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The time-independent and incompressible blood-based hybrid nanofluid flow, including Au and Cu nanoparticles across an expanding sheet, has been studied. To illustrate the non-Newtonian performance of the blood-based hybrid nanofluid flow, a non-Newtonian model known as the Carreau–Yasuda model is used. The hybrid nanofluid flow is studied under the influence of magnetic effects, thermal radiation, Brownian motion, thermophoresis, and chemical reactivity. Homotopy analysis method (HAM) is employed to evaluate the modeled equations. A study is conducted on the convergence analysis of HAM, and the HAM and numerical analyses are compared. From the present analysis, the velocity profile increases with an increase in Weissenberg number and decreases with increasing magnetic factor. The temperature, concentration, and microorganisms profiles increase in tandem with the higher thermal Biot, concentration Biot, and microorganism Biot numbers. The thermal and concentration profiles, respectively, have decreased due to the larger thermal and concentration relaxation time factors. The microorganism profiles have decreased due to the increased bioconvection of Lewis and Peclet populations. The modeled equations can be solved by both the HAM and the numerical approaches, validating both approaches to solution.

The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation (Rd). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command ‘nftool’. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index (R), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10−10, 1.64 × 10−9, 1.03 × 10−9, 302 9.35 × 10−10, 8.56 × 10−10, 1.08 × 10−9, and 6.97 × 10−10, respectively. It is noted that f′(η), θ(η), and ϕ(η) satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes (Cfx, Nux, and Shx) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase (M=0.01, 0.05, 0.1), then the solution bifurcates at different critical values, i.e., λc=−1.06329,−1.097,−1.17694. The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement.

In this current work, we assume the mathematical modelling of non-Newtonian time-dependent hybrid nanoparticles via a cylindrical stenosis artery. In this work, blood is used as a base fluid, and the nanoparticles (copper and aluminum oxide) of cylindrical shape are inserted inside the artery to combine with blood to form hybrid nanofluid (HNF). The homotopy analysis method (HAM) is deployed for the solution of nonlinear resulting equations. For the validation of this current work, the results of the existing work have been compared with our proposed model results. A comparison of key profiles like velocity, temperature, wall shear stress, and flow rate is also performed at a specific critical height of the stenosis. It is also observed that the thermal conductance of hybrid nanofluids is greater than that of nanofluids. Including the hybrid nanoparticles (copper and aluminum oxide) inside the blood enhances the blood axial velocity. These simulations are applicable to the magnetic targeting treatment of stenosed artery disorders and the diffusion of nanodrugs.

Roland Glowinski published 8 books and more than 300 articles. He was also an editor of many very well cited proceedings. Hence this attempt to summarize his scientific work is not likely to do justice to his work. Nevertheless, we will try to extract his major contributions, such as the augmented Lagrangian algorithm, various domain decomposition and fictitious methods and their performance on the Navier–Stokes equations in a moving domain. Roland has created a school of applied mathematicians remarkable by their rigor and efficiency for industrial applications. He marked his time and his books will be authorities as long as computer architectures are similar to their present structures.

The Bingham fluid simulation model was constructed and validated using a physically consistent particle method, i.e., the Moving Particle Hydrodynamics (MPH) method. When a discrete particle system satisfies the fundamental laws of physics, the method is asserted as physically consistent. Since Bingham fluids sometimes show solid-like behaviors, linear and angular momentum conservation is especially important. These features are naturally satisfied in the MPH method. To model the Bingham feature, the viscosity of the fluid was varied to express the stress-strain rate relation. Since the solid-like part, where the stress does not exceed the yield stress, was modeled with very large viscosity, the implicit velocity calculation was introduced so as to avoid the restriction of the time step width with respect to the diffusion number. As a result, the present model could express the stopping and solid-like behaviors, which are characteristics of Bingham fluids. The proposed method was verified and validated, and its capability was demonstrated through calculations of the two-dimensional Poiseuille flow of a Bingham plastic fluid and the three-dimensional dam-break flow of a Bingham pseudoplastic fluid by comparing those computed results to theory and experiment.

In most of practical situation multiple slips (velocity, temperature and concentration) has importance in manufacturing, medicinal, imaging processes and design of materials. In view of this, the present work considered the multiple slips on Magneto hydrodynamic (MHD) dissipative non-Newtonian fluid (Casson fluid) above a curved type of a stretching surface are studied. Multiple slips with Casson fluid have significance in controlling the blood flow distribution in human and animal bodies. The R–K fourth-order via shooting technique is used to convert the nonlinear governing equations. The impact of governing parameters is shown and explored graphically. The present investigation explores the multiple slip effects in governing equations under the influence of the magnetic field; the fluid's temperature and velocity have reverse characteristics. In a few unique situations, the current findings have been in reasonable agreement with the current results. As opposed to when viscous dissipation is absent, the temperature distribution is higher when viscous dissipation is present. It helps us to decide depending on the industrial and manufacturing processes, whether dissipation has to be applied or not. The stretching parameter enhances the Skin friction coefficient and rate of heat transfer, while decreases the rate of mass transfer. Also, the fluid's temperature decreases because an increase in Casson fluid parameter enhances the plastic dynamic viscosity, which creates resistance in the fluid motion. [ABSTRACT FROM AUTHOR]

The causes of coating irregularities in high-speed slot-die coating of catalyst slurries for polymer electrolyte fuel cells (PEFCs) have not been determined. Accordingly, in this study, slot-die-coating experiments and computer simulations of two-phase gas–liquid flow were conducted to explore coating instability in the high-speed coating of PEFC catalyst slurries applied through slot-die coating. The results obtained from experiments and simulations were consistent. A thinner target layer and a faster coating, causing non-uniform coating. This is caused by movement of the gas–liquid interface on the upstream side and side of the die, which entraps the gas phase. Viscosity and surface tension are important, and a lower ethanol content in the solvent increases surface tension and lowers viscosity, improving coating stability. [Display omitted] • PEFC catalyst slurry coating uniformity studied through experiments and simulations. • Results were consistent across experiments and simulations. • Coating is non-uniform at high speed, low thickness, and high ethanol ratio. • The coating occurs in a region with weak non-Newtonian behavior. [ABSTRACT FROM AUTHOR]

This article concerns the dynamic transitions of a non‐Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is performed by deriving the principle of exchange of stability condition, which shows the system loses stability when the thermal Rayleigh number exceeds a threshold. Second, we consider the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transition types. Our results show that both continuous and jump transitions can occur for certain parameters when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, but only continuous transition induced by real eigenvalues is observed when the diffusivities from big to small is the opposite of the previous case. [ABSTRACT FROM AUTHOR]

The control mechanism of the pressure drop and bubble size has a guiding significance for selecting the micropump, the pressure resistance design, and the precise control of the microfluidics. In this study, single-phase flows and gas-non-Newtonian fluid two-phase flows are studied in a microchannel containing curved structures. Sodium carboxymethyl cellulose solutions are used as the non-Newtonian fluids; water and nitrogen are used as Newtonian fluid and gas phases, respectively. The pressure drop and the bubble length are measured. The influences of operating conditions are discussed. The non-Newtonian properties of the solutions are found to affect the parameters measured significantly. The experimental results are compared with the existing models, and the fanning friction factor is used to evaluate the pressure drop. The two-phase flow pressure drop can be predicted by the Lockhart-Martinelli method with a newly developed C-coefficient as a function of the fluid characteristic parameters and microchannel structure parameters. The new correlation for two-phase pressure drop prediction has an error within 18%, smaller than existing models. A new prediction method for the dimensionless bubble length containing the two-phase friction multiplier is also given with an error of 16%. [Display omitted] • A novel microchannel containing curved structures was studied experimentally. • Empirical models for predicting pressure drop and bubble length were developed and compared with existing models. • The prediction accuracy of the pressure drop was improved by considering structural and non-Newtonian fluid parameters. • The prediction accuracy of the bubble length was improved by considering the influence of pressure drop. [ABSTRACT FROM AUTHOR]

An experimental investigation is conducted to study the two-phase heat transfer behavior of a shear-thinning Non-Newtonian (NN) fluid, i.e., "Massecuite," at atmospheric pressure over bi-directional microstructured surfaces for the heat flux range from 70 to 200 kW/m2. Two-phase heat transfer characteristics of a Newtonian Fluid, that is, distilled water, is also studied for the sake of comparison. Both aqueous XG solution and water exhibit higher heat transfer rate over microstructured surfaces as compared to plain surface. The heat transfer coefficient (HTC) of aqueous XG solution was found to increase over the microstructured surface from B-90-3-2-0.4-R to B-90-3-2-0.4-C to B-60-3-2-0.4-Nil. An enhancement of 83.35% is observed in the aqueous XG solution's two-phase HTC over a bi-directional inclined tunnel-based microstructure surface (B-60-3-2-0.4-Nil) compared to the plain surface. [ABSTRACT FROM AUTHOR]

Multi-layer fabrics are commonly used in ballistics shields with a lower bulletproof class to protect against pistol and revolver bullets. In order to additionally limit the dynamic deflection of the samples, layers reinforced with additional materials, including non-Newtonian fluids compacted by shear, are additionally used. Performing a wide range of tests in each case can be very problematic; therefore, there are many calculation methods that allow, with better or worse results, mapping of the behavior of the material in the case of impact loads. The search for simplified methods is very important in order to simplify the complexity of numerical fabric models while maintaining the accuracy of the results obtained. In this article, multi-layer composites were tested. Two samples were included in the elements subjected to shelling. In the first sample, the outer layers consisted of aramid fabrics in a laminate with a thermoplastic polymer matrix. The middle layer contained a non-Newtonian shear-thickening fluid enclosed in hexagonal (honeycomb) cells. The fluid was produced using polypropylene glycol and colloidal silica powder with a diameter of 14 µm in the proportions of 60/40. The backing plate was made using a 12-layer composite made of Twaron® para-aramid fabrics with a DCPD matrix—not yet used in a wide range of ballistics. Then, numerical simulations were carried out in the Abaqus/Explicit dynamic analysis. The Johnson–Cook constitutive strength model was used to describe the behavior of elastic–plastic materials constituting the elements of the projectiles. For the non-Newtonian fluid, a Up-Us EOS was used. The inner layers of the fabric were treated as an orthotropic material. Complete homogenization of the sample layers was carried out, thanks to which each layer was treated as a homogeneous continuum. As a parameter of fracture mechanics for shield components, the strain criterion was used with the smooth particles hydrodynamics method (SPH). Then, the results of simulations were compared with the results of the ballistic test for both samples placed next to each other, which resulted in the formation of a multi-layer composite in one ballistic test subjected to impact loads during firing with a 9 × 19 mm Parabellum FMJ projectile with an initial velocity of 370 ± 10 m/s. The results of numerical tests are very similar to the ballistic tests, which indicates the correct mapping of the process and the correct conduct of layer homogenization. The applied proportions of the components in the non-Newtonian fluid allowed a reduction in the deflection compared to previous studies. Additionally, the proposal to use a DCPD matrix allowed to obtain a much lower deflection value compared to other materials, which is a novelty in the field of production of ballistic shields. [ABSTRACT FROM AUTHOR]

The present work aims to explore the ability to simulate flow patterns and the velocity field in the powder injection molding (PIM) process using the smoothed particle hydrodynamics (SPH) method. Numerical simulations were performed using the DualSPHysics platform. A feedstock formulated from 17-4 PH stainless steel powder (60 vol. % of powder) and a wax-based binder system was prepared to experimentally obtain its rheological properties that were implemented in DualSPHysics using two different viscosity models. The numerical simulations were calibrated, and then validated with real-scale injections using a laboratory injection press. During the calibration step, the feedstock flow momentum equation in the DualSPHysics code was modified and boundary friction coefficients at different injection rates were adjusted to create a frictional effect. During the validation step, these calibrated conditions were used to simulate the flow behavior into a more complex shape, which was compared with experimental measurements. Using an appropriate boundary friction factor, both the frictional effect of the boundaries and the stability of the numerical solution were taken into account to successfully demonstrate the ability of this meshless SPH method. The flow front length and feedstock velocity obtained in a complex cavity were satisfactorily predicted with relative differences of less than 15%. [ABSTRACT FROM AUTHOR]

This study compared the behavior of food boluses describing Newtonian and non-Newtonian fluids through a validated human swallowing simulator based on moving particle simulation. The simulation was qualitatively and quantitatively validated through comparisons with videofluorography images. The positions and configurations of the food boluses and normalized brightness of the simulated and videofluorography images during every timestep were similar, and we thought that the simulator can be used to study the mechanism of food bolus behavior. The validated swallowing simulator results show that the key factors for the optimal design of the thickener are the control of the bolus inflow velocity, which is influenced by rheological and tribological properties, prevention of small splash particles, and bolus discharge flow rate from the epiglottis to the esophagus. In addition, we propose an evaluation index for the degree of bolus coherence based on the bolus flow rate and velocity. [ABSTRACT FROM AUTHOR]

Two‐phase flow involving non‐Newtonian fluids in fractured media is of vital importance in many natural processes and subsurface engineering applications, such as rock grouting, groundwater remediation, and enhanced oil recovery. Yet, how the displacement dynamics is impacted by the non‐Newtonian rheology remains an open question. Here, we conduct primary drainage experiments in which a shear‐thinning Xanthan gum solution displaces a silicone oil in a transparent rough fracture for a wide range of shear‐thinning property (controlled by polymer concentration) and flow rates. We first evaluate the effects of shear‐thinning property on displacement efficiency. Based on qualitative and quantitative analyses of the observed fluid morphologies, we present an experimental phase diagram of the obtained displacement patterns. We characterize a novel displacement pattern where the fluid‐fluid interface changes from stable (plug flow) to unstable (fingering) as the fracture aperture, averaged over the transverse direction, varies along the mean flow direction. We demonstrate that the existence of this mixed displacement pattern can be explained by local viscosity heterogeneity induced by the coupling of the shear‐thinning behavior and the spatial variability of apertures. Finally, we propose a theoretical model elucidating the mechanisms behind the flow regime transitions. The interface stability criterion predicted by this model exhibits good agreement with the experimental measurements, and stresses the potentially important role of fluid rheology, coupled to aperture variability, in immiscible displacements in rough fractures. These findings provide new insights into the dynamics of immiscible two‐phase flows with non‐Newtonian effects, and has potential implications for the aforementioned engineering applications. Key Points: We conduct drainage experiments in which a shear‐thinning fluid displaces a Newtonian fluid in a transparent rough fractureWe present an experimental phase diagram of displacement patterns in the space of flow rate and shear‐thinning rheological propertyWe propose a theoretical model of stability criterion and elucidate the mechanisms behind the flow regime transitions [ABSTRACT FROM AUTHOR]

The difficulty in determining the rheological characteristics of tailings inside reservoirs as well as their intrinsic variability adds uncertainty to tailings dam failures in flood studies. Uncertainty propagation in non-Newtonian hydrodynamic models stands as a great scientific challenge. This article explores the sensibility of tailings dam breach flood mapping to rheological parameters in Bingham and Herschel-Bulkley (H-B) models. The developed approach was based on the probabilistic Latin Hypercube Sampling of rheological parameters. It was automated to propagate uncertainty throughout multiple hydrodynamic simulations using the HEC-RAS v.6.1 software. Rheological parameter ranges and distributions were based on a broad bibliographic review. Bingham models were revealed to be more sensitive than H-B in terms of simulated min-max area values: for Bingham, flood areas, maximum depths, and arrival times varied by 17.9%, 9.3%, and 8.2%, respectively; for H-B, variations were 25.7%, 5.1%, and 3.9%. However, Bingham was less sensitive in terms of hydrodynamically associated probability: high probability ratios were related to a small range of simulated areas in Bingham, while H-B presented great variability. Finally, for each model, the parameters that affect uncertainty the most were identified, reinforcing the importance of determining them properly. Furthermore, the identified parameter ranges for both models should be valuable for defining variable value boundaries for flood sensitivity tests on specific tailings materials for other case studies. The automated algorithm can be used or adapted for specific tests with other hydrodynamic simulations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The poor mixing caused by zinc powder deposition in purification process is a serious problem which can't be avoided in treatment of zinc-containing solid waste. Here, to enhance the purification efficiency of zinc-containing solid waste treatment reactor, two kinds of multi-blade combined stirring systems are compared with single layer four straight-blade and double-layer straight-blade (DFB) stirring systems which are traditionally chosen by industry. This study simulated and explored the flow field characteristics and purification effects of these four kinds of stirred-tank reactor, further proposes the unit ion purification energy (UIPE) as a criterion for purification energy consumption and effect evaluation. The results show that multi-blade combined (MBC) stirring system enhances axial flow by 12.56% in water. Meanwhile it effectively inhibits the growth of isolated mixing region which scope has decreased by 56.25%. In high viscosity Carboxymethylcellulose sodium solution, the fluid axial speed can be increased by up to 1407 times with MBC. MBC can increase the purification rate by 24.79% while the UIPE decreases by 29.45% compared with DFB which is used in industrial purification process. MBC paddle has exhibited a wide range of fluid viscosity applicability and axial velocity improvement effect. The improvement increases collisions between the impurity particles and the zinc powder particles, which increased rate of substitution reactions. The application of MBC solves the purification problem in the process of treating zinc-containing solid waste. [ABSTRACT FROM AUTHOR]

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This study's aim was to examine the effect of non-Newtonian fluid (NN) shoe and ethylene vinyl acetate (EVA) shoe on human lower limb biomechanics and muscle activation during running in hot temperatures. Thirty-five men utilizing a rearfoot strike ran 5 km at a self-selected tempo at an average summer temperature of 41.7 ± 1.0 °C and relative humidity of 80.7 ± 3.5%. The kinematics, kinetics, and muscle activation of the right leg were monitored from landing until the pedal was off the ground. A two-way repeated-measures ANOVA was conducted to investigate the main effects of the shoe condition, temperature, and interaction effect. Wearing NN at high temperature resulted in increased hip range of motion (ROM) (p = 0.001). The knee torque increased significantly when wearing EVA and NN shoes after the temperature increased (p = 0.006). When wearing EVA and NN, the ground reaction force (GRF) and loading rate (LR) increased significantly after the temperature increased (p = 0.001; p = 0.009). When wearing NN after running for 5 km at a high temperature, the displacement range of center of pressure (COP) was significantly reduced (p < 0.001), while the EVA was significantly increased (p < 0.001). Neither pair of shoes substantially altered muscle activity. After excluding the factor of fatigue, the increase in temperature not only changed the properties of the material inside the shoe, but also changed the parameters of the biomechanics of the human lower limbs. After the temperature increases, the shoes made of non-Newtonian fluid materials can quickly stabilize under the condition of increased shear stress and reduce the displacement of the human body. Thus, it indicated that non-Newtonian fluid shoes may lower the risk of injury when running in extremely hot conditions. [ABSTRACT FROM AUTHOR]

This study examines the viscous fingering phenomenon of immiscible displacement in Hele-Shaw cells using the volume of fluid approach (HSC). The displaced fluid has various power law indices and is shear-thinning. Both the distribution properties of pressure and velocity were examined during the development process as well as the morphological evolution characteristics of non-Newtonian fluid when the air was moved. The findings indicate that pressure decreases in the fingering direction throughout the whole non-Newtonian fluid region. The non-Newtonian fluid's velocity close to the HSC pipe wall is virtually zero, and the highest velocity in the air phase is scattered throughout the finger's center. Its relative width gets less as development progresses. Viscous fingering then exhibits a high degree of stability and practically constant relative breadth. The outstretched fingers are shorter and thicker under different power-law indices, and the displacement efficiency is higher. The lower the power-law index n, the better the shear thinning properties. According to the aforementioned features, high-quality and high-efficiency oil displacement can be achieved in petroleum engineering by using new power rate fluid. [ABSTRACT FROM AUTHOR]

This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to zero. Moreover, this convergence has an exponential rate given by a suitable rate function. To establish such asymptotic result, we follow the weak convergence approach introduced by Budhiraja, Dupuis and Ellis. [ABSTRACT FROM AUTHOR]

Direct ink writing (DIW) process is a facile additive manufacturing technology to fabricate three-dimensional (3D) objects with various materials. Its versatility has attracted considerable interest in academia and industry in recent years. As such, upsurging endeavors are invested in advancing the ink flow behaviors in order to optimize the process resolution and the printing quality. However, so far, the physical phenomena during the DIW process are not revealed in detail, leaving a research gap between the physical experiments and its underlying theories. Here, we present a comprehensive analytical study of non-Newtonian ink flow behavior during the DIW process. Different syringe-nozzle geometries are modeled for the comparative case studies. By using the computational fluid dynamics (CFD) simulation method, we reveal the shear-thinning property during the ink extrusion process. Besides, we study the viscosity, shear stress, and velocity fields, and analyze the advantages and drawbacks of each syringe-nozzle model. On the basis of these investigations and analyses, we propose an improved syringe-nozzle geometry for stable extrusion and high printing quality. A set of DIW printing experiments and rheological characterizations are carried out to verify the simulation studies. The results developed in this work offer an in-depth understanding of the ink flow behavior in the DIW process, providing valuable guidelines for optimizing the physical DIW configuration toward high-resolution printing and, consequently, improving the performance of DIW-printed objects. [ABSTRACT FROM AUTHOR]

In this study, we focused on the heat transfer through a uniformly inclined rectangular duct caused by the electro-osmotic peristaltic flow of an unsteady non-Newtonian nanofluid. With couple stress, the fluid obeys the Papanastasiou model. The flow is through a porous medium that follows Darcy's law in a modified form. In addition, Dufour and Soret effects, mixed convection, the impacts of a chemical reaction, and the effects of viscous couple stress dissipation are all considered. The governing equations that explain the velocity, temperature, and concentration of nanoparticles are simplified when wave transformation is used. The homotopy perturbation method was used to solve these equations analytically. Additionally, a collection of figures is used to discuss and visually illustrate the consequences of the physical characteristics. In fact, the modified Darcy's law makes the velocity gradient appear in the momentum equation, which increases the contribution of the velocity gradient to the velocity profile. In addition, the electro-osmotic parameter and Helmholtz-Smoluchowski velocity have a significant impact on the velocity gradient's direction, as well as the velocity gradient's ability to be either positive or negative, depending on their values. In addition, in the case of forced convection, the values of the Nusselt number and the Sherwood number are highly affected by the value of Helmholtz–Smoluchowski velocity. The current findings have applications in biology and medicine, particularly in cancer therapy, which involves peristaltic blood pumps(arteries) and suspended gold nanoparticles (nanofluid). According to our knowledge, no prior studies have merged the couple stress Papanastasiou model and the modified Darcy's law. [ABSTRACT FROM AUTHOR]

To compensate for the decrease of velocity and pressure of waxy crude oil flow in a pipeline under the conditions that it exhibits non-Newtonian behavior, engineers would have to optimize the transmission power. This objective requires correct modeling of the rheological behavior and estimating the distributions of velocity, pressure, and temperature in the fluid along the pipeline. The rheological behavior of crude oil is highly dependent on wax content, shear rate, and temperature. In this work, to study the influence of wax content, two types of crude oils with different paraffin contents, referred to as reference crude oils, were studied. The results of shear-rotary tests using an Anton Paar MCR 302 indicate that in a specific range of shear rates, the reference crude oils are non-Newtonian at the studied temperatures of pipe wall and inlet. Considering the Power-law model for describing the rheological behaviors of these fluids, two dimensionless numerical models are proposed. Using Computational Fluid Dynamics (CFD) technique, the velocity, pressure, and temperature of each reference crude oil were modeled. The accuracy of the model and input data were successfully evaluated against results reported in the literature. [ABSTRACT FROM AUTHOR]

This study employs OpenFOAM to analyze the behavior of a single laser-produced cavitation bubble in a Newtonian/non-Newtonian fluid inside a rigid cylinder. This research aimed to numerically calculate the impact of liquid disc microjet resulting from the growth and collapse of the laser-produced bubble to the cylinder wall to take advantage of the cavitation phenomenon in various industrial and medical applications, such as modeling how to remove calcification lesions in coronary arteries. In addition, by introducing the main study cases in which a single bubble with different initial conditions is produced by a laser in the center/off-center of a cylinder with different orientations relative to the horizon, filled with a stationary or moving Newtonian/Non-Newtonian liquid, the general behavior of the bubble in the stages of growth and collapse and the formation of liquid disk microjet and its impact is examined. The study demonstrates that the presence of initial velocity in water affects the amount of microjet impact proportional to the direction of gravity. Moreover, the relationship between the laser energy and the initial conditions of the bubble and the disk microjet impact on the cylinder wall is expressed. [ABSTRACT FROM AUTHOR]

We show the upper and lower bounds of convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under a large initial perturbation. [ABSTRACT FROM AUTHOR]

Recent studies have attempted to find methods and techniques that enable the development of heat transfer within thermal transformers. For this purpose, this paper includes a numerical simulation of a non-Newtonian fluid inside a chamber with four hot bodies. The chamber is exposed to a magnetic field of constant and uniform intensity. Also, the upper wall of the chamber has a horizontal movement. The study is based on the quality of heat transfer between the heated parts of the chamber and the complex fluid under the influence of a set of criteria, namely Reynolds number (= 1 to 40); Hartmann number (= 0 to 100); power-law index (= 0.6 to 1.4) and Richardson number (0 to 100). The interpretation of the results is done by displaying the pathlines and isotherms distribution. Also, the amount of thermal transfer of the hot bodies is given in terms of the Nusselt number. The results showed that the positioning of the hot bodies plays an important role in heat transfer. Moreover, increasing the value of the power-law index makes the fluid stickier, which reflects its negative effect on heat transfer. [ABSTRACT FROM AUTHOR]

The gas–liquid mixing phenomenon that occurs in a mixing tank containing a non-Newtonian fluid is an important process in many industrial applications, such as chemical and biochemical processing. The design and optimization of an aerated mixing tank with such characteristics is a challenging task. Most of these challenges are due to the non-Newtonian behavior of the fluid, which can lead to compartmentalization of the mixing tank and the formation of oxygen-segregated zones. These issues become more pronounced at larger scales. Therefore, the primary objective of this study was to identify the mixing dead zones and determine their impact on the overall mixing process in a coaxial mixing system at two different scales. This research focused on the evaluation of the hydrodynamics attained by a coaxial gas–liquid mixing tank through numerical and experimental methods. The study was conducted using computational fluid dynamics (CFD) and the electrical resistance tomography (ERT) method. The effects of the aeration rate, inner impeller speed, and rotating mode on the creation of dead zones were investigated. [ABSTRACT FROM AUTHOR]

This paper discusses the existence and uniqueness of local strong solution for a class of 1D non-Newtonian fluids with non-Newtonian potential and damping term. Here we allow the initial vacuum and viscosity term to be fully nonlinear.

The goal of this paper is to examine the strong convergence of the velocity of a non-Newtonian incompressible fluid whose viscosity follows the power law with Coulomb friction. We assume that the fluid coefficients of the thin layer vary with respect to the thin layer parameter $ \varepsilon $. We give in a first step the description of the problem and basic equations. Then, we present the functional framework. The following paragraph is reserved for the main convergence results. Finally, we give the detail of the proofs of these results.

This article reports on the emission of H2S (hydrogen sulfide) during the excavation of disturbed material covering a former ocean shoreline. Operators of the excavators expressed concerns about the strong odors of H2S, the insensitivity of workplace instruments, and the safety of the work. This situation demanded an immediate and appropriate response. The literature contains no information concerning worker exposure to H2S in these situations. Levels detected by the Jerome 631-X ranged from 1 ppb (part per billion) to 25 ppb in 1-min samples during various activities. Levels decreased to zero when activity ceased. Unpredicted excursions peaking at 2500 ppb superimposed onto background levels immediately followed exposure to material containing H2S. Excursion levels rose abruptly, peaked, and decreased rapidly to the background. Excursions occurred once per day and lasted about 10 min. These emissions share characteristics of shear-thinning, pseudoplastic non-Newtonian fluids. A very conservative estimation of exposure during this work compared to the Threshold Limit Value-Time-Weighted Average of 1 part per million (ppm = 1000 ppb) suggested that this was considerably less than the lowest level of regulatory concern and that work under these conditions can proceed without overexposure to H2S. This work has relevance and application in similar situations occurring globally.

Tuned liquid dampers (TLDs) have been broadly applied to suppress structural vibrations. In the present study, a novel vibration mitigation device consisting of non-Newtonian fluids coupled with an elastic baffle is proposed. The fluid-structure interaction is studied numerically. To optimize the system, different fluids, including the Bingham fluid, the Pseudoplastic fluid, and the Dilatant fluid are used as the damping fluids and the vibration suppression ability of each fluid is studied. Moreover, the energy dissipation mechanisms of different liquids are obtained. The results show that the optimal vibration suppression in the container without a baffle can be achieved by using the Bingham fluid. In this case, the average amplitude decay rate of the container is 12.662% with about 0.199% improvement in the damping ratio when compared to water. In the container with an elastic baffle, however, both the Pseudoplastic fluid and the Dilatant fluid outperform water in the damping capacity. The average amplitude decay rates of these fluids are 50.960% and 43.794%, respectively. Moreover, their damping ratios are 0.035% and 0.019% higher than that of water, respectively.

This investigation theoretically describes the exact solution of an unsteady fractional a second-grade fluid upon a bottom plate constrained by two walls at the sides which are parallel to each other and are normal to the bottom plate. The flow in the fluid is induced by the time dependent motion of the bottom plate. Initially the flow equation along with boundary and initial conditions are considered which are then transformed to dimensionless notations using suitable set of variables. The Laplace as well as Fourier transformations have been employed to recover the exact solution of flow equation. The time fractional differential operator of Caputo-Fabrizio has been employed to have constitutive equations of fractional order for second-grade fluid. After obtaining the general exact solutions for flow characteristics, three different cases at the surface of bottom plate are discussed; namely (i) Stokes first problem (ii) Accelerating flow (iii) Stokes second problem. It has noticed in this study that, for higher values of Reynolds number the flow characteristics have augmented in all the three cases. Moreover, higher values of time variable have supported the flow of fractional fluid for impulsive and constantly accelerated motion and have opposeed the flow for sine and cosine oscillations.

The filling of a plane gap with a non-Newtonian fluid under non-isothermal conditions is considered by assuming viscous dissipation and curing reaction induced by the heat supplied through the walls of the gap. The rheology of the medium is described by the modified Cross-WLF model accounting for the effect of temperature, strain rate intensity, and the extent of a chemical reaction on the viscosity. The curing reaction kinetics is determined by the equation based on the n-th order reaction with self-acceleration. The problem is solved numerically using an original computational technique. The curable fluid flow structure is revealed to include three characteristic zones during the filling process: a fixed layer on the solid wall with a high degree of curing; a central “core” with an almost uniform distribution of characteristics; and a transition zone serving as a "lubricating" layer between two abovementioned zones. The structure is governed by heating of the fluid through the wall, since the heating affects the rheological characteristics of the medium and the rate of the cured layer formation. Analysis of the similarity criteria for the considered flow conditions shows that the fluid flows in a creeping regime (Re < 0.01); the temperature distribution is mainly affected by convective heat transfer (Pe > 100); the influence of dissipative heating and exothermic effect of the curing reaction is insignificant. The effect of curing on the mass distribution of the liquid portions entering through the inlet section is shown. The variation of the pressure distribution is analyzed at various flow conditions.

We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field p. The latter has been chosen for solutions correlated explicitly with the critical maximal non-zero level of stress τs in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for two functions, p and τs. As a result, a set of new semi-analytical solutions are presented and graphically plotted.

Background: Abdominal aortic aneurysms (AAAs) present a formidable public health concern due to their propensity for localized, anomalous expansion of the abdominal aorta. These insidious dilations, often in their early stages, mask the life-threatening potential for rupture, which carries a grave prognosis. Understanding the hemodynamic intricacies governing AAAs is paramount for predicting aneurysmal growth and the imminent risk of rupture. Objective: Our extensive investigation delves into this complex hemodynamic environment intrinsic to AAAs, utilizing comprehensive numerical analyses of the physiological pulsatile blood flow and realistic boundary conditions to explore the multifaceted dynamics influencing aneurysm rupture risk. Our study introduces novel elements by integrating these parameters into the overall context of aneurysm pathophysiology, thus advancing our understanding of the intricate mechanics governing their evolution and rupture. Methods: Conservation of mass and momentum equations are used to model the blood flow in an AAAs, and these equations are solved using a finite volume-based ANSYS Fluent solver. Resistance pressure outlets following a three-element Windkessel model were imposed at each outlet to accurately model the blood flow and the AAAs’ shear stress. Results: Our results uncover elevated blood flow velocities within an aneurysm, suggesting an augmented risk of future rupture due to increased stress in the aneurysm wall. During the systole phase, high wall shear stress (WSS) was observed, typically associated with a lower risk of rupture, while a low oscillatory shear index (OSI) was noted, correlating with a decreased risk of aneurysm expansion. Conversely, during the diastole phase, low WSS and a high OSI were identified, potentially weakening the aneurysm wall, thereby promoting expansion and rupture. Conclusion: Our study underscores the indispensable role of computational fluid dynamic (CFD) techniques in the diagnostic, therapeutic, and monitoring realms of AAAs. This body of research significantly advances our understanding of aneurysm pathophysiology, thus offering pivotal insights into the intricate mechanics underpinning their progression and rupture, informing clinical interventions and enhancing patient care.

This article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and the existence of their solutions is proved. The necessary exponential estimates for the solutions are established. Then, based on these estimates, the existence of trajectory and global attractors in the problem under study is proved.

Flows of incompressible Navier–Stokes (Newtonian) fluids between adjacent surfaces are encountered in numerous practical applications, such as seal leakage and bearing lubrication. In seals, the flow is primarily pressure-driven, whereas, in bearings, the dominating driving force is due to shear. The governing Navier–Stokes system of equations can be significantly simplified due to the small distance between the surfaces compared to their size. From the simplified system, it is possible to derive a single lower-dimensional equation, known as the Reynolds equation, which describes the pressure field. Once the pressure field is computed, it can be used to determine the velocity field. This computational algorithm is much simpler to implement than a direct numerical solution of the Navier–Stokes equations and is therefore widely employed by engineers. The primary objective of this article is to investigate the possibility of deriving a type of Reynolds equation also for non-Newtonian fluids, using the balance of linear momentum. By considering power-law fluids we demonstrate that it is not possible for shear-driven flows, whereas it is feasible for pressure-driven flows. Additionally, we demonstrate that in the full 3D model, a normal stress boundary condition at the inlet/outlet implies a Dirichlet condition for the pressure in the Reynolds equation associated with pressure-driven flow. Furthermore, we establish that a Dirichlet condition for the velocity at the inlet/outlet in the 3D model results in a Neumann condition for the pressure in the Reynolds equation.

The current paper aims to utilize non-Newtonian fluid and improve the cooling performance of turbine blades. To implement impinging fluid flow through a porous channel on a hot lower wall, in the first step, the rheology of non-Newtonian behavior is introduced. Then differential quadrature procedure is used to convert these highly nonlinear equations of motion to some simple algebraic expressions. There is a reasonable agreement between the present findings with previous research work. Finally, some vital parameters such as the cross-viscosity parameter and power law index are changed to evaluate how these factors improve the cooling performance of turbine blades. The findings show that a rising Prandtle number results in a 19% decrement in temperature pattern. For a constant cross-viscosity parameter, Reynolds number enhancement leads to wall friction augmentation of around 15%. Moreover, a 32% Nusselt number increment is observed by increasing the power law index for the same Reynolds number.

Based on the field of the coal chemical industry, exploring the applicability of high-performance heat exchangers for coal water slurry and their flow and heat transfer mechanism is of great significance for promoting the development of clean coal technology. In this paper, the flow pattern and forced convection heat transfer of a pair of tandem heated cylinders with different distances were discussed using the bi-viscous Bingham model by numerical simulation. And a novel spiral wound heat exchanger with variable diameter tubes was proposed. The results illustrate that the heat transfer coefficient under unit pressure drop h/△P of the heat exchanger decreases with the increase of the diameter of the variable tubes. When the diameter of variable tubes is 12 mm, h/△P is 19.83% larger than that of the original structure with uniform tube diameter. The empirical correlation between operating and structural parameters and heat exchanger performance is obtained. The research results provide guidance for the design of coal water slurry preheaters and the structural optimization of spiral wound tube heat exchangers.

The present study concentrates on the motion of a third-grade fluid with magneto-hydrodynamics (MHD) over a stretching surface. Additionally, the Cattaneo–Christov model is employed to derive information about the heat flux, which is subsequently utilized to ascertain the heat transmission properties. The inquiry involves an assessment of the impact of thermal relaxation time on the boundary layer. The considered fluid is a type of non-Newtonian fluid that deal with both shear thinning and shear thickening behaviors. The study also involved calculating all normal stress components that are not accounted for by either the power law model or the second grade model. The motion of fluid is attributed by linear stretching, and the momentum flow is observed with the help of Soret–Dufour effects. The Cattaneo and Christov model is particularly beneficial for describing transmission of heat in materials with high thermal conductivity, where the classical Fourier’s law may not be accurate. The examination of the transport properties of velocity, heat, and mass involves the consideration of the temperature effect on variable viscosity and thermal conductivity, which are linearly associated with each other. A set of partial differential equations (PDEs) that are nonlinear in nature has been derived, and some boundary conditions have been identified that yield satisfactory results. Using similarity transformation a system of nonlinear PDE’s are modify into dimensionless system of ordinary differential equations (ODE’s). The homotopy analysis method (HAM) is applied in a convenient manner to obtain solutions for transform equations, while the impact of relevant flow parameters is visually demonstrated. Adequate graphical and tabular results are achieved using a semi-analytical approach. Moreover, the Cattaneo–Christov equation can provide a better understanding of the thermal behavior. It allows for a more comprehensive analysis of the thermal response, ensuring that the heat transfer models used are appropriate for such conditions.

ABSTRACT Non-Newtonian rheology effects, such as pseudoplasticity and viscoplasticity, are understood as shear stresses, incorporated to the energy slope term in the Shallow-Water Equations (SWE). However, non-Newtonian shear stresses are dependent of the shear rate, whose formulation is a function of the gradient of the velocity profile in the bottom. This study investigated two shear rate formulations that are commonly applied in the SWE literature: 1) a non-parameterized function; and 2) a function based on the Herschel-Bulkley rheological model. Their influence in steady uniform flows of non-Newtonian fluids was evaluated through numerical-theoretical comparisons. A Lax-Friedrichs scheme was implemented to solve the SWE system and allowed employing the shear rate formulations. Experimental tests were carried out and numerical simulations of hypothetical scenarios were performed. It was found that the non-parameterized formulation presented deviation in normal depth up to 14% in comparison with theoretical solution, while the formulation based on the Herschel-Bulkley model provided a good agreement, corroborated by punctual Computational Fluid Dynamics simulations (deviation less than 2%) and experimental data. The ratio of both shear rate formulations is strongly correlated to the deviation of normal depth, indicating that the non-parameterized shear rate function does not provide an acceptable result in the steady uniform flow.

This work reported to investigate convective flow of non-Newtonian fluid effect on an exponentially stretchable surface. Effect of nanoparticle is considered in heat and mass equation. The transformation technique utilized on dimensionless equations is converted to non-dimensionless equations are solved thought numerical approach Bvp4c. Influence of approatiate analysis of velocities, heat and mass transport are scrutinized through figures. Furthermore, the comparative analysis of drag forces, Nusselt number and Sherwood number are evaluated over and done with tabulated values. It is give details that the temperature field strengthens with intensification in thermophoresis and random diffusions. Similarly, rises in thermophoresis effect parameter both temperature and concentration profile increasing.