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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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In this paper, steady creeping motion of non-Newtonian falling drop through a viscous fluid is investigated analytically. Here, the Upper Convected Maxwell model (UCM) is used for drop phase and Newtonian model is considered for external fluid. The perturbation technique is used to solve both exterior and interior flows and Deborah number that indicated the elastic effect is considered as the perturbation parameter. The present solution is derived up to second order of perturbation parameter so the present solution has a suitable accuracy for drops that made from dilute polymeric solutions. We found that the Newtonian drop has a spherical shape during the creeping motion but the non-Newtonian drop loses this shape and takes an oblate form. By increasing the elastic effect, a dimple at the rear end of the drop is created and developed. Here, it is shown that the present results have more agreement with experimental data than the previous analytical studies. The origin of drop deformation is also considered and it is proofed that the elastic property of drop phase creates a concentrated normal stress at the rear end of the drop that causes the dimple shape in this region.

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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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One of the challenging problems of tribology is cam and follower elastohydrodynamic lubrication due to the simultaneous effect of various lubrication mechanisms. These mechanisms are transient, squeeze film, elastic deformation of contacting surfaces and variation of lubricant properties with pressure. In this paper, besides studying the mentioned factors, the effect of using a non-Newtonian lubricant such as grease is numerically investigated. The lubrication governing equations and Oswald’s grease behavior equation have been discretized using finite difference technique. The system of equation has been solved via Multi-Grid method which is an advanced iterative method in solving system of partial differential equations. The results are showed for Newtonian oil comparing to grease for different cam rotational speed. Also different grease behaviors are investigated. The results are verified by a comparison to the results obtained using the famous Newton-Raphson method. Finding shows that the minimum lubricant thickness as well as the maximum pressures is lower when using grease compared to the case that a Newtonian lubricant is used. In the case of Newtonian lubricant, increasing the speed results in an increase in the lubricant film thickness but it is shown that the speed does not affect the lubricant thickness in the case of non-Newtonian lubricant.

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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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In this study, the natural convection heat transfer is numerically examined in a square enclosure filled with a non-Newtonia power-law fluid. Two fixed temperature baffles are mounted on the left wall of the enclosure. The left wall of the enclosure and the baffles installed on it, are at a constant temperature of T_h and the right wall of the enclosure is at a constant temperature of T_c, while its horizontal walls are thermally insulated. 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 study investigates the effects of relevant parameters such as the Rayleigh number (〖10〗^3≤Ra≤〖10〗^6), the power-law index (0.8≤n≤1.4), the baffles length (0≤B≤0.5) and the baffles distance from each other (0.1≤D≤0.8) on flow and temperature fields and the rate of heat transfer. The results show that an increase in Rayleigh number, particularly when n

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In this paper, the effects of temperature and nanoparticles volume fraction on the viscosity of non-Newtonian hybrid nanofluid, containing water and ethylene glycol as a base fluid and multi-walled carbon nanotubes (MWCNTs) and silica (SiO2) as additives, have been investigated experimentally. The measurements have been carried out in temperatures range of 27.5°C - 50°C by using a Brookfield DV-I PRIME digital Viscometer for different shear rates. The stable and homogeneous samples, with the solid volume fractions of 0.0625%, 0.25%, 0.5%, 0.75%, 1%, 1.5% and 2%, were prepared by dispersing the equal volumes of dry MWCNTs and SiO2 nanoparticles in a specified amount of the binary mixture of water/EG (50:50 %vol.). The measurement results at different shear rates showed that the base fluid possessed Newtonian behavior, while all nanofluid samples exhibit a pseudoplastic rheological behavior with a power law index of less than unity (n<1). Moreover, the consistency index and power law index have been obtained by accurate curve-fitting for all nanofluid samples. The results also revealed that the apparent viscosity generally increases with an increase in the solid volume fraction and decreases with temperature rising.

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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, steady motion of non-Newtonian falling drop through a Newtonian fluid at low Reynolds number is investigated analytically. Here, the Upper Convected Maxwell model (UCM) is used for drop phase and Newtonian model is considered for external fluid. During the past few decades, studies relating to non-Newtonian instabilities especially those involving free surfaces are amongst the most striking. These types of studies can be used to optimize design processes in, for example, the petroleum and medicine related processes, metal extraction, and paint and power-plant related fields. Analytical solution is obtained using the perturbation method. Reynolds and Deborah numbers are used to linearize the equations governing the problem in analytical method. Deborah number indicates the elastic effect of drop. The drag force increases by the growth of the elastic effect of non-Newtonian Drop’s. The non-Newtonian drop loses its shape and exchanges to an oblate form. Increment in Deborah number enhances the dimple at the bottom of the drop and results in an increment in its drag force and as a consequence its terminal velocity decreases. A hole is created at the rear of the drop due to the presence of inertia force and focus of normal component of stress at the rear of the drop. The novelty of this study is to consider the convection (non-linear) term of the momentum equations which was neglected in the previous studies due to the creeping flow.

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Underbalanced drilling and managed pressure drilling with foam have been gained attention of the world oil companies due to its many benefits. The advantages of this method include oil and gas production during drilling, high-speed drilling, drill bit life increase, better cutting transfer and reduced formation damage. In this paper cutting handling by foam was investigated in which foam was assumed to be a homogeneous, single-phase, compressible and non-Newtonian fluid whose rheological properties can be well described by power law model. The assumptions and governing equations of transient two-fluid model were expressed in Euler-Euler coordinate for fluid-particle (foam-cuttings). The upstream method is used to discretizing the equations and the results of the numerical solution are reported in the form of pressure, speed, cutting concentration, quality and density of the foam logs along the well. The impact of back-pressure, ROP, injection rate of gas and liquid, shape and size of cuttings, water influx and oil production on cutting concentration and bottom-hole pressure have been investigated. With increasing parameters such as back-pressure, liquid and gas flow rate, size of the cuttings and ROP, bottom hole pressure and cutting concentration increases. Cutting concentration decreases with increasing liquid and gas flow rate and increases by increasing back-pressure, cutting size and ROP. For validating, the results of the numerical solution are compared with field data obtained from well FR-1 located in the Santa Catarina state of Brazil which show about 16.5 percent errors.

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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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Free convection heat transfer of a non-Newtonian thickening power law fluid in a closed asymmetrical enclosure with fixed aspect ratio was investigated in this study. Many of the previous studies, addressed the case with symmetrical heat transfer enclosure and for a given inclination. The governing equations were established by the finite volume method and solved by the SIMPLEC algorithm. In order to evaluate the code, its results were compared to those of other papers in the field of Newtonian and non-Newtonian fluids. The impact of the enclosure inclination and the Rayleigh number on the heat transfer and the flow field were investigated. It was found that for Rayleigh numbers smaller than , inclination has little impact on heat transfer, while at Rayleigh numbers larger than , the lowest heat transfer was observed at an angle of . Moreover, the results pertaining to Newtonian and non-Newtonian thickening fluids were compared. The results show that heat transfer by thickening non-Newtonian fluids, in addition to other parameters, depends on the parameter (n) and in the case of the angle of inclination , the heat transfer of Newtonian and non-Newtonian thickening fluids is equal. Considering the non-Newtonian behavior of the fluid and nondimensionalization of the problem, a new dimensionless number known as the extended Prandtl number 〖(Pr〗^*) appeared in the equations that depends on fluids characteristics, flow geometry, and the power law exponent . Its optimal value was observed at 〖(Pr〗^*=0.07) where heat transfer from the enclosure was at maximum.

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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.