, the more complicated structures of the DCMC/collagen solutions required more time to recover after removing external force. These data can be directly applied to the utilization of DCMC/collagen solutions, whilst also provide a basis for the prediction of printability or spinnability of collagen-based materials.

Modeling of the Peristaltic Lithogeic Bile Flow in the Calculus Duct Under the Influence of Heat Transfer with Slip Boundary Conditions

This paper deals with a mathematical model that represents non-Newtonian bile flow through a calculus duct under the influence of heat transfer with wall slip conditions. The peristaltic flow of bile is characterized by a generalized Carreau's model. An ordinate transformation is initiated to map the cosine geometry of the stone into a rectangular grid. It allows evaluation velocity, pressure distribution, flow rate, and reflux occurrence conditions, adopting the perturbation technique, the analytical solution obtained under various parameters, such as Knudsen number, amplitude ratio, Grashof number, Weissenberg number, and power index. These mathematical expressions are analyzed by plotting the graph in MATLAB R2018b software and observed that the axial velocity and the pressure gradient are strongly affected by heat and wall slip parameters.

Melting and entropy generation of infinite shear rate viscosity Carreau model over Riga plate with erratic thickness: a numerical Keller Box approach

The current investigations are related to presenting the characteristics of flow at very high and low shear rates along with the melting process over the geometry of Riga plate. Carreau nanofluid is most appropriate mathematical viscosity model that can deal with low and high shear rates. Transportation of energy is discussed through melting conditions, thermal radiation and viscous dissipation. In this study, electromagnetic hydrodynamic aspect of nanofluid is discussed by using electromagnetic surface (Riga plate) and this system generates Lorentz force parallel to wall that keeps its effect on velocity of nanofluid. Partial differential equations (PDEs) are moved in ordinary differential equations and numerical approach named Keller Box and Shooting scheme are exercised to fetch the numerical solution of the system. An augmentation in Q leads to an enrichment in an external magnetic field. The velocity as well as momentum boundary layer booms by the virtue of an improvement in an external magnetic field. The viscosity of the nanofluid increases by the virtue of a magnification in β. Nanofluid becomes more radiated and absorbs more heat as a result of magnification in Nr, which escalates the heat transfer rate.

The effect of pharmaceutical nanoparticles and atherosclerosis in aorta artery on the instable blood velocity based on numerical method.

In medicine field, dynamic investigation of aorta artery has received attention due to its notable functions and significance upon performance of heart and individual health. Because, aortic injuries cause lethal occurrences having numerous mortality rates. Therefore, more probes, in particular, dynamic response of aorta arteries conveying blood flow containing pharmaceutical nanoparticles is essential. In present research, we attempt to model biomechanically the dynamic instability assessment of aorta arteries with atherosclerosis in tissue matrix conveying blood including pharmaceutical magnetic nanoparticles. Thus, according to classical cylindrical shell theory, the aorta arteries will be considered as elastic cylindrical vessels and symmetric lipid tissue is utilized in order to model atherosclerosis in the artery. Applying magnetic field to nanoparticles results in attraction of lipid tissue in artery. Moreover, the nature of blood flow is regarded non-Newtonian based on Casson, Carreau, and power law models. Using Hamilton's principle, the motion equations are derived and based on differential quadrature method, the dynamic instability region of aorta artery is obtained. The influences of different variables such as magnetic field, magnetic nanoparticle's volume percent, combined effects of the tissue, lipid's height and length, and non-Newtonian models upon dynamic behavior of aorta artery are investigated. According to the results, increase in lipid's height leads to increase in resonance frequency of aorta arteries.