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The incompressible Newtonian and non-Newtonian fluid flow in a tube with disk insert is studied numerically using finite volume and boundary fitted coordinate method. The non-Newtonian fluid is time independent purely viscous that is simulated by the power law model. The effects of power law index, thickness, aspect ratio, Prandtl number and the distance between insert tubes on heat transfer, pressure drop and overall enhancement ratio (OER) are investigated for the Reynolds numbers 500, 1000 and 1500. The results show that the effect of power law index on pressure drop and overall enhancement ratio is more than the other parameters.

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In this paper, numerical solution of non-Newtonian fluid flow through a channel with a cavity is studied. Carreau-Yasuda non-Newtonian model which represent dependence of stress on shear rate well is used and the effect of n index of model on attribute of flow is considered. Governing equations are discretized using finite difference method on staggered mesh and the form of allocating flow parameters on staggered mesh is based on marker and cell method. For dependence between continuity and momentum equations, artificial compressibility method is used. Numerical results express that with decrease of n index, the developing length is increased and the velocity in center of channel and pressure drop of flow are decreased.

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In this paper, the immersed boundary-lattice Boltzmann method has been employed to simulate non-Newtonian flow around curve boundaries. The pressure base lattice Boltzmann equations have been used to solve the Eulerian domain to estimate proper pressure gradient in the Poiseuille flow. In addition Immersed boundary method (IBM) utilizes a discrete set of force density is also used to represent the effect of boundary on flow domain. In addition to simulate the real physical dominate problem and study the right effects of non-Newtonian fluid properties, scaling parameters have been introduced to notice the relationship between physical and lattice variables. At First, the capability of present method is examined for simulating the power-law fluid flow around a confined circular cylinder and the results show good agreement with previous study. In the following, the power-law fluid flow around elliptical cylinder in a channel is investigated for three aspect ratios eta=1,1.5,2 and for 5

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This Study presents a numerical investigation of the hydro-thermal behavior of a Non-Newtonian ferrofluid (non-Newtonian base fluid and 4% Vol. Fe3O4) in a rectangular vertical duct in the presence of different magnetic fields, using two-phase mixture model, power-law model, and control volume technique. Considering the electrical conductivity of the base fluid, in addition to the ferrohydrodynamics principles, the magnetohydrodynamics principles have also been taken into account. To study the effects of non-Newtonian base fluid using power-law model, assuming the same flow consistency index with viscosity of Newtonian fluid, two different power law indexes (i.e., n=0.8 and 0.6), have been investigated and the results have been compared with that of Newtonian ones (i.e., n=1). Three cases for magnetic field have been considered to study mixed convection of the ferrofluid: non-uniform axial field, uniform transverse field and another case when both fields are applied simultaneously. The results indicate that the overall influence of magnetic fields on Nusselt number and friction factor is similar to the Newtonian case, although, by decreasing the power law index, the effect of axial field on velocity profile, Nusselt number and friction factor become more significant. Moreover, the results indicate that electrical conductivity has a significant effect on the behavior of ferrofluid and cannot be neglected and also negative gradient axial field and uniform transverse field act similarly and enhance both the Nusselt number and the friction factor, while positive gradient axial field decreases them.

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Compliance mismatch is one of the reasons of the coronary artery bypass graft (CABG) failure. The purpose of this study is to investigate the effect of compliance mismatch on the End to Side bypass graft. In order to model non Newtonian behavior of the blood flow, the Carreau–Yasuda model was employed and the graft and artery wall was assumed to be isotropic and modeled as a linearly elastic. In this study also the effects of blood rheology and wall distensibility on the wall shear stress distribution and velocity profile were investigated. The results of the simulation show that the maximum deformation occurs in the critical position of graft-artery junction and compliance mismatch cause smaller wall deformation in comparison to the cases in which the materials of the graft and artery are the same which leads to a higher intramural shear stress in graft-artery junction. The anastomotic wall deforms in a way that always tends to separate the graft and artery. Wall shear stress distribution on the bed centerline and the toe of the bypass graft indicates that the differences between the homologous and non-homologous material case are visible only when the internal pressure is lower than the external one. In the distal location of the artery after the toe of the anastomotic, the values of wall shear stress in the homologous material case are lower than the non-homologous material one.

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Non-Newtonian fluid flows experience turbulent regime in some industrial applications. Several approaches have been proposed for numerical simulation of turbulent flows that each one has specific features. RANS turbulence models have reasonable computational costs, while include several sources of uncertainties affecting simulation results. In addition, developed RANS models for non-Newtonian fluids are modified versions of available models for Newtonian fluids, therefore, they cannot provide reliable estimation for viscoplastic stress term. On the contrary, DNS delivers accurate results but with high computational costs. Consequently, use of DNS data for estimation of uncertainty in RANS models can provide better decision making for engineers based on RANS results. In the present study, a turbulence model based on for power-law non-Newtonian fluid is developed and employed for simulation of flow in a pipe. Then, an efficient method is proposed for quantification of available model-form uncertainty. Moreover, it is assumed that uncertainties originating from various sources are combined together in calculation of Reynolds stress as well as viscoplastic stress. Deviation of the stresses, computed using RANS turbulence model, from DNS data are modeled through Gaussian Random Field. Thereafter, Karhunen-Loeve expansion is employed for uncertainty propagation in simulation process. Finally, the effects of these uncertainties on RANS results are shown in velocity field demonstrating the fact that the presented approach is accurate enough for statistical modeling of model-form uncertainty in RANS turbulence models.

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Since the majority of fluids in engineering and biologic applications are non-Newtonian, the study on mixing of non-Newtonian fluids is very important. Secondary flows are used in curved micromixers to improve the mixing of fluids. In this study, a numerical study was performed on the mixing of non-Newtonian fluids in curved micromixers using Open source CFD code of OpenFOAM. The flow was assumed three-dimensional, steady and incompressible and Reynolds numbers were between 0.1-300. Also, water and CMC solution were used for simulation of Newtonian and non-Newtonian fluid flows, respectively. The effect of Reynolds number, power-law viscosity parameters and micromixer geometry on mixing index and non-dimensional pressure drop was studied and results were compared with those of the straight channel micromixer. The results showed that the mixing index decreased by decreasing the power law index. The mixing index was high for shear thinning flows in micromixers with sharp turns. Also, by increasing the Reynolds number, and therefore velocity, centrifugal force effects increased and mixing improved. Simultaneous investigation of mixing index and pressure drop showed that for low Reynolds numbers and small power law indexes micromixer-b had better performance.

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In this paper, the non-Newtonian immiscible two-phase polymer flow in a petroleum reservoir has been investigated numerically. The fluid flow in a porous medium is simulated as a compressible flow. The Carreau-Yasuda constitutive equation is employed as the model of non-Newtonian fluid. The IMPES method is used for numerical simulation, in which the pressure equation is discretized and solved by an implicit approach and the saturation equation is solved by an explicit method. Results reveal that zero-shear rate viscosity has a high impact on the sweep efficiency of the reservoir and also controls the channeling and viscous fingering effects. In addition increasing the viscosity of non-Newtonian fluid improves cumulative oil production and diminishes the viscous fingering phenomenon caused by injected fluid. The relaxation time of Carreau-Yasuda fluid, which is the elastic characteristic of the non-Newtonian fluid, for low permeability values cannot influence flow characteristics inside the reservoir, however for higher permeability values its effect becomes more sensible. Increasing the injection rates leads to the increase of fluid production, while the injection rate has an optimum range to reach the optimum oil production. In addition, the effect of variation of the injected fluid properties on the polymer breakthrough time has been investigated and results presented.

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Ultrasonic waves have variety of applications in bio field. The most important applications are diagnosis and treatment of diseases, drug delivery, cell separation and cell study. Passing ultrasonic waves through tissues and organs, which creates heat, bubble, stress and vibration, can result in chemical reactions, physical and biological changes. What exacerbated the researchers' scientific activities in this area is reducing the harmful effects and increasing the usefulness of this beneficial tool. In current research, the interaction of two nonlinear phenomena, acoustic streaming due to passing ultrasonic waves through bio-fluid and non-Newtonian viscosity is studied numerically. Taking into account nonlinear effects of ultrasonic field, continuity, momentum and state equations are used. In this paper, parametric effects of wall impedance, inlet flow velocity and non-Newtonian viscosity models on acoustic streaming are investigated. Results indicate influence of inlet speed on acoustic streaming velocity magnitude and its ineffectiveness on acoustic streaming profile. By increasing wall impedance, acoustic streaming magnitude decreases. This reduction is more intensive for non-Newtonian fluid. Considering non-Newtonian viscosity model for bio-fluid leads to velocity changes near boundaries, while it has less influence at domain middle.

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The cavity problem always has been considered as a classic and fundamental problem. Specific materials like Bingham viscoplastic which is sort of Non-newtonian fluids shows resistance in a certain range of stress, calling yield stress, and almost acts like rigid body in this limited area. In case of increase applied stress, flows like fluid. Considering heat transfer in this type of material and investigate it, yield stress and viscosity variations with temperature as in practice we face will not be far-fetched. In the present work the numerical solution of the problem of Bingham material inside lid-driven cavity, investigating fluid flow and heat transfer in view of the changes in material properties has been done and results have shown with change in dimensionless numbers and parameters of Re=10-1000, Bn=1-2000, Pr=0.01-100 and E=5000-50000. In this study, using the finite volume method to discretize governing equations and the use of collocated grid, effect of viscosity and yield stress dependence to temperature compared with independence mode and then distribution of horizontal and vertical components of velocity, yield areas and flow inside cavity, center of vortex and then heat transfer due to the stream lines next to side walls, have been analyzed.

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In this article, mixing in the combined electroosmotic/pressure driven flows of non-Newtonian fluid in a microchannel with rectangular obstacles and non-homogeneous ζ-potential has been studied numerically. The non-Newtonian behavior of the fluid is considered for the flow field using power law rule. Also, the nonlinear Poisson-Boltzmann equation is used to model the distribution of ions across the channel and the electric potential. Numerical solutions of coupled equations of momentum, electric field and concentration field are performed by means of finite element method. In this study, the effects of various parameters such as pressure gradient, rheological behavior of the fluid and the geometrical and physical parameters of obstacles on the mixing quality are investigated. The results indicate that applying adverse pressure gradient to the flow, the dilatant behavior of the fluid, as well as the height of barriers, are highly effective in the enhancement of the mixing quality within the microchannel. It is found that for microchannels with heterogeneous ζ-potential, increasing the length of obstacles significantly increases the mixing efficiency while for the microchannels with homogeneous ζ-potential, barrier length has a slight effect on mixing efficiency.

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In this paper, natural convection heat transfer is numerically investigated in a square enclosure filled with power law non-Newtonian fluid model and central heat source for steady and quiet state. The top wall of the enclosure is thermally insulated and the vertical walls are at constant temperature of TC. The down wall of the enclosure also has four equal parts at constant temperature of TC and TH. The governing equations for the power-law fluid flow are solved with the numerical finite difference method based on the control volume formulation and SIMPLE algorithm. The results show that for small Rayleigh numbers the Nusselt number will not be affected by changes of the power law index but in Ra=106, thermal performance changes are more significant with the change in power law index. With a smaller the Rayleigh number in all indexs, the center of flow lines rotation, regarding to the axis parallel to axis Y, in the middle of the enclosure, will be more symmetrical. Also with stronger natural convection in the square enclosure, the average of Nusselt number for non-Newtonian fluid increase with increased power law index and improved thermal performance by increasing the Rayleigh number is impressive for the density power law fluid (n˃1). Results also show that the Rayleigh number for the start of natural convection in the square enclosure is reduced by increasing the power law index.

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In this paper, the goal is to provide analytical solutions for the thin film flow of a non-Newtonian fluid in different geometries and boundary conditions. An analytical solution for the non-Newtonian fluids is one of the most important and challenging issues that helps in understanding the physics of these fluids. For this purpose, the theory of micropolar fluids has been used. Thin film in three specific geometries, including flow downward on an inclined surface, flow on a moving ribbon, and flow downward on a vertical cylinder is considered. In order to solve the governing equations and obtaining the velocity and rotational fields, in the first two geometries, an analytical methods and in the third geometry a combined analytic and numerical methods are used with respect to the complexity of the equations. The rotational and velocity fields are plotted for all three cases and the results are discussed for different values of the parameters of a micropolar fluid. Also, the effect of the concentration of microelements in the fluid has been studied. It was observed that with the increase of the micropolar fluid parameter, the magnitude of velocity and rotation decreases.

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The collision of droplets on solid surfaces is widely used in oil and gas industry, surface painting, hot surface cooling and spraying of agricultural products. In the present study, the spreading factor of Boger non-Newtonian fluid is experimentally investigated on the dry solid surface such as an acrylic (Plexiglas) and stainless steel sheet and is compared with Newtonian droplets (water and glycerin). The plates of Plexiglas and stainless steel both have a hydrophilic surface. In this research, the Newtonian and non-Newtonian fluids droplets collapse at two heights of 27 and 47 cm from the dry solid surface and are examined in the range of Weber numbers 245≤We≤"538" . The purpose of this study is to investigate the effects of contact velocity on the spreading factor of non-Newtonian and Newtonian droplets during the collision. The results of this study show that with the growth of Weber number (increasing contact velocity), the maximum value and velocity of spreading and receding are increased for the Newtonian or non-Newtonian droplets. Also, with increasing the viscosity of droplets, the value and velocity of spreading and receding are decreased for the Newtonian and non-Newtonian droplets. By increasing the velocity of collision on the Plexiglasas surface (raising the Weber number) up to 32%, the maximum value of droplets spreading is increased 22, 31 and 20 percentage respectively for the fluids of Boger, water and glycerin.

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The impact problems associated with water entry have important applications in various aspects of naval architecture and ocean engineering. Also the calculation of impact force is favorable to many researchers. The purpose of this study is to simulate the impact problem of a wedge into the Newtonian and also Herschel Bulkley dilatant non-Newtonian fluids using the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. Some non-Newtonian fluids, such as dilatant or Herschel Bulkley dilatant fluids can resist against the wedge entry due to their shear thickening effect. In this research a prediction and correction algorithm is used to solve the governing equations. Density correction and also artificial viscosity (which is used only in Newtonian fluids) are used to prevent the numerical instability. To show the validation, ability and robustness of the generated code to capture the free surface in Newtonian and non-Newtonian fluids, the dam break problem with the image boundary condition is simulated. After validating the code and the used method, the impact problem of a wedge with Monaghan repulsive force boundary condition in Newtonian and Herschel Bulkley Dilatant non-Newtonian fluids are investigated and the results of force, pressure coefficient and velocity of the wedge are presented and compared with experiments and also with each other. To save time, the initial values of hydrostatic pressure are imposed as an initial condition of the fluid.

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The coastal waves caused by landslide in the lake of reservoir dams can threaten the safety of the dam. Therefore, the exact recognition of hydraulic flow due to coastal waves has always been of interest to researchers. So far, extensive laboratory and numerical research has been devoted to it. Also, the phenomenon of landslide in the lake of dams and rivers, and the production and propagation of waves resulting from it, is one of the most important and complex issues in the field of hydraulic engineering. Today, the expansion of numerical relations and the modeling process have somewhat contributed to a rational understanding of these phenomena. In this research, a Lagrangian method is used for solving governing equations. Initially, the hydrodynamic method is defined as an explicit three-step incompressible smoothed particle hydrodynamic. This method, by replacing the fluid with a set of particles, provides an approximate solution to the fluid dynamics equations. In this simulation, there are a series of arbitrary interpolation points that can be assumed to be fluid particles. All variables are calculated by these points and are calculated by an interpolation function. In order to validate the method, the dam break problem on dry bed and the subsurface landslide problem have been used. In the first issue, the correlation coefficient of 0.9998, the mean absolute error of 0.5426 and the efficiency coefficient of the Nash-Sutcliff model 0.974 for the calculated parameters indicate that the model is accurately calibrated, which demonstrates the high capability of this method in simulating free surface fluids and wave-related phenomena. Also, comparing the measured results with the experimental data in the sub-surface landslide simulation showed that the correlation and mean square error correlation coefficients were 0.95 and 0.0071 respectively, which indicates the high accuracy of the model in calculating the water surface profile caused by landslide subsurface. The results showed that at times after 2 seconds, numerical waves tended to release more than its experimental state, with a difference between the ranges of 5 to 10 cm. This is due to the turbulence of the free surface of water causing the flow of complexity. For smaller body weights and deeper depths of submergence, these differences will be lower in scope.
Then three landslide modeling scenarios were designed and implemented. In this study, slopes and non-rigid bodies were considered as a rheological material (pseudoplastic fluid) and entered into modeling as Carreau Yasuda non-Newtonian fluid. The results were reported at 0.3 and 0.6 seconds, and then they were analyzed.
The innovation aspect of this research is that the study of non-rigid slopes during landslide and falling and sliding of non-rigid bodies on them, as well as the production and propagation of waves from it, have not been investigated so far. The purpose of this paper is simulation and review it by an explicit three-step incompressible smoothed particle hydrodynamic. On the other hand, the choice of non-Newtonian Carreau Yasuda fluid to simulate the slope and non-rigid body is another aspect of the innovation of the present study.

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In this paper, an asymmetric breakup of non-Newtonian droplet (with power law behavior) in a new geometry (network junction) has been investigated. The geometry can break an initial droplet into six unequal size droplets. The research method is numerical simulation with Volume of Fluid (VOF) algorithm. The numerical results are compared with the results of a benchmark problem and a very good agreement is seen. The results showed that in areas close to the wall, mixing of materials of inside droplet is performed better, which is important in industrial applications of droplet based flows, especially in pharmaceutical and chemical industries. The results showed that the maximum vorticity magnitude in the K1 branch (the lowest output branch in the system) is 26, 44 and 28 % more than the maximum vorticity magnitude of the branches of K2, K3 and K4 (K4 is the highest output branch is in system). Also, maximum effective viscosity in the K1 branch is 27, 29 and 24 % less than the maximum effective viscosity in the K2, K3 and K4 branches, respectively. Therefore, K1 branch has the best performance in mixing of the material of inside droplet among the output branches. It was also revealed that the pressure of inside of droplet (both before and after breakup) is constant along the channel width.