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The dynamics of a tracer particle in a bath of quasi-hard colloidal spheres is studied by Langevin dynamics simulations and mode coupling theory (MCT); the tracer radius is varied from equal to up to seven times larger than the bath particles radius. In the simulations, two cases are considered: freely diffusing tracer (passive microrheology) and tracer pulled with a constant force (active microrheology). Both cases are connected by linear response theory for all tracer sizes. It links both the stationary and transient regimes of the pulled tracer (for low forces) with the equilibrium correlation functions; the velocity of the pulled tracer and its displacement are obtained from the velocity auto-correlation function and the mean squared displacement, respectively. The MCT calculations give insight into the physical mechanisms: At short times, the tracer rattles in its cage of neighbours, with the frequency increasing linearly with the tracer radius asymptotically. The long-time tracer diffusion coefficient from passive microrheology, which agrees with the inverse friction coefficient from the active case, arises from the transport of transverse momentum around the tracer. It can be described with the Brinkman equation for the transverse flow field obtained in extension of MCT, but cannot be recovered from the MCT kernel coupling to densities only. The dynamics of the bath particles is also studied; for the unforced tracer the dynamics is unaffected. When the tracer is pulled, the velocity field in the bath follows the prediction of the Brinkman model, but different from the case of a Newtonian fluid. [ABSTRACT FROM AUTHOR]

Investigating thermal convection within porous media permeated by fluids and micro-organisms stands as a significant inquiry with broad relevance across geophysical and engineering domains. Studying convection within porous media can aid in controlling temperature and nutrient distribution for cell growth and tissue regeneration, as well as the efficiency of biofuel fermentation and production processes. Hence, the primary objective of this study is to investigate the influence of time-periodic gravitational forces on Darcy–Brinkman bio-thermal convection within a porous medium layer. This medium is saturated with a Newtonian fluid that encompasses gyrotactic micro-organisms. The gravity modulation amplitude is assumed to be very small. A weak nonlinear stability analysis is performed to analyze the stationary mode of bioconvection. The heat transport, measured by the Nusselt number, is governed by a non-autonomous Ginzburg–Landau equation. The research explores the influence of several parameters on heat transport, including the Vadaszs number, the modified bioconvective Rayleigh–Darcy number, cell eccentricity, modulation frequency, and modulation amplitude. The results are presented graphically, illustrating the impact of these parameters on heat transfer. The findings reveal that both the Vadaszs number and the modulation amplitude have a positive effect on heat transfer, enhancing the process. On the other hand, an increase in the modified bioconvection Rayleigh–Darcy number and cell eccentricity leads to a decrease in heat transfer. Furthermore, a comparison between the modulated and unmodulated systems indicates that the modulated systems have a more significant influence on the stability problem compared to the unmodulated systems. This highlights the effectiveness of external modulation in controlling heat transport within the system. [ABSTRACT FROM AUTHOR]

This research measures the flow of synovial fluid through permeable membrane. It is assumed in this study that the ultrafiltration of blood plasma is a continuous function and repeatedly forms the action to keep synovial fluid normal in the joints. The novelty of this research is to analyze the rheology of synovial fluid under the periodic filtration rate within the membrane. To estimate the pressure and shear stress which are essential for the flow of synovial fluid between the synovial joints, mathematical modeling has been made for the synovial fluid flow through permeable membrane by the laws of mass and momentum and viscoelastic LPTT fluid model. The LPTT fluid has the viscoelastic effects in the presence of relaxation time, therefore for synovial fluid the present fluid model represents the best rheological properties. To find the analytical results for the rheology of the synovial fluid, a method proposed by Langlois is used. This research concludes that the pressure difference and transverse velocity are high when the periodic filtration is cosine type whereas the shear stress on the wall is high for sine type of filtration. [ABSTRACT FROM AUTHOR]

Inquisitive researchers have studied the movement of peristaltic nanofluids due to the enlightening impact of nanoliquids in various technological and therapeutic fields, particularly in the fluids transport mechanisms known as peristalsis. The Casson fluid belongs to a group of non-Newtonian fluids that, according to a particular stress threshold, exhibit elastic solid behavior before changing to liquid behavior. These fluids are known as viscoelastic fluids and have several uses in engineering, food preparation, drilling and other fields. The Casson nanofluid model is used in this investigation. In order to better understand this, this study examines the peristaltic motion of a Casson nanofluid in a vertical layer with suction/injection. The resulting flow model is successfully simulated under the realistic assumptions of long wavelength and low Reynolds number after obtaining the governing conservation equations. By using workable transformations, the derived partial differential equations are mathematically converted into a dimensionless form. Analytical solutions have been found for the resulting flow problem's temperature distribution, velocity, pressure rate per wavelength and concentration of nanoparticles. Using Wolfram Mathematica software, the impacts of all physical characteristics on temperature, velocity, concentration fields, pressure rate, frictional force and pressure gradient are graphically studied. The influences of thermophoresis parameter Nt raise the temperature and diminish fluid concentration. By raising the suction and injection parameter k values, the velocity in the directions of x and y is decreased. The pressure rate enhances by raising the Reynolds number and diminishes by enhancing the Grashof number. [ABSTRACT FROM AUTHOR]

The advancement of non-Newtonian nanofluid innovation is a crucial area of research for physicists, mathematicians, manufacturers, and materials scientists. In engineering and industries, the fluid velocity caused by rotating device and nanofluid has a lot of applications such as refrigerators, chips, heat ex-changers, hybrid mechanical motors, food development, and so on. Due to the tremendous usage of the non-Newtonian nanofluid, the originality of the current study is to explore the influence of nanoparticle radii and inter-particle spacing effects on the flow characteristics of Casson methanol-based aluminium alloy (AA 7072) nanofluid through a rotating disc with Joule heating and magnetic dipole. The present problem is modeled in the form of partial differential equations (PDEs), and these PDEs are converted into ordinary differential equations with the help of suitable similarity transformations. The analytical solution to the current modeled problem has been obtained by using the homotopy analysis method (HAM) and numerical solutions are obtained by employing Runge–Kutta–Fehlberg method along with shooting technique. The main purpose of the present research work is to analyze the behavior of the velocity and temperature of the nanofluid for small and large radius of the aluminium alloy (AA 7072) nanoparticles and inter-particle spacing. The radial and tangential velocities are enhanced due to rising ferro-hydrodynamic interaction parameter and the skin friction force for radial and tangential directions are enhanced 10.51% and 2.16% when h = 0.5. Also, the heat transfer rate is reduced 18.71% and 16.70% when h = 0.5% and R p = 1.5. In fact, the present results are compared with the published results and they met good agreement. [ABSTRACT FROM AUTHOR]

A semi-numeric study is presented to explore the nonlinear, radiative, mixed convective boundary layer flow of non-Newtonian Eyring-Powell fluid (EPF) over a porous stretching wedge in the existence of suction/injection, viscous dissipation, activated energy, and ohmic heating. The governing coupled partial differential equations (PDEs) in the flow regime are transformed into coupled ordinary differential equations (ODEs) under suitable boundary conditions (BCs). Computations are performed for variations of various pertinent parameters on velocity, temperature distribution, surface drag force, and heat transfer rate number. It is noted that with increasing Eyring Powell parameter velocity increases for stretching parameter greater than free stream velocity, but decreases when wedge stretches slowly than free stream velocity. An increase in the local non-Newtonian fluid parameter decreases velocity when the wedge stretches faster as compared to free stream velocity. However, velocity increases when the wedge stretches faster. Temperature velocity decreases for both cases of wedge stretches faster or slower as the local non-Newtonian fluid parameter increases. Similar behavior is seen in the case of Eyring Powell parameter. Increasing heat generation or absorption decreases the momentum as well as thermal boundary layer thickness. When the suction/injection parameter is enhanced the velocity shows a declines behavior for both the cases of stretching parameter as it increases. Temperature profiles decline as the mass transfer parameter is enhanced for both the case's velocity ratio parameters, respectively. Excellent agreement is achieved with the differential transform method and numerical result. [ABSTRACT FROM AUTHOR]

Present analysis deals with the impact of nonlinear convection on MHD non-Newtonian fluid flow considering exponentially stretched sheet through porous media. Additionally, the effects of radiation, Joule heating and energy dissipation have been taken into account. The considered flow situation of nonlinear PDEs is transmuted to nonlinear ODEs using similarity analysis. The numerical computations are derived using a fourth-order Runge–Kutta scheme with a shooting technique. Meaningful observations are discussed for velocity and energy profiles. Further, the impact of pertinent parameters considering pseudoplastic fluids (n = 0. 6) and dilatant fluids (n = 1. 3) is briefed through graphs. It is noted that the escalation in the values of the power-law index declines the velocity and energy profile. Higher values of the nonlinear parameter decline the energy profile. [ABSTRACT FROM AUTHOR]

Inspired by significant physiological applications of peristaltic transport, a mathematical model for the peristaltic pumping of a Jeffrey nanofluid containing gyrotactic microorganisms through a flexible and vertical symmetric channel is investigated, along with the effects of thermal radiation, heat source/sink, chemical reaction, porous medium and Hall current. Swimming microorganisms in a model of non-Newtonian fluid has several biological and ecological benefits, including in the pharmaceutical industry, biofertilizers, biofuel technology, biosensors, etc. With these presumptions in mind, a conducting Jeffery fluid flow containing microorganisms via a porous vertical conduit is proposed. The expressions for the flow quantities are established by solving the governing equations of this study analytically using the homotopy perturbation method (HPM). A detailed examination is performed using the tables and graphical representations to comprehend the impact of significant components on this analysis. In addition, the results for Newtonian nanofluid are obtained as a special case and discovered that its velocity is lower than the Jeffrey nanofluid. It is observed that the best velocity distribution can be seen at larger thermal Grashof number and Darcy number. The size of the trapped bolus enhances with the increase of the Hall parameter. Furthermore, the density of the motile microorganism distribution declines for higher bioconvection Peclet number and bioconvection constant. [ABSTRACT FROM AUTHOR]

This study aims to compare the dual solutions of the problem describing the magnetized motion of a Newtonian and second‐grade fluid induced by a curved stretching/shrinking surface using the associations of homogeneous–heterogeneous reaction and Cattaneo–Christov model. The model is further developed using the properties of convective heat transfer, suction velocity, Joule heating, heat source/sink, and viscous dissipation with the porous medium. The relevant transformations are applied to the governing partial differential equations (PDEs) resulting in the system of nonlinear ordinary differential equations (ODEs). The solution technique makes use of the computational scheme in MATLAB known as the bvp4c technique. All relevant findings are obtained using a wide range of dimensionless parameters. The Cattaneo–Christov model and the second‐grade fluid transmits heat faster than the classical Fourier law and Newtonian fluid as well as the heat transfer rate of both fluids was found to drop as the values of Eckert number and curvature parameter enhances. Moreover, the Newtonian fluid has lower friction drag than the second‐grade fluid and the concentration of the bulk fluid is declined by the rising values of hetrogeneous and homogeneous reaction parameter. With potential applications in a variety of engineering fields, including thermal management systems and nanofluid‐based technologies, this work is significant for understanding MHD flow of second‐grade nanofluids over curved surfaces, incorporating heterogeneous reactions and the Cattaneo–Christov model. The results also aid in improving heat transfer efficiency and understanding of fluid behavior under various parameter situations, providing information for improving industrial processes and advanced materials engineering design considerations. [ABSTRACT FROM AUTHOR]

This work is focused on Magneto hydrodynamic unsteady flow of Newtonian fluid flow over a perpendicular porous plate along with chemical reaction, heat, and mass transfer. The induced magnetic field and viscous and magnetic dissipation properties are considered throughout the porous plate. Heat source is the added effect in the model to observe the nature of flow in this work. This study finds its applications in understanding the storage of flues, disposal of radioactive waste materials, flow in water purifies, etc. The nonlinear behavior of the governing equation motivates us to use a finite difference approach for solving equations. The major resolution of this research is to work on how the physical elements affect velocity, temperature, concentration, and magnetic field. Fascinating facts are noticed as the unsteady fluid velocity rises with the heat source parameter because as the heat of a material increases, the movement of the fluid particle will be fast. Due to the presence of a magnetic field high thermal radiation is observed at high temperature and concentration. As the magnetic parameter and magnetic field are inversely proportional according to an induced magnetic field, it is noticed that their magnetic field declines for higher values of magnetic Prandtl number & magnetic parameter. This work has dynamic prominence in the field of medicine and engineering, which develops interest among young researchers. [ABSTRACT FROM AUTHOR]

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems. [ABSTRACT FROM AUTHOR]

Measuring viscosity in volumes smaller than a microliter is a challenging endeavor. A new type of microscopic viscometers is presented to assess the viscosity of Newtonian liquids. Micron-sized flexible polymer cantilevers are created by two-photon polymerization direct laser writing. Because of the low stiffness and high elasticity of the polymer material the microcantilevers exhibit pronounced Brownian motion when submerged in a liquid medium. By imaging the cantilever's spherically shaped end, these fluctuations can be tracked with high accuracy. The hydrodynamic resistance of the microviscometer is determined by fitting the power spectral density of the measured fluctuations with a theoretical frequency dependence. Validation measurements in water-glycerol mixtures with known viscosities reveal excellent linearity of the hydrodynamic resistance to viscosity, allowing for a simple linear calibration. The stand-alone viscometer structures have a characteristic size of a few tens of microns and only require a very basic external instrumentation in the form of microscopic imaging at moderate framerates (~ 100 fps). Thus, our results point to a practical and simple to use ultra-low volume viscometer that can be integrated into lab-on-a-chip devices. [ABSTRACT FROM AUTHOR]

Among many unexpected phenomena of active matter is the recently observed superfluid-like thinning (viscosity drop) behavior of bacteria suspensions. Understanding this peculiar self-propelled thinning by active matter is of theoretical and practical importance. Here, we find that, although distinct in driving mechanisms, active matter and shear flows exhibit similar thinning behaviors upon the increase of self-propulsion and shear forces, respectively. Our structural characterizations reveal that they actually share the same cluster-breaking mechanism of thinning. How fast and how shattered the cluster is broken determines the (dis)continuity of the thinning. This explains why adding active particles to Newtonian fluids can cause thinning, in which rotation of active particles play a key role in breaking clusters. Our work proposes a mechanism of self-propelled thinning and further establishes the underlying connections between active matter and shear flows. [ABSTRACT FROM AUTHOR]

Urinary exfoliated tumor cells have emerged as promising biomarkers for predicting, diagnosing, and guiding therapy in bladder cancer. Several methodologies based on biological and physical differences between normal cells and malignant tumor cells have been developed over the past few years. However, these methods still did not have sufficient sensitivity or specificity. In this study, a remote analysis protocol was devised utilizing motion microscopy. This technique amplifies vibrations within a recorded video by re-rendering motions, thereby generating highly magnified visuals. This approach aims to detect dynamic motions that may not be perceptible to the human eye under normal observation. Remarkably, motion microscopy unveiled discernible fluctuations surrounding bladder malignant tumor cells, which we referred to herein as cellular trail. The cellular trails were predominantly evident at around 1 Hz in amplified video images, with a velocity of 22 μm/s. Moreover, cellular trails were observed regardless of whether they were in a non-Newtonian or Newtonian fluid environment. Significantly, this phenomenon was distinguishable even in urine samples. In conclusion, we suggest motion microscopy as an innovative approach for detecting urinary malignant tumors with potential clinical utility as a complementary tool to cytology. [ABSTRACT FROM AUTHOR]

Process of transportation of heat in ferrofluids has innumerable applications in the fields of electronics and automobile industry. By tracing the materials, the ferrofluid got popularity among researchers and engineers, also most ferrofluids are non-Newtonian in nature so here the non-Newtonian fluid is under consideration. In this study, the influences of viscous dissipation and magnetic parameter in the flow of ferromagnetic Carraeu fluid for a stretching surface are examined. Suitable similarity transformations in the system that consists of nonlinear form of Partial Differential Equations (PDEs) are transformed into a system of nonlinear form of ODEs, then the resulting Ordinary Differential Equations (ODEs) are resolved by use of a mathematical technique known as bvp4c. Effects of ferromagnetic interaction factor, Curie temperature, viscous dissipation and material parameter are examined for temperature profile as well as velocity fields. Moreover, the variations in velocity and thermal gradients are analyzed and described with the help of graphs. An upsurge in the values of magnetic interaction parameter and Weissenberg number causes a decline in the velocity field while the thermal gradient shows opposite behavior. It is detected that the temperature of Carreau fluid intensifies for larger and  λ. [ABSTRACT FROM AUTHOR]

Nanofluids have attracted a lot of attention since their significant enhancement in thermal properties, however there are few reports on the study of the viscosity of nanofluids from an experimental point of view. In this work, the rheological behavior of functionalized multi-walled carbon nanotubes (F-MWCNTs) and coated with MoS2 (MWCNTs-MoS2) in a commercial palm oil as base fluid was evaluated. The purification and functionalization process of the MWCNTs was performed by acid leaching and investigated by FTIR, and stable nanofluids were prepared with MWCNTs concerning time. The rheological behavior of nanofluids with MWCNTs was performed as a function of temperature at different concentrations (0.1, 0.5 and 1% wt.). The effect of time, temperature, shear rate and shear stress versus shear rate were determined. The results indicate that the nanofluid behaves as a Newtonian fluid independently of the MWCNTs concentrations and temperatures evaluated. The viscosity index increases by 16% at a concentration of 1% wt. of F-MWCNTs and for nanofluids added with MWCNTs-MoS2 had significant effect on the effect of temperature. [ABSTRACT FROM AUTHOR]

Most models employed for fluid forces in drill-string dynamics are of reduced order. The simplified nature of these models often fails to describe the complex behavior of the fluid force, in particular, when the drill-string movement is non-trivial or even when non-Newtonian behavior is predominant. In this work, the fluid forces are estimated by modeling the dynamic of the drilling fluid for both Newtonian and non-Newtonian fluids, and compared with reduced-order models. To achieve it, the lattice-Boltzmann method is implemented to solve the fluid model, while prescribed movements are set for the tool-joint. With the obtained fields, the forces are calculated and compared with recurrent models. Finally, it is observed that some models are capable of describing the interaction as long as the dynamic of the tool-joint is simple. In the presence of other trajectories--e.g., bouncing and chaotic--the models fail to describe the details of the dynamic. [ABSTRACT FROM AUTHOR]

In this paper, we aim at the simulation of setup for vortex generation and measurement. This project will lead to designing the experimental setup to create vortices and development of heat flow sensors. The working fluid for the vortex generator is hybrid nanofluid such as Iron (III) Oxide-MWCNT and propanol. The usage of these hybrid fluids was considered due to their better physical and chemical properties compared to water and other conventional fluids. Ansys Fluent was used to simulate the experiment. Viscosity of the fluid increases for both hybrid nanofluids, from inlet to outlet by a magnitude of 10 times (for Fe3O4 + MWCNT: 5.3 × 10−5 Pa.s to 6.3 × 10−4 Pa.s; for Al2O3 + MWCNT: 7.5 × 10−5 Pa.s to 6.5 × 10−4 Pa.s), for laminar flow (Reynolds number = 400). Vortex generation increases the viscosity of the hybrid mixture but not water (for water, it stays constant across the channel at 4.9 × 10−4 Pa.s). Vortex induced viscosity is seen in hybrid mixtures. Strain thinning due to vortex formation is not observed, therefore the behavior of the mixtures is along the lines of Newtonian fluids. [ABSTRACT FROM AUTHOR]

Food rheology is key to manage the swallowing safety of people affected by swallowing disorders (dysphagia). Simple approaches to assess the flow properties of texture-modified drinks are widely used, but relatively poorly understood. This study focuses on the International Dysphagia Diet Standardisation Initiative (IDDSI) flow test, adopted by caregivers worldwide. This test considers the gravity-driven flow in a vertical syringe. Newtonian liquids and non-Newtonian fluids obtained using a commercial starch-based thickener were considered in this study. An accurate theoretical description of the flow is proposed for Newtonian and power-law fluids considering the effect of fluid properties and of the syringe geometry. A rheological map is proposed, based on the results of several thousand simulations, to capture quantitatively the effect of rheological properties and density on the IDDSI classification, highlighting the important effect of the fluid density which is usually ignored. The sensitivity of the IDDSI results with respect to the syringe outlet diameter is discussed, as well as the different average shear rates at which different IDDSI levels are tested. The rheological map also shows quantitatively that different combinations of the fluid rheological properties and density can result in the same IDDSI classification, suggesting interesting directions for future clinical research. [ABSTRACT FROM AUTHOR]

The transition from concentric primary flow to non-tangential secondary flow of blood was investigated using experimental steady shear rheometry and numerical modelling. The aims were to: assess the difference in secondary flow in a Newtonian versus shear-thinning blood analogue; and measure the secondary flow in the blood. Both experiments and numerical modelling showed that the transition from primary to secondary flow was the same in a Newtonian fluid and a shear-thinning blood analogue. Experiments showed whole blood transitioned to secondary flow at lower modified Reynolds numbers than the Newtonian fluid; and transition was haematocrit dependent with higher RBC concentrations transitioning at lower modified Reynolds numbers. These results indicate that modelling blood as a purely shear-thinning fluid does not predict the correct secondary flow fields in whole blood; non-Newtonian effects beyond shear-thinning behaviour are influential, and incorporating effects such as multiphase contributions and viscoelasticity, yield stress and thixotropy is necessary. [ABSTRACT FROM AUTHOR]

[Display omitted] Processing of electrode slurry, which is highly non-Newtonian fluid, is a critical step in the mass production of lithium-ion batteries (LIBs). While extensional flow plays an important role in the electrode slurry processes such as coating, most previous studies have focused only on the shear rheology, due to the lack of a reliable method to measure the extensional rheological properties of the slurry. Here, it is demonstrated that the extensional rheological properties of the anode slurries can be successfully characterized using the stop-flow-dripping-onto-substrate/capillary break-up rheometry (SF-DoS/CaBER). Using this system, it is observed that the extensional rheology of the anode slurry is significantly affected by the blend ratio of the natural and synthetic graphite, as well as the binder and conductive concentrations. Furthermore, the shear rheology-based model predicts much shorter pinch-off times than those measured experimentally, indicating that the yield-stress of the anode slurry is much larger in extensional flow than in shear flow. [ABSTRACT FROM AUTHOR]

In this work, an algorithm for topology optimization of incompressible structures is proposed, in both small and finite strain assumptions and in which the loads come from the interaction with a surrounding fluid. The algorithm considers a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially to simulate the interaction between them. Several stabilized mixed finite element formulations based on the Variational Multi-Scale approach are considered to be capable of tackling the incompressible limit for the numerical approximation of the solid. The fluid is considered as an incompressible Newtonian fluid flow which is combined with an Arbitrary-Lagrangian Eulerian formulation to account for the moving part of the domain. Several numerical examples are presented and discussed to assess the robustness of the proposed algorithm and its applicability to the topology optimization of incompressible elastic solids subjected to Newtonian incompressible fluid loads. [ABSTRACT FROM AUTHOR]

In this analysis, Cross‐fluid model along wall properties is investigated. Impact of the magneto‐hydrodynamic on the non‐Newtonian model is also considered. Numerical algorithm MATLAB bvp4c function is adopted for the solution of coupled nonlinear equations along long‐wavelength and low Reynolds number approximations. Viscous dissipation phenomena are counter to discuss the energy possession during flow. Fluid velocity and stream lines for the flow are also precisely determined in this analysis. The various parameters that influence the physical characteristics of flow are plotted through the graph, and their effects are discussed in detail. From the conclusions, the consequence of the flow model parameters is found to be substantial and also noted that the present model has the potential applications to comprehend the bile conduit drive via bladder, gallstones, and blood flow features in living organisms in a much better way than prior. [ABSTRACT FROM AUTHOR]

Non‐Newtonian fluid plays a vital role in the field of manufacturing and engineering sector, because of its immense heat transfer rate. The two‐dimensional incompressible unsteady Maxwell nanofluid thin‐film flow with MHD and viscous dissipation over an inclined surface is investigated. One of the mechanisms in the second law of thermodynamics, that is irreversibility which also analyzed. The Maxwell nanofluid thin film energy and motion equations in the additional information have been turned into a coupled differential system of the third order. The transformed ODE equations are further evaluated by using the Homotopy Analysis Method (HAM). The variations of entropy rate, velocity, Bejan number and temperature field with the various emerging parameters are analyzed. This could potentially lead to the development of solar energy systems that are both affordable and highly efficient, so enabling the more efficient use of renewable energy sources and reducing our dependence on fossil fuels. [ABSTRACT FROM AUTHOR]

The subject under consideration in this research has various geophysical and astrophysical applications. Specifically, we investigate the impact of variable gravity on the onset of thermal instability within a layer of Jeffrey nanofluid confined in a Darcy-Brinkman porous medium. The solution of the fluid layer, which is positioned between two free-free boundaries, is determined using a linear stability analysis employing the normal mode technique. The Rayleigh number on the onset of convection is derived by using the Galerkin method. For stationary convection, the effects of different variable gravity parameters on the Jeffrey parameter, Darcy-Brinkman number, Lewis number, moderated diffusivity ratio, porosity of porous media and nanoparticle Rayleigh number are analyzed and presented graphically. The choices of using Jeffrey nanofluid as the base fluid for the study add novelty. Non-Newtonian fluids encompass a diverse range of substances, such as engine oils, oil extraction, wallpaper paste, and various biological liquids like blood etc. [ABSTRACT FROM AUTHOR]

Superhydrophobic (SHS) and liquid‐infused surfaces (LIS) have shown great potential in various engineering applications. Due to their heterogeneous surface properties, a mathematical description of the flow behavior along such surfaces is challenging. Circular textured surfaces are of particular importance. They are modeled as either axially traversed tubes or annuli consisting of no‐slip walls that are padded with rotationally symmetric finite‐shear regions. The latter represents a viscous interaction zone with a second fluid, assumed with layer thickness zero. Zimmermann and Schönecker provide analytical equations that describe the flow field and effective slip length for such geometries. They are applicable to Newtonian fluids of arbitrary viscosity ratio. This article emphasizes the development of principles and guidelines for the design of SHS and LIS to enhance sliding effects, based on these analytical models. The approach presented here facilitates an geometric evaluation of slippery circular surfaces, aiming to offer insights for the design. Through this research, the potential for significant energy savings and enhanced fluid transport performance can be realized, contributing to the development of more efficient fluid engineering systems. [ABSTRACT FROM AUTHOR]

Light levitation of droplets over a locally heated gas–liquid interface by an infrared focus laser has been recently reported, but the hydrodynamics of light levitated droplet evolution remains unclear. Herein, we report that the condensed droplet experiences a periodic damped vortex motion process before evolving to a stably levitated droplet. In the later stage of the periodic damped vortex motion, the velocity decay rate is linearly proportional to the growth of condensed droplets. The linear scaling factor approximates the dynamic viscosity of the ambient fluid, which is analogous to the shear stress–shear relationship in the Newtonian friction law. This study deepens the understanding of the underlying mechanism of light levitated droplet evolution. [ABSTRACT FROM AUTHOR]

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 ( R d ). 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 ( C f x , N u x , and S h x ) 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., λ c = − 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. [ABSTRACT FROM AUTHOR]

Magneto-thermomechanical applications range from magnetic resonance imaging to electric diodes and the design of dielectric grease. To contribute significantly to the biomedical industry for proper prediction and treatment of diseases such as cancer, stenosis, and technological advancement in the design of electronic tools. This study presents the significance of magneto-thermomechanical modeling of Reiner–Philippoff fluid flow subject to thermal radiation influence. The Reiner–Philippoff fluid encapsulates the properties of shear-thinning, shear-thickening, and Newtonian fluids in different viscosity regimes. The main-stream velocity ue is considered in its generalized form as well as taking into account the influence of thermal radiation and thermal conductivity. To obtain the computational model analysis, a numerical tool via the bivariate spectral collocation method is deployed on the resulting transformed PDEs. Upon validation of the method, the profile distributions of respective boundary layers with respect to the Bingham number, magneto-thermomechanical parameter, and Reiner–Philippoff fluid parameter are analyzed and discussed. The results of the engineering quantities of skin friction and Nusselt number are presented in graphical and tabular form. Among the findings of this study is that the Newtonian fluid is a turning point for skin drag force and heat transfer rate. Besides, the ferrohydrodynamic parameter recedes the velocity of shear-thinning fluid the most, although, boosts its (shear-thinning fluid) heat transfer coefficient. [ABSTRACT FROM AUTHOR]

[Display omitted] Achieving rapid capillary wetting is highly desirable in nature and industries. Previous endeavors have primarily concentrated on passive wetting strategies through surface engineering. However, these approaches are inadequate for high-viscosity fluids due to the significant viscous resistance, especially for non-Newtonian fluids. In contrast, forced wetting emerges as a promising method to address the challenges associated with achieving rapid wetting of non-Newtonian fluids in capillaries. To investigate the forced wetting behavior of viscoelastic fluids in capillaries, we employ Xanthan Gum (XG) aqueous solutions as target fluids with the storage modulus significantly exceeding the loss modulus. We utilize smooth glass capillaries connected to a syringe pump to achieve high moving speeds of up to 1 m/s. Our experiments reveal a significant distinction in the power-law exponent that governs the scaling relationship between the dynamic contact angle and velocity for viscoelastic fluids compared to Newtonian fluids. This exponent is considerably smaller and varies based on the concentration of viscoelastic fluids and the diameter of the capillaries. We suggest that the viscosity dominates the wetting dynamics of viscoelastic fluids, manifested by the contact line morphology-dependent behavior. This insight has significant implications for microfluidics and drug injectability. [ABSTRACT FROM AUTHOR]

Working fluids that incorporate solid microencapsulated phase change materials (MPCMs) can benefit from properties such as density and viscosity, which are crucial for improving heat capacity and transfer. However, limited data are available on these parameters for specific slurry and mass ratios. In this study, we present a comparative analysis of the experimental results on the viscosity of three different MPCM aqueous dispersions, namely MPCM 31-S50, MPCM 25-S50, and Micronal 5428X. Varying MPCM mass ratios of distilled water were used to obtain different mass concentrations of the phase change material (PCM), and the resulting slurries were analysed at temperatures ranging from 15 to 40 °C. Our findings showed that all slurries exhibited non-Newtonian characteristics at low shear rates, with viscosity stabilising at higher shear rates, resulting in the characteristics of a Newtonian fluid. The viscosity results were highly dependent on the type of MPCM base dispersion, particularly at high mass ratios, with the slurries having viscosities higher than those of water. Furthermore, we conducted density experiments as a function of temperature, using a flow test setup and a Coriolis flowmeter (Endress+Hauser, Reinach, Switzerland) to determine the density of two MPCMs, namely MPCM 25-S50 and Micronal 5428X. The test samples were prepared at mass concentrations of 10%, 15%, and 20% of the phase change material. We found significant differences in density and viscosity for different MPCM slurries as a result of both the PCM concentration and the material studied. Our results also revealed an apparent PCM phase change process, in which the slurry density significantly decreased in the temperature range of the phase transition from solid to liquid. [ABSTRACT FROM AUTHOR]

In this paper, inscribed non-Newtonian Williamson fluid relaxation and contraction phenomena due to the effect of magnetohydrodynamics (MHD) is taken into account. This issue is modeled, and precise solutions are handled using a low Reynolds number and long wavelength approximation. Graphical depiction of the consequences of various parameters on temperature and velocity are provided. It becomes clear that the temperature reactions to increases in Biot numbers are decreased. Considering a cylindrical coordinate system, the impact of various physical parameters on the temperature distribution, velocity, the pressure gradient, and frictional force are secured from the flow for non-Newtonian Williamson fluid exposed from MATLAB. Additionally, it has been discovered that the velocity profile at the tube's center increases for shear-thinning a fluid and decreases for thickening a fluid. Furthermore, the peristaltic walls show the opposite behavior. [ABSTRACT FROM AUTHOR]

Bacteria exhibit swimming behavior through the rotation of helical flagellar filaments, a common mode of propulsion for artificial micro-swimmers as well. However, most studies have focused on helical filaments with a uniform radius, leaving limited research on filaments with nonuniform radii. This paper presents a simulation of the hydrodynamics of a rotating helical filament with a nonuniform radius. The degree of nonuniformity is characterized by a radius ratio, β. Using the OpenFOAM platform, a simulation module for non-Newtonian Stokes flow was developed and integrated. The kinematics of the filament were predefined by fixing either the pitch or the helical angle, in addition to the helical radius. Thrust acting on the filament were analyzed with regards to the helical radius ratio, rotation speed, and fluid viscoelasticity. Certain modifications were made to apply the resistive force theory (RFT) to filaments with nonuniform helical radii. Results revealed that when the pitch was fixed, the thrust of the helix varied non-monotonically with the radius ratio, with excessive ratios leading to increased resistance. In contrast, helices with fixed helical angles exhibited an increasing thrust with a higher radius ratio. The thrust was greater in Newtonian fluids compared to non-Newtonian fluids, and the propulsion of the helix was influenced by the Deborah number. As the Deborah number approached zero, the thrust of viscoelastic swimming speed approached that of viscous swimming speed. For small, β (, β =1 and 4), the ratio of the thrust in viscoelastic fluid to the thrust in viscous fluid was always less than unity. At, β = 9, elasticity hindered propulsion at low De (De<1.5), while the opposite was observed at high De (De>1.5). A new approach was proposed to evaluate the impact of viscoelasticity on the helix, it was expected that the new calculation method can reduce the computational effort effectively. [ABSTRACT FROM AUTHOR]

The modeling of moving solid particles in fluid flow has been the focus of many studies and has succeeded to attract significant attention from researchers. However, commonly used modeling approaches such as discrete element modeling (DEM) and direct numerical simulations (DNS) lack simplicity and have been computationally intensive. The aim of this paper is to develop a new approach to simulate solid transport in an incompressible Newtonian fluid flow. This method is based on the Finite element method with penalization of the deformation tensor. The fluid behavior is governed by the Navier-Stokes equations within the investigation domain. To take into account collisions, we present an algorithm which allows us to handle contacts between rigid particles. In this paper, 2D fluid/particles flow simulations are performed; the results are validated by comparison with results from other methods. We attempt to simulate the conveying of solid particles behavior of circular particles in a fluid flow inside a pipe. The numerical tests show that the present method provides a very efficient approach to directly simulate the solid transport inside the channels. [ABSTRACT FROM AUTHOR]

Transition to turbulence in pipe has been extensively studied but is still not completely understood and even more for non-Newtonian fluids. We focus here on yield stress shear-thinning fluids and the mechanism leading to the transition in pipe, the so-called rheo-inertial transition to turbulence. An experimental setup has enabled us to identify flow regimes in a cylindrical pipe, using both flow visualizations and pressure drops measurements for a range of Reynolds numbers. We delimited the non-Newtonian specific regime in the laminar-turbulent transition triggered at a critical Reynolds number below the turbulent puffs onset. This pre-transition regime is associated with a velocity profile asymmetry in which its degree and position evolve as the Reynolds number increases. The origin for the stability of this rheo-inertial regime is discussed, as it could be due to a competition between the nonlinear contributions of rheological behavior and flow inertia. Beyond this regime, we quantified the intermittence of puff transit, revealing the delay to turbulence. We spotted for the first time a different rheo-inertial transitional behavior in the intermittency evolution vs Reynolds number, displaying a smoother transition on a broader range. Finally, the critical Reynolds numbers for different yield stresses are compared with previous works, and the novelty is the linear increase in the delay to turbulent puffs with the yield stress. [ABSTRACT FROM AUTHOR]

Gas dispersion in non-Newtonian fluids has numerous applications in many chemical and biochemical applications. However, the effect of the power-law model constants describing the rheological behavior of the pseudoplastic fluid has never been investigated. Thus, a numerical model was developed to simulate the hydrodynamics of gas dispersion in non-Newtonian fluids with a coaxial mixer. Then, a set of experiments was conducted to assess the mass transfer efficacy of a coaxial mixer to benchmark the numerical model. In this regard, various methods, including dynamic gassing-in and electrical resistance tomography methods, were used to quantify the mass transfer and gas hold-up profiles. The influence of fluid rheological properties, gas flow number, and rotating mode on the power consumption, mass transfer coefficient, bubble size profile, and hydrodynamics were examined both experimentally and numerically. The response surface model (RSM) was employed to explore the individual effects of power-law model constants on mass transfer. The RSM model utilized five levels for the consistency index (k), five levels for the flow index (n), and three levels for the gas flow number. The statistical model proposed that the absolute model constants for the flow and consistency indices were 0.0012 and 0.0010, respectively, for the co-rotating mixer. Conversely, for the counter-rotating mixer, these constants were 0.0010 and 0.0013, respectively. Therefore, this study revealed that the co-rotating coaxial mixer was well-suited for dispersing gas within a fluid with high consistency. In contrast, the counter-rotating mixer proved effective in enhancing gas dispersion within a fluid with a lower flow index. [ABSTRACT FROM AUTHOR]

The internal flow within an evaporating sessile droplet is one of the driving mechanisms that lead to various particle deposition patterns seen in applications such as inkjet printing, surface patterning, and blood stain analysis. Despite decades of research, the causal link between droplet internal flow and particle deposition patterns has not been fully established. In this study, we employ a three-dimensional (3D) imaging technique based on digital inline holography to quantitatively assess the evolution of internal flow fields and particle migration in three distinct types of wetting droplets, namely water droplets, sucrose aqueous solution droplets, and sodium dodecylsulfate aqueous solution droplets, throughout their entire evaporation process. Our imaging reveals the three-stage evolution of the 3D internal flow regimes driven by changes in the relative importance of capillary flow, Marangoni flow, and droplet boundary movement during evaporation. Moreover, the migration of individual particles from their initial locations to deposition can be divided into five categories, with some particles depositing at the contact line and others inside the droplet. In particular, we observe the changing migration directions of particles due to competing Marangoni and capillary flows. We further develop an analytical model that predicts the droplet internal flow, deposition patterns, and determines the deposition mechanisms depending on their initial locations and evolving internal flow. The model, validated using different types of droplets from our experiment and the literature, can be further expanded to other Newtonian and non-Newtonian droplets, potentially serving as a real-time assessment tool for particle deposition in various applications. [ABSTRACT FROM AUTHOR]

Lid-driven cavity (LDC) flow is a significant area of study in fluid mechanics due to its common occurrence in engineering challenges. However, using numerical simulations (ANSYS Fluent) to accurately predict fluid flow and mixed convective heat transfer features, incorporating both a moving top wall and a heated hemispherical obstruction at the bottom, has not yet been attempted. This study aims to numerically demonstrate forced convection in a lid-driven square cavity (LDSC) with a moving top wall and a heated hemispherical obstacle at the bottom. The cavity is filled with a Newtonian fluid and subjected to a specific set of velocities (5, 10, 15, and 20 m/s) at the moving wall. The finite volume method is used to solve the governing equations using the Boussinesq approximation and the parallel flow assumption. The impact of various cavity geometries, as well as the influence of the moving top wall on fluid flow and heat transfer within the cavity, are evaluated. The results of this study indicate that the movement of the wall significantly disrupts the flow field inside the cavity, promoting excellent mixing between the flow field below the moving wall and within the cavity. The static pressure exhibits fluctuations, with the highest value observed at the top of the cavity of 1 m width (adjacent to the moving wall) and the lowest at 0.6 m. Furthermore, dynamic pressure experiences a linear increase until reaching its peak at 0.7 m, followed by a steady decrease toward the moving wall. The velocity of the internal surface fluctuates unpredictably along its length while other parameters remain relatively stable. [ABSTRACT FROM AUTHOR]

The present investigation entails experimental evaluations for examining the heat transfer and flow attributes of hybrid nanofluids in a heat exchanger equipped with helically corrugated tubes (HCTs) under laminar flow conditions. The study includes evaluating the effect of various factors, such as the particle volume fraction, pseudoplastic behaviour of the fluid, the choice of the working fluid and geometric properties of the heat exchanger tube. The study specifically focuses on two types of hybrid nanofluids: SiC-MWCNT and Al2O3-MWCNT, with a water-ethylene glycol mixture. Three helically corrugated tubes have been introduced, namely HCT-1, HCT-2, and HCT-3. Corrugation pitches are chosen as 27.5, 12.1 and 9.5 mm and corrugation heights as 1.04, 1.57 and 1.97 mm. The findings indicate that, out of the different tubes employed, HCT-3 demonstrated the maximum rise in the Nusselt number, exhibiting a 61.3% increase compared to the smooth tube. This is due to increased corrugation height and reduced corrugated pitch which facilitates rapid mixture flow thereby improving its heat transfer rate. Both investigated hybrid nanofluids exhibit a transition from Newtonian to shear-thinning behaviour beyond a volume fraction of φ = 0.1% in a water-ethylene glycol mixture. Prior to this volume fraction, the nanofluids exhibit Newtonian behaviour. Both the nanofluids show a thermal performance factor (THPF) exceeding unity. Moreover, SiC-MWCNT hybrid nanofluid reveals the highest THPF of 1.97 for HCT-3 at a Reynolds number = 2000. [ABSTRACT FROM AUTHOR]

An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid's fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme. [ABSTRACT FROM AUTHOR]

An ear-flow front is discovered in the industrial practice of injection molding, especially for fiber-reinforced composites; the advance of the flow front in the center of the cavity is obviously slower than at the edges. To date, such a peculiar flow has not yet been predicted theoretically or computationally and is beyond the predictive capabilities of existing commercial computer aid design (CAE) packages for the injection molding process. Recently, the GNF-X (Generalized Newtonian Fluid eXtended) model of weighted shear/extensional viscosity has been incorporated availably in state-of-the-art predictive engineering software of the 3D-CFD (three-dimensional computational fluid dynamics) framework to show the extension-induced vortex growth in contraction flows of polymer melts. Through 3D-CFD coupled with GNF-X in injection molding simulations, it is significant to demonstrate the importance of extensional viscosity on the ear-flow formation in relation to the weighted viscosity and extension fraction for long-branched and fiber-filled polymer materials. In addition, one can point out that the ear-flow front probably occurs in fast filling conditions for anisotropic fluids. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for non-Newtonian fluids together with the Maxwell correction for the Ampère law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables. [ABSTRACT FROM AUTHOR]

Cross‐diffusion gradients, such as the Soret and Dufour effects, play a big role in the formation of binary alloys, the movement of oil and groundwater contaminants, and the separation of gas mixtures. Other applications where cross‐diffusion gradients are useful include: Temperature fluctuations cause matter diffusion, known as Soret effects. Concentration gradients drive heat diffusion, or the Dufour effect. This effect is named after its French discoverer. These findings could be applied to many engineering and industrial contexts and have many intriguing and potentially useful effects. Joule heating unites Soret and Dufour's work. The traditional nonlinear differential approach yields enough permutations. Convergent series can be used to solve temperature, velocity, and concentration problems. These changes can occur in temperature, velocity, or concentration. The drawings clarify all about the system's most important qualities and components. A comprehensive analysis of the Nusselt and Sherwood values is also done. After graphing the Nusselt and Sherwood values, they are analyzed. We are discussing computer science. This study found that Hartman number increases reduce one's perception of radial velocity. As Prandtl and Soret molecules increase, fluid temperature decreases. In this study, we employ numerical methods to solve the micropolar fluid flow problem on a stretched and curved disk. Our methods allow us to model fluid flow in three dimensions. We focus on micropolar fluid flow. Applying the necessary transformations to a set of partial differential equations simplifies it into a set of ordinary differential equations. The equations in both sets are transformed using similarities to convert one set of partial differential equations into another set of ordinary differential equations. The gunshot method and the Runge–Kutta algorithm can solve coupled equations numerically. The nondimensional radius of curvature can quantify and characterize many physical phenomena. Strain, microrotation velocity, and fluid velocity are examples. Due to the variances between curved and flat stretched sheets, the border layer strain cannot be neglected. Due to differences in stretching sheets, [ABSTRACT FROM AUTHOR]

The improvement of the cooling performance of liquid‐cooled microchannel heat sinks used for densely packed electronic circuits is sorted via passive techniques like tuning substrate or coolant properties. We propose a design for enhancing heat sink performance by simulataneously modifying the channel geometry and tuning the fluid rheology. By modeling the coolant as a power law fluid, its rheological behavior is varied ranging from shear‐thinning to shear‐thickening, alongside Newtonian fluid. We introduced tapering to the middle wall that separates the bottom and top channels of a double layered microchannel heat sink (DL‐MCHS), causing both channels to converge. This convergence not only increases the flow velocity within the downstream microchannel but also reduces the apparent viscosity of the shear‐thinning fluid being subjected to shear, resulting in enhanced thermal and hydraulic performance. We analyze the results from both the first and the second law of thermodynamics context, demonstrating that a tapered DL‐MCHS with shear‐thinning fluid outperforms a straight partition wall DL‐MCHS with Newtonian coolant. However, we also discovered that extreme tapering compromises thermodynamic viability, but by fine‐tuning the extent of tapering, we inferred that a DL‐MCHS with shear‐thinning fluid can become viable with little compromise in the thermal performance. [ABSTRACT FROM AUTHOR]

How far can a person sink downwards in quicksand? Experience would seem to suggest that there is low risk of submerging completely, but it is not easy to demonstrate this because of the complex rheology of granular suspensions. We study several mathematical models for the sinking of a vertical cylinder downwards into quicksand, finding that an approach with a buoyancy equation modified by drag force gives an unphysical answer. We instead argue that our proposed conclusion is supported by considering the dynamics of vibration-induced compactification of liquid-saturated granular suspensions. We compare quicksand with other non-Newtonian fluids, emphasising that in this case the same model does not apply and that the risk of drowning could be much more significant. We finish by suggesting some relevant experiments that can be performed in a classroom setting. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the well-posedness of a diffuse interface model of non-Newtonian two-phase flows in ℝ 3 . First, we prove the local existence of a unique strong solution provided that the initial velocity and initial concentration of two phases are sufficiently regular. Then, by using the energy estimates and standard continuity argument, we show that there exists a unique global strong solution provided that the initial velocity and initial concentration are sufficiently small. [ABSTRACT FROM AUTHOR]

Single-screw extruders (SSE) are commonly used in a wide variety of applications, ranging from polymer-extrusion to pellet additive manufacturing (PAM). Existing mathematical models focus on Newtonian and power-law rheologies to model melt flow in the last screw vanes. However, molten polymers usually follow more complex rheological patterns, and a generalized extrusion model is still lacking. Therefore, a semi-analytical model aiming at describing the flow of molten polymers in SSE is presented, to encompass a wide range of non-Newtonian fluids, including generalized non-Newtonian fluids (GNF). The aim is to evaluate the molten polymer flow field under the minimum set of dimensionless parameters. The effect of dimensionless extrusion temperature, flow rate, channel width, and height on the flow field has been investigated. A full factorial plane has been chosen, and it was found that the impact of dimensionless flow rate is the most prominent. The results were initially compared to numerical computations, revealing a strong agreement between the simulations and the proposed GNF method. However, significant deviations emerged when employing the traditional power-law model. This is particularly true at high values of flow rate and extrusion temperature: the mean error on overall flow speed is reduced from 12.91% (traditional power-law method) to 1.04% (proposed GNF method), while keeping a reasonable computational time (time reduction: 96.70%, if compared to fully numerical solutions). Then, the predicted pressure drop in the metering section was benchmarked against established literature data for industrial-scale extruders, to show the model's accuracy and reliability. The relative errors of the traditional model range between 34.33 and 62%. The proposed method reduces this gap (errors ranging between 5.34% and 10.97%). The low computational time and high accuracy of the GNF method will pave the way for its integration in more complex mathematical models of large-scale additive manufacturing processes. [ABSTRACT FROM AUTHOR]