Newtonian Fluid Model Research Articles

Numerical solution of magnetohydrodynamics effects on a generalised power law fluid model of blood flow through a bifurcated artery with an overlapping shaped stenosis.

This paper presents a numerical analysis of blood flow in a diseased vessel within the presence of an external magnetic field. The blood flow was considered to be incompressible and fully developed, in that the non-Newtonian nature of the fluid was characterised as a generalised power law model for shear-thinning, Newtonian, and shear-thickening fluids. The impact of a transverse directed external magnetic field on blood flow through a stenosed bifurcated artery was investigated. The arterial geometry was considered as a bifurcated channel with overlapping shaped stenosis. The problem was treated mathematically using the Galerkin Least-Squares (GLS) method. The implementation of this numerical method managed to overcome the numerical instability faced by the classical Galerkin technique when adopted to a highly viscous flow. The benefit of GLS in circumventing the Ladyzhenskaya-Babuška-Brezzi (LBB) condition was utilized by evaluating both the velocity and pressure components at corner nodes of a unstructured triangular element. The non-linearity that emerged from the convective terms was then treated using the Newton-Raphson method, while the numerical integrals were computed using a Gaussian quadrature rule with six quadrature points. The findings obtained from this study were then compared with available results from the literature as well as Comsol multiphysics software to verify the accuracy and validity of the numerical algorithms. It was found that the application of magnetic field was able to overcome flow reversal by 39% for a shear-thinning fluid, 26% for a Newtonian fluid, and 27% for a shear-thickening fluid. The negative pressure and steep wall shear stress which occurs at the extremities of an overlapping stenosis throat were diminished by rise in magnetic intensity. This prevented thrombosis occurrence and produced a uniform calm flow.

Three-dimensional simulation of capillary rheometry for an estimation of extensional viscosity

Abstract It is difficult to directly measure the steady extensional viscosity of thermoplastic composite materials, especially at high extension rates. The famous Cogswell method was derived analytically from the pressure drop of entrance flow in commercial capillary rheometers for estimating the extensional viscosity. However, using Cogswell´s extensional viscosity has always resulted in over-predictions of pressure drop. Recently, the GNF-X (eXtended Generalized Newtonian Fluid) model with a weighted shear/extensional viscosity was proposed to show the typical extension-induced vortex growth in entrance flow simulations. Under given various values of Trouton’s ratio for extensional viscosity, the GNF-X model is introduced to perform three-dimensional flow simulations of capillary rheometry over a range of apparent shear rates. The difference between the predicted pressure drops and the relevant experimental data is minimized such that the estimation of extensional viscosity is optimized herein.

Impact of viscosity modeling on the simulation of aortic blood flow

Modeling issues for the simulation of blood flow in an aortic coarctation are studied in this paper. From the physical point of view, several viscosity models for non-Newtonian fluids as well as a Newtonian fluid model will be considered. From the numerical point of view, two different turbulence models are utilized in the simulations. The impact of both, the physical and the numerical modeling, on clinically relevant biomarkers is investigated and compared.

Impact of hydrodynamics and rheology of the ion partitioning effect on electrokinetic flow through a soft annulus with a retentive and absorptive wall.

The theoretical analysis for the mass transfer process of an oscillatory electroosmotic flow (EOF) in the fractional Jeffrey fluid model is studied through a polyelectrolyte layer (PEL) coated cylindrical annulus with reversible and irreversible wall reactions. The ion partitioning effect is observed due to the difference in permittivity of the PEL and the electrolyte solution, which is accounted for by the Born energy. Considering ion partitioning effects, analytical solutions for induced potential and axial velocity are presented, respectively in both the PEL and electrolyte region from the modified Poisson-Boltzmann equation and the Cauchy momentum equation with a proper constitutive equation, respectively. The Maxwell fluid and classical viscous Newtonian fluid models can be achieved separately by adjusting the relaxation and retardation time in the constitutive equation of this model. The analytical solution of the convection-diffusion equation for solute transport is established in the full domain. The separation of species is found to be dependent mainly on the Damköhler number, absorption parameter, phase partitioning coefficient, etc. It is observed that the osmotic pressure increases with the thickness and fixed charge density of the PEL. The velocity decreases with an increase in the permittivity difference of these layers. Our results suggest that the separation may be achieved through a difference in absorption kinetics.

Unsteady solute dispersion in pulsatile Luo and Kuang blood flow (K - L Model) in a tube with wall reactive absorption

Unsteady solute dispersion in pulsatile non-Newtonian flow in a circular tube has been investigated considering higher order moments using the Aris’s method of moments. The Luo and Kuang(1992) (K - L Model) constitutive relation is used for the non-Newtonian fluid. The axial mean concentration of solute is estimated by considering exchange, convective, dispersion coefficients. In addition, considering the 3rd and 4th central moments, the skewness, and kurtosis in the mean concentration is examined. Variations of these five moments against the absorption parameter, K-L fluid parameters, and Womersley frequency parameter are thoroughly investigated. The increase in the Womersley frequency parameter led to the occurrence of a double frequency period for the dispersion coefficient, which influenced the skewness and kurtosis coefficients that led to the deviation from usual normal distribution of the mean concentration distribution at the starting of the dispersion process. The concentration distribution is skewed towards the central region of the tube. The concentration contours also reveal that the solute convection is more in the central region of the tube. The results for Newtonian, Bingham, and Casson fluid models are retrieved as special cases. The mean concentration has the highest peak for the K-L model and the lowest for the Newtonian fluid model. It is scattered axially more for the Bingham fluid than the Casson fluid. This investigation emphasizes that higher moments provide precise information about the solute dispersion in the flow field and its deviation from the normal distribution at small time scales. • This investigation examining the unsteady axial dispersion of a solute in the non-Newtonian pulsatile flow in a cylindrical tube, considering the impact of an irreversible first-order boundary reaction. Solute dispersion in K-L model has been introduced, which gives the shear thinning and thickening behaviour of blood flow even if yield stress is zero. • The present study initiated skewness and kurtosis analysis for steady/ unsteady, non-pulsatile/ pulsatile and Newtonian/ non-Newtonian fluid flow by using method of moments. Here analytical results for all transport coefficient with skewness and kurtosis has been discussed. • The perturbation and numerical solution of coupled and non-linear equation of shear stress and momentum equation has been obtained to get the velocity profile. A new class of computationally explicit Runge–Kutta (CERK) numerical method (Yadav et. al. (2022)) has been used to solve this stiff problem. A detailed comparison of perturbation and numerical solutions is also given in this manuscript. • The solution of the concentration equation is obtained analytically adopting the Aris0 s method of moments, with fourth-order precision. In the presence of boundary reaction, the transport coefficients are affected not only by time but also by the Womersley frequency parameter, other chemical variables, the wall absorption parameter, the yield stress, the amplitude of the fluctuating pressure component, and plasma viscosity. The non-Gaussian distribution of solute is visible for small time after injection. • The mean concentration as well as the two-dimensional concentration distribution are accurately described. The results for the Bingham model, the Casson model, and the Newtonian model are derived directly from this analysis.

Numerical modeling of the dam-break flood over natural rivers on movable beds

Abstract In the present work, a modified numerical model was developed to simulate the water flow during a dam break with the mud layer transfer of different heights, consisting of three phases (water, air, and a phase for deposition). To carry out a numerical simulation of this process, a mathematical model based on the VOF (volume of fluid) method was modified, taking into account the movement of the water-free surface, which is carried out by the movement of water flow based on the Newtonian fluid model, and the movement of mud impurities is based on the non-Newtonian fluid model. Validation of the constructed model for the influence of three-dimensional features of the flow on morphological changes is carried out by a modified mathematical model and compared with the results of calculation for two-dimensional (2D) and three-dimensional (3D) models. The proposed method for modeling is applied on a real complex terrain, which was based on the Kargalinka – a river in Almaty and the Almaty region of Kazakhstan, the right tributary of the Kaskelen River. Simulation analysis is carried out for cases with different deposit heights. All results of the numerical simulation can be visually viewed using graphs and illustrations.

Investigation of Newtonian and non-Newtonian Bingham fluid models for lateral flow simulation of liquefied soil

This study applies a Newtonian model and non-Newtonian Bingham model to simulate the lateral flow of liquefied soil and investigates the models’ parameters. First, the study derives analytical solutions for the lateral flow velocity under free-field conditions in both the transient and steady states for both models. The study determines that the solution derived for the Newtonian model can be applied to derive that for the Bingham model through a simple transformation considering the contribution of undrained residual shear strength of liquefied soil. Second, three-dimensional numerical analyses are executed using COMSOL to investigate the boundary conditions of experimental models, which significantly affect the fluid behavior of liquefied soil. The results reveal that the model length and sidewall effects can be ignored at a length-to-thickness ratio of >30 and width-to-thickness ratio of >6, respectively. The Bingham model can describe the behavior of liquefied soil under different boundary conditions using a single set of parameters. Through normalization, the Bingham and Newtonian models can share the same normalized velocity–time curve. Additionally, the Bingham model with boundary conditions can have a similar curve to that under the free-field condition through the replacement of the original viscosity coefficient with an apparent viscosity coefficient.

Asymptotic Analysis of Peristaltic Hydromagnetic Flow of Carreau Fluid in a Curved Channel

The boundary layer peristaltic hydromagnetic flow of Carreau fluid in a curved type has been investigated in this article. Carreau fluid model is a generalized Newtonian fluid model having four parameters namely, infinite-shear-rate viscosity (μ∞), zero-shear-rate viscosity (μ0), relaxation time constant (Γ) and power-law index (n). The governing equations of the flow is obtained under long wavelength and low Reynolds number assumptions. An asymptotic solution to this problem is obtained when the strength of the applied magnetic field is large. It is observed the that asymptotic solution is independent of Weissenberg number. The asymptotic solution is also validated against numerical solution obtained via finite difference method.

Asymptotic Analysis of Peristaltic Hydromagnetic Flow of Carreau Fluid in a Curved Channel

The boundary layer peristaltic hydromagnetic flow of Carreau fluid in a curved type has been investigated in this article. Carreau fluid model is a generalized Newtonian fluid model having four parameters namely, infinite-shear-rate viscosity (μ∞), zero-shear-rate viscosity (μ0), relaxation time constant (Γ) and power-law index (n). The governing equations of the flow is obtained under long wavelength and low Reynolds number assumptions. An asymptotic solution to this problem is obtained when the strength of the applied magnetic field is large. It is observed the that asymptotic solution is independent of Weissenberg number. The asymptotic solution is also validated against numerical solution obtained via finite difference method.

Mechanics of nonlinear visco-hyperelastic-hysteresis membranes

This contribution aims at developing a general formulation for the large deformation analysis of membranes considering both hysteresis and viscoelastic effects. Firstly, the kinematics of the deformation of thin membranes in three-dimensional space is formulated. Afterward, the visco-hyperelastic-hysteresis formulation of membranes is derived based upon the multiplicative decomposition of the deformation gradient tensor in the hysteretic and viscoelastic branches of the model. Evolution equations of the hysteresis and viscoelastic internal variables are obtained based on dissipation inequality. The formulation admits using both Newtonian and non-Newtonian fluid models to model the viscous dashpots. For the time integration of the evolution equations, the implicit Euler-backward method is employed. Variational formulation of the problem for development of a nonlinear finite element formulation, in the Total Lagrangian framework, is presented. To investigate the capability of the developed formulation, several numerical examples are provided. The results are in excellent agreement with the data available in the literature.

Entropy generation on Casson hybrid nanofluid over a curved stretching sheet with convective boundary condition: Semi-analytical and numerical simulations

The present study reports a computational analysis of entropy generation on the MHD flow behavior of two-dimensional Casson hybrid nanofluid over a porous curved stretching sheet in the appearance of thermal radiation. To examine the rheology of the blood we have incorporated Casson fluid model in which comparison is done for both Newtonian and non-Newtonian models. In this investigation, we used the blood as based and Tantalum ( Ta) and Cobalt ( Co) are nanoparticles due to an extensive range of biomedical applications such as an agent to prevent the heat transfer of blood and wounded tissue, treatments of anemia, and treatment of cancer therapeutics. The governing non-linear coupled partial differential equations are altered into non-linear coupled ordinary differential equations by using the similarity variables. The Homotopy Perturbation Method is used to solve the newly renovated equations semi-analytically. The semi-analytical outcomes are validated with numerical outcomes obtained through the shooting method, and they are also compared to available literature as a limiting case. Graphical projections are supplied with the influence of active parameters for velocity, temperature, Bejan number, entropy production, skin friction, and Nusselt number. The velocity profile increases for higher values of curvature parameter, and mixed convection parameter. The temperature profile increases, when increases the thermal radiation and magnetic parameters. Higher values of the nanoparticle’s volume fraction enhance the rate of heat transfer. Compare to the Newtonian fluid model non-Newtonian provide higher heat transfer.

Modelling and Simulation of Transverse Homogeneity of Slotted Coating Process

Slot coating is a kind of precise coating process, which is widely used in the production of membrane materials. The thickness deviation of coating along the transverse direction is the key index to measure the coating quality. The homogeneity of the transverse distribution of the coating velocity at the exit of the die is the most direct factor leading to the transverse thickness deviation of the coating. To predict the transverse homogeneity of slot coating, a mathematical model for the internal flow field in the die was established, where the incompressible Navier-Stokes equations were used to describe the fluid flow and generalized Newtonian fluid model was used to describe the rheological behaviour of non-Newtonian coating. An efficient explicit splitting algorithm based on finite element method is proposed to solve the model. To verify the effectiveness of the model and the algorithm, the internal flow field of a trapezoidal double cavity die with equal section was simulated. The transverse homogeneity obtained was close to the experimental measured value, which verified the validity of the model. Furthermore, the influence of measuring slot width on the transverse homogeneity of outlet velocity is studied, and the simulation results are consistent with the theoretical expectations.

A proof-of-concept study for the simulation of blood flow in a post arterial segment for different blood rheology models.

Cardiovascular disease (CVD) and especially atherosclerosis are chronic inflammatory diseases which cause the atherosclerotic plaque growth in the arterial vessels and the blood flow reduction. Stents have revolutionized the treatment of this disease to a great extent by restoring the blood flow in the vessel. The present study investigates the performance of the blood flow after stent implantation in patient-specific coronary artery and demonstrates the effect of using Newtonian vs. non-Newtonian blood fluid models in the distribution of endothelial shear stress. In particular, the Navier-Stokes and continuity equations were employed, and three non-Newtonian fluid models were investigated (Carreau, Carreau-Yasuda and the Casson model). Computational finite elements models were used for the simulation of blood flow. The comparison of the results demonstrates that the Newtonian fluid model underestimates the calculation of Endothelial Shear Stress, while the three non-Newtonian fluids present similar distribution of shear stress. Keywords: Blood flow dynamics, stented artery, non-Newtonian fluid. Clinical Relevance- This work demonstrates that when blood flow modeling is performed at stented arteries and predictive models are developed, the non-Newtonian nature of blood must be considered.

Flow of two immiscible non-Newtonian fluids in an elastic tube

PurposeThis paper aims to investigate the flow of two-layered non-Newtonian fluids with different viscosities in an axisymmetric elastic tube.Design/methodology/approachA mathematical model was considered for this study to describe the flow characteristics of two-layered non- Newtonian Jeffrey fluids in an elastic tube. Because Jeffrey fluid model is a better model for the description of physiological fluid motion. Further, this model is a significant generalization of Newtonian fluid model. Analytical expressions for flux, stream functions, velocities and interface velocity have been derived in terms of elastic parameters, inlet, outlet and external pressures. The effects of various pertinent parameters on the flow behavior have been studied.FindingsThe volumetric flow rate was calculated by different models of Mazumdar (1992) and Rubinow and Keller (1972); from this it was found that the flux of Jeffrey fluid is more in the case of Rubinow and Keller model than Mazumdar. A comparative study is made between single-fluid and two-fluid models of Jeffrey fluid flows and it was observed that more flux and higher velocities were observed in the case of two-fluid model rather than single-fluid model. Furthermore, when both the Jeffrey parameter tends to zero and ratios of viscosities and radii are unity, the results in this study agree with those of Rubinow and Keller (1972).Originality/valueTo describe the fluid flow in an elastic tube with two-layered systems, the models and solutions developed here are very important. These results will be highly suitable in analyzing the rheological characteristics of blood flow in a small blood vessel because of their elastic nature.

Impact of inclined magnetic field on peristaltic flow of blood fluid in an inclined asymmetric channel in the presence of heat and mass transfer

The present investigation studies the peristaltic flow of the Newtonian fluid model through an inclined asymmetric channel. Mathematical analysis has been carried out in the presence of an inclined magnetic field and heat and mass transfer in the peristaltic flow of blood fluid in an inclined asymmetric channel. The flow is examined in a wave frame of references moving with the velocity of the wave. The physical problem is the first model, and then, the analytical solution is carried out under long-wavelength and low Reynolds number approximation. Expressions of the velocity, temperature, concentration, pressure gradient, tangential stress, and heat transfer coefficient are obtained. The results in the pressure rise and frictional force have also been computed numerically. The effects of thermal radiation, Hartman number, thermal slip, Grashof number, phase difference, aligned magnetic field, and inclination of the asymmetric channel to the vertical are studied. Numerical results are graphically discussed for various values of physical parameters of interest and the phenomenon of trapping is also discussed.

Heat transfer analysis of Cu and Al2O3 dispersed in ethylene glycol as a base fluid over a stretchable permeable sheet of MHD thin-film flow

The process of thin films is commonly utilized to improve the surface characteristics of materials. A thin film helps to improve the absorption, depreciation, flexibility, lighting, transport, and electromagnetic efficiency of a bulk material medium. Thin-film treatment can be especially helpful in nanotechnology. As a result, the current study investigates the computational process of heat relocation analysis in a thin-film MHD flow embedded in hybrid nanoparticles, which combines the spherical copper and alumina dispersed in ethylene glycol as the conventional heat transfer Newtonian fluid model over a stretching sheet. Important elements such as thermophoresis and Brownian movement are used to explain the characteristics of heat and mass transfer analysis. Nonlinear higher differential equations (ODEs) were attained by transforming partial differential equations (PDEs) into governing equations when implementing the similarity transformation technique. The resulting nonlinear ODEs have been utilized by using the homotopy analysis method (HAM). The natures of the thin-film flow and heat transfer through the various values of the pertinent parameters: unsteadiness, nanoparticle volume fraction, thin-film thickness, magnetic interaction, and intensity suction/injection are deliberated. The approximate consequences for flow rate and temperature distributions and physical quantities in terms of local skin friction and Nusselt number were obtained and analyzed via graphs and tables. As a consequence, the suction has a more prodigious effect on the hybrid nanofluid than on the injection fluid for all the investigated parameters. It is worth acknowledging that the existence of the nanoparticles and MHD in the viscous hybrid nanofluid tends to enhance the temperature profile but decays the particle movement in the thin-film flow. It is perceived that the velocity and temperature fields decline with increasing unsteadiness, thin-film thickness, and suction/injection parameters. The novel part of the present work is to investigate the hybrid nanofluid including Cu–Al2O3 dispersed in Ethylene glycol as a base fluid in the presence of a magnetic field, which has not been investigated yet. So, in limiting cases the present work is validated with published work and found in excellent agreement as shown in Table 3.

Significance of binary chemical reaction, enthalpy and variable thermophysical properties over a radioactive heated rotated disk

In present work, we assume the thermo-physical characteristics of viscous fluid on a heated rotating disk. We used the modified Newtonian fluid model for temperature dependent viscosity and calculated the mean flow profiles under the viscosity effect near the heated rotating disk. We determine the behavior with modified activation enthalpy and radiation effects by utilizing the heat phenomena while the mass transfer process is investigated by using thermophoretic, chemical reaction and activation energy. The rudimentary flow can be solved numerically via von Kàrmàn similarity solution that has been cracked by using a shooting method. We regulate the base flow profiles and provide a physical clarification of the problem through graphs and tables. Correlations in term of velocity, viscosity, temperature and concentration are plotted graphically.

Magnetohydrodynamics Boundary Layer Flow of Hybrid Nanofluid in a Thin-Film Over an Unsteady Stretching Permeable Sheet

This analysis explored the computational process of heat transfer analysis in a thin-film MHD flow embedded in the hybrid nanoparticles, which combine the spherical copper and alumina dispersed in ethylene glycol as the conventional heat transfer Newtonian fluid model over a stretching sheet. The nonlinear ordinary differential equations (ODEs) was attained by transforming partial differential equation (PDEs) as governing equations when implementing the similarity transformations technique. The resulting nonlinear ODEs have been utilized by using the Keller box method. The natures of the thin-film flow and heat transfer through the various values of the pertinent parameters: unsteadiness, nanoparticle volume fraction, thin-film thickness, magnetic interaction and intensity suction/injection are deliberated. The approximate results for velocity and temperature distributions and physical quantities in terms of local skin friction and Nusselt number have been obtained and analyzed via graphs and tables. As a consequence, the suction expresses a more prodigious effect on the hybrid nanofluid rather than injection fluid for all the investigation parameters. It is worth acknowledging that the existence of the nanoparticles and MHD in the viscous hybrid nanofluid tends to enhance the temperature profile but decay the particle movement in the thin-film flow. It is perceived that the velocity and temperature profiles decline for the growth of the unsteadiness, thin-film thickness and suction/injection parameters.

Numerical simulation of generalised Maxwell-type viscous dampers with an efficient iterative algorithm

In this work, an extended numerical model for viscous dampers, which can be deemed as a generalised Newtonian fluid model, is proposed based on the conventional power-law fluid viscosity. With a flexible definition of damping coefficient, a wide range of damper response can be simulated using the new damper model. An efficient direct integration algorithm with an iterative scheme is proposed for the state determination of the corresponding Maxwell model that employs the proposed dashpot and spring with either elastic or elastoplastic response. Compared to an ODE solver based approach, which has limitations in terms of applicability/accuracy, compatibility/consistency and efficiency/robustness, the proposed algorithm has a higher computational performance and is less sensitive to numerical instability issues. The proposed viscous damper model and the state determination algorithm can be readily used in simulations of various damped dynamic systems.

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.