Fluid Motion Research Articles

O sushchestvovanii upravleniya s obratnoy svyaz'yu dlya odnoy drobnoy modeli Foygta

We study the feedback control problem for a mathematical model that describesthe motion of a viscoelastic fluid with memory along the trajectories of the velocity field. Weprove the existence of an optimal control that delivers a minimum to a given bounded and lowersemicontinuous cost functional.

The existence problem of feedback control for one fractional Voigt model

In this paper, we study the feedback control problem for a mathematical model that describes the motion of a viscoelastic fluid with memory along velocity eld trajectories. We prove the existence of an optimal control that gives a minimum to a given bounded and semi-continuous from below quality functional. The proof uses the approximation-topological approach, the theory of regular Lagrangian flows, and the theory of topological degree for multivalued vector elds.

Analysis of Shallow Water Equation Based on Tsunami Simulations: Evidence from the Pacific Ocean

Tsunamis, particularly prevalent in the Pacific Ocean's "Ring of Fire" region, present both a scientific intrigue and a societal concern due to their potential for devastation. Central to understanding and predicting these phenomena is the Shallow Water Equations (SWEs), which describe the horizontal motion of water waves. This study delves into the specific behaviors of tsunamis in the Pacific coast, utilizing comprehensive oceanographic and seismological data from the Pacific Oceanographic Institute (POI) spanning two decades. Through the lens of the SWEs, the impacts of bathymetric features and coastal topography on tsunamis are analyzed from the perspective of propagation, wave period, and frequency. Findings highlighted the significant role of solitons or solitary waves and the destructive force they exert, especially in shallow waters. While the SWE-based models have greatly assisted in developing real-time warning systems, reducing fatalities and damages, they also present certain limitations, e.g., assuming a flat seafloor and neglecting factors such as Earth's rotation, vertical fluid motion, and real-world marine conditions like turbulence. The study underscores the need for continuous refinement of these models, emphasizing the integration of observational data with advanced computational methods to enhance tsunami prediction and preparedness.

An in-depth study of the effect of ultrasonic field on the melting characteristics of pure and nano-enhanced PCMs using thermal and digital imagery

In this laboratory study, an attempt has been made to explore the details of the effect of an ultrasonic field on the melting behavior of pure phase change materials (PCMs) and nano-enhanced PCMs using images recorded with digital and thermal cameras. A 50/50 mixture of beeswax and coconut oil was employed as the pure PCM and the copper oxide nanoparticles were used to improve the thermal aspects of the pure PCM. Three different mass concentrations i.e., (1 %, 2 %, and 4 %) were considered for nanoparticles. The required ultrasonic field was generated using two stainless steel 27 kHz 40 W piezoelectric transducers. It was revealed that the application of ultrasonic field to the pure PCM and nano-enhanced PCM containing 1 %, 2 %, and 4 % of nanoparticles reduces their complete melting time by 58.33 %, 60.00 %, 61.39 % and 64.44 %, respectively. The images taken with the digital and thermal cameras confirmed that agitation oscillating fluid motion and cavitation are two mechanisms that definitely contribute to the improvement of PCM melting characteristics in the presence of ultrasonic field.

Irreversibility and thermal performance of nonlinear radiative cross-ternary hybrid nanofluid flow about a stretching cylinder with industrial applications

SignificanceThe suspension of nanoparticles in the base fluid has significant attention from researchers and industries with an aspect of improving the thermo-physical properties of the fluid. The significance is more prominent for ternary hybrid nanofluids by improving energy production, storage and efficiency, and play a huge role in global sustainable energy development and cleaner energy production. AimThe aim of the present problem is to analyze the flow and thermal behavior of a cross-ternary SWCNT, MWCNT, and GO nanoparticles composite water-based ternary hybrid nanofluid past a stretched cylinder. Thermal expansion phenomena feature joule heating and non-linear thermal radiation under convective conditions. Research methodologyTransformed nonlinear equations are solved numerically by the homotopy analysis method. The flow feature with the physical interest quantities such as skin friction and Nusselt number has been displayed through graphs and tables. Further, the optimized entropy of the system with the Bejan number has been discussed and displayed through graphs and tables. A comparison was made with the existing literature. Each graph features a comparison of ternary hybrid, hybrid, and mono nanofluid with other significant physical parameters. Major conclusionEntropy generation is observed to nonlinearly slow down with improvements in the Brinkman and radiation parameters, while a reverse procedure develops for the Bejan number with the above parameters. An improvement in Weissenberg and curvature parameters accelerates the fluid velocity and heat transfer rate, while fluid motion is controlled by an increase in magnetic field strength. Outcomes may help to understand the performance of the ternary hybrid nanofluids applications in different industries under certain circumstances.

Relativistic Exploration of Dark Matter Effectsin Rotating Galaxy, Studied Fluid-Dynamically

Galactic space is filled with interstellar clouds of neutral gases. Motion of the space-clouds is viewed as a flow of continuous fluid in curved space with gravity. Dynamical motions of the space-fluid of rotating galaxies are investigated by extending Fluid Dynamics to that in the frame of general relativity. Fluid flow field to be extended to that of a relativistic theory is reinforced by the fluid gauge theory equipped with a background (dark) gauge field conditioning the fluid continuity. The Gravity-space Fluid Dynamics thus developed captures main feature of the dark-matter effect as the action of the gauge field on the motion of space fluids. In the present formulation, the stress-energy tensor in the general relativity is revised in order to take account of general nature of stress field by extending the isotropic pressure to an-isotropic stress field.

Ensemble fluid simulations on quantum computers

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to its linearity, such an equation is in principle more amenable to quantum computing than the dynamic equations of fluid motion. After suitable marginalization and associated closure, the Liouville approach is shown to require several hundreds of logical qubits, hence calling for a major thrust in current noise correction and mitigation techniques.

Spinning a Liquid Wheel and Driving Surface Thermomagnetic Convection with Light.

A typical Tesla thermomagnetic engine employs a solid magnetic wheel to convert thermal energy into mechanical energy, while thermomagnetic convection in ferrofluid is still challenging to observe because it is a volume convection that occurs in an enclosed space. Using a water-based ferrofluid, a liquid Tesla thermomagnetic engine is demonstrated and reports the observation of thermomagnetic convection on a free surface. Both types of fluid motions are driven by light and observed by simply placing ferrofluid on a cylindrical magnet. The surface thermomagnetic convection on the free surface is made possible by eliminating the Marangoni effect, while the spinning of the liquid wheel is achieved through the solid-like behavior of the ferrofluid under a strong magnetic field. Increasing the magnetic field reveals a transition from simple thermomagnetic convection to a combination of the central spin of the spiky wheel surrounded by thermomagnetic convection in the outer region of the ferrofluid. The coupling between multiple ferrofluid wheels through a fluid bridge is further demonstrated. These demonstrations not only unveil the unique properties of ferrofluid but also provide a new platform for studying complex fluid dynamics and thermomagnetic convection, opening up exciting opportunities for light-controlled fluid actuation and soft robotics.

A new two-step particle tracking and channels model method for preferential 3-D flow and transport in large DFNs of fractured aquifers

A new two-step method has been developed for predicting three-dimensional (3-D) pollutant plumes and breakthrough curves (BTC) in fractured aquifers. Predicting fluid motion fields and pollutant concentrations in groundwater is a challenging task, due to the difficulties in building a 3-D discrete fracture network (DFN) with the same geometry of fractures and interconnections as in the studied aquifer and the computational complexity of the problem being modeled. To improve the representation of DFN, geological characterization of fracture apertures was performed using field well-pumping data as the prerequisite for the modeling approach. The modeling was performed in two steps: first, 3-D particle tracking following streamline (PTFS) simulations in DFN backbones, and second, a 3-D channels model (CM) analytical solution. The PTFS simulations captured the mean properties of the 3-D velocity field relevant to spatial and temporal transport along preferential flow pathways of a fractured aquifer. The 3-D CM solution yielded the exact BTC of concentrations accounting for the slowest flow pathways typically excluded from DFN backbones extraction methods. The PTFS/CM simulations were initially performed at the lab scale on a 3-D 20 m rock block from the Bari (South Italy) fractured aquifer. Results were consistent with the chlorophyll-A BTC obtained from a well-to-well tracer experiment. Subsequently, the capability of the new method was tested by increasing the scale of simulations to a larger 3-D DFN of 200 m with 2,200 fractures. The resultant BTC was obtained in 32 min, showing the proposed PTFS/CM technique can rapidly determine complex 3-D solutions in heterogeneous fracture-dominated aquifers. The applied Lagrangian and Eulerian techniques can provide quasi-deterministic BTCs and 3-D maps of pollutant concentrations, avoiding extensive computations required for conforming mesh methods. Moreover, the solution does not require multiple randomly arranged DFN realizations, as in particle tracking-based stochastic methods. These results have significant implications in modeling transport at the aquifer scale, where DFNs are composed of thousands of fractures.

Core shift limitation in investment casting process of hollow turbine blade

The deviation in wall thickness caused by core shift during the investment casting process significantly impacts the strength and service life of hollow turbine blades. To address this issue, a core shift limitation method is developed in this study. Firstly, a shift model is established based on computational fluid dynamics and motion simulation to predict the movement of the ceramic core in investment casting process. Subsequently, utilizing this model, an optimization method for fixturing layout inside the refractory ceramic shell is devised for the ceramic core. The casting experiment demonstrates that by utilizing the optimized fixture layout, not only can core shift during the investment casting pouring process be effectively controlled, but also the maximum wall thickness error of the blade can be reduced by 42.02%. In addition, the core shift prediction is also validated, with a prediction error of less than 26.9%.

Investigation of cross-diffusion effect on radiative Jeffery-Hamel flow in convergent/divergent stretchable channel with Lorentz force and Joule heating

This article documents the hydro-magnetic, incompressible Jeffery-Hamel flow in convergent/divergent (CD) channels with stretchable walls. Although there seem to be several works on the subject in the available literature, only a few attempts have been made to work into mass and heat transfer analysis. Consequently, novelty of present study is to investigate the significance of Soret/Dufour. Joule heating, and chemical reaction effects on Jeffery-Hamel flow. The governing coupled system of PDEs showing the mathematical framework of the current physical problems is converted into ODEs through proper transformations. The numerical solution of the obtained couple of ODEs is simulated with the assistance of Mathematica-11 solver NDSolve. The computed outcomes depict that Lorentz force developed due to the magnetic field decays the fluid motion for both convergent and divergent channels. Furthermore, incorporating the heat source and Dufour effects yields a sustainable increase in temperature distribution, whereas the Soret number has reverse features on concentration. Furthermore, the numerical outcomes reflect the significant variation in Nusselt number against magnetic, radiation parameter and Soret number.

Simulation of micropolar fluid flow with ternary nanoparticles over a permeable stretching surface involving nonlinear thermal radiation

ABSTRACT The primary goal of this research is to look into the rheological aspects of blood flow that contains ternary nanoparticles ( C u O + T i O 2 + A l 2 O 3 ). For this, the micropolar fluid model is adopted to simulate blood flow transport. Inclined magnetization and porosity characteristics are used to reveal the momentum attributes of flowing fluid, and nonlinearized radiating thermal flux is used to predict the thermal characteristics of the concerned flow. Further, the aspects of suction and injection of fluid over a permeable stretching sheet are also acknowledged. Governing system of partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformation. An effective built-in routine known as bvp4c, which is based on finite differencing, is used to acquire the solution. The results showed that the trihybrid nanofluid significantly boost fluid motion and temperature profiles more in the mass injection effect in comparison to suction phenomena. The increase in heat transfer rate is also noticed for augmented values of non-linear radiation parameter and micropolar parameter. There is a detailed discussion of the effects of the contributing parameters on the resulting dimensionless profiles. This research has significant implications for the delivery of magnetized blood, hyperthermia therapy, understanding of the bloodstream, transfer of complex bio-waste liquids, and capillary heat exchange.

Effects of Soret and Dufour on Unsteady Magneto-Convective Transport through a Vertical Perforated Sheet with Chemical Reaction

An investigation of the effects of Soret and Dufour on an unsteady MHD convective transmission over a vertical porous sheet with chemical reaction was introduced throughout this study. The model that formed nonlinear governing equations is transformed by applying the similarity analysis with the help of the finite difference method. The numerical resolutions of the fluid characteristics like velocity, concentration, and temperature are explained graphically. This research also presented the mass transmission rate, heat transmission rate, and the local skin friction coefficient, which are explained in tabular form. The results give the fluid motion and temperature improvement for growing values of the Dofour effect. Also, the fluid velocity and concentration improve for elevated amounts of the Soret effect. The local skin friction improves by around 66% whereas the mass transmission rate lessens by around 247% with the growing Soret number (0.5–2.0).

Magnetohydrodynamic effects on a pathological vessel: An Euler–Lagrange approach

For numerically studying blood flow in a pathological vessel under the influence of a magnetic field, it is necessary to develop an approach that tracks the moving tissue and accounts for interactions between the fluid, the arterial wall, and the magnetic field. The current study discusses a mathematical approach of the fluid's motion under the influence of a magnetic field using fluid mechanics principles. A mixed Euler–Lagrange formulation is introduced to mathematically describe the blood flow in the aneurysm during the entire cardiac cycle. Blood is considered a Newtonian, incompressible, and electrically conducting fluid, subjected to a static and uniform magnetic field. Generalized curvilinear coordinates are used to transform the transport equations into body-fitted geometries and provide a manageable form of equations. The system of equations related to motion consists of a coupled and nonlinear system of partial differential equations (PDEs). The discretization of the PDEs is performed using the finite volume method. The addition of the Lorentz force in the momentum PDEs describes the applied uniform magnetic field in the blood flow. Due to strong coupling and nonlinear terms, a simultaneous solution approach is applied. The results show that the magnetic field strongly influences blood flow, reducing the velocity field q¯ and increasing the pressure drop, Δp.

Porous and Magnetic Effects on Modified Stokes’ Problems for Generalized Burgers’ Fluids

In this paper, exact analytical expressions are derived for dimensionless steady-state solutions corresponding to the modified Stokes’ problems for incompressible generalized Burgers’ fluids, considering the influence of porous and magnetic effects. Actually, these are the first exact solutions for such motions of these fluids. They can easily be particularized to give similar solutions for Newtonian, second-grade, Maxwell, Oldroyd-B and Burgers’ fluids. It is also proven that MHD motion problems of such fluids between infinite parallel plates can be investigated when shear stress is applied at the boundary. To validate the obtained results, the velocity fields are presented in two distinct forms, and their equivalence is proven through graphical representations. The obtained outcomes are utilized to determine the time required to reach a steady state and to elucidate the impacts of porous and magnetic parameters on the fluid motion. This investigation reveals that the attainment of a steady state occurs later when a porous medium or magnetic field is present. Additionally, the fluid’s flow resistance is augmented in the presence of a magnetic field or through a porous medium. Thus, as was expected, the fluid moves slower through porous media or in the presence of a magnetic field.

Wave Motion in a Viscous Homogeneous Fluid with a Surface Electric Charge

Wave Motion in a Viscous Homogeneous Fluid with a Surface Electric Charge

Initial-boundary value problem for the equations of dynamics of a rotating viscous stratified fluid

We study the problem of small motions of a viscous stratified fluid partially filling a container that uniformly rotates around an axis co-directed by gravity. The problem is studied on the basis of an approach related to the application of the so-called operator matrix theory. To this end, we introduce Hilbert spaces and some their subspaces, as well as auxiliary boundary value problems. The original initial-boundary value problem is reduced to the Cauchy problem for a first-order differential equation in some Hilbert space. After a detailed study of the properties of the operator coefficients corresponding to the resulting system of equations, we prove a theorem on the solvability of the Cauchy problem. On this basis, we find sufficient conditions for the existence of a solution of the original initial-boundary value problem describing the evolution of the hydro-system.

Analysis of blood and cerebrospinal fluid flows in preclinical AD. Preliminary results from ALFA+ cohort

AbstractBackgroundIntracranial cerebrospinal fluid (CSF) motion is driven by the wave pressure associated with arterial blood flow into the skull (Figure 1). Since one of the roles of CSF is the clearance of neural waste, it was investigated the relationship between blood and CSF flow parameters (as measured by magnetic resonance imaging [MRI]) and CSF Ab42/40 and ptau‐181 levels in the preclinical stages of Alzheimer’s disease (AD).MethodThree hundred sixty‐five subjects from the ALFA+ cohort underwent two MRI phase‐encoded velocity sequences (30 frames per cardiac cycle) to measure (1) blood flow in carotids below carotid bifurcation and (2) CSF flow through foramen magnum. The scanner’s Q‐flow tool was used to quantify stroke volume (volume per cardiac cycle), percent of vessel’s area increase and flow velocity increase, as a proxy for vessel elasticity and flow pulsatility, respectively. Associations between flow parameters and age, CSF Ab42/40 and ptau‐181 concentrations were sought, correcting for sex, age and time between lumbar puncture and MRI (P<0.05).ResultOne hundred thirty‐two subjects were excluded because the scanning session was not completed, showed missing or outlier values or did not pass quality control (artifacts or unbalanced outwards‐inwards CSF flow measures), resulting in a final sample size of 233 participants (mean age [SD]: 60.8±4.5 years; male: n = 73 [31.3%]). Figure 2 shows the plots with the most significant relationships between flow parameters, CSF biomarkers, CSF volume and age. It was observed that a higher stroke volume in CSF flow was associated with lower Ab42/40 and higher ptau‐181 concentrations in CSF.ConclusionThese results indicate that, despite the role of CSF in waste clearance, the accumulation of amyloid and tau in the brain might be neither caused nor enhanced by a global deficit in CSF circulation. We hypothesize that a higher volume of CSF associated with age and high ptau‐181 levels and/or the loss of parenchyma elasticity might reduce the global intracranial compressibility, resulting in an enhanced response to pressure increase due to blood flow into the skull, which could explain the observed increase in CSF flow associated with the early stages of AD.

Numerical Analysis of Williamson-Micropolar Ternary Nanofluid Flow Through Porous Rotatory Surface

This research introduces an advanced nanofluid model for optimizing the rate of heat transmission. The trihybrid nanofluid is constructed by suspending three distinct nanoparticles in a base fluid with diverse physical and chemical affinities. This study confronts the heat transfer characteristics of TiO2, Al2O3, and SiO2 boundary layer flow involving thermal radiation and slip scenarios. The controlling boundary layer equations are modified through an array of ordinary differential equations employing suitable similarity transformations, which have been solved by using bvp4c algorithm in MATLAB. As of yet, no prior investigation has ever been conducted on the flow of tri-hybrid nanofluid TiO2, Al2O3, and SiO2/H2O via rotatory surface. As a result, the current investigation has been undertaken to fill this gap, and the primary objectives of this work is to look into the aspects that optimise the heat transfer of base fluid (H2O) dissolved with tri-hybrid nanoparticles (TiO2, Al2O3, and SiO2) past a rotatory surface with slip conditions. The figures indicate that the presence of distinct nondimensional parameters in this analysis has a tremendous impact on the fluid motion inside the boundary layer. The plots obtained reveal that the diminution in particle movement is addressed simply by raising the Williamson parameter, magnetic parameter, and Forchheimer parameter. While the temperature profiles of the magnetic parameter, rotation parameter, and Williamson parameter demonstrate a reverse pattern. The findings are visualized in graphical format, and it is predicted that the tri-hybrid nanofluid has a greater thermal conductivity than the hybrid nanofluid and traditional fluid.

Evolution of solitary hydroelastic strain waves in two coaxial cylindrical shells with the Schamel physical nonlinearity

The paper considers the formulation and solution of the hydroelasticity problem for studying wave processes in the system of two coaxial shells containing fluids in the annular gap between them and in the inner shell. We investigate the axisymmetric case for Kirchhoff–Lave type shells whose material obeys a physical law with a fractional exponent of the nonlinear term (Schamel nonlinearity). The dynamics of fluids in the shells is considered within the framework of the incompressible viscous Newtonian fluid model. The derivation of the Schamel nonlinear equations of shell dynamics makes it possible to develop a mathematical formulation of the problem, which includes the obtained equations, the dynamics equations of two shells, the fluid dynamics equations and the boundary conditions at the shell-fluid interfaces and at the flow symmetry axis. The asymptotic analysis of the problem is performed using perturbation techniques, and the system of two generalized Schamel equations is obtained. This system describes the evolution of nonlinear solitary hydroelastic strain waves in the coaxial shells filled with viscous fluids, taking into account the inertia of the fluid motion. In order to determine the fluid stress at the shell-fluid interfaces, we perform linearization of the fluid dynamics equations for fluids in the annular gap and in the inner shell. The linearized equations are solved by the iterative method. The inertial terms are excluded from the equations in the first iteration, while, in the second iteration, these are the values found in the first iteration. A numerical solution of the system of nonlinear evolution equations is obtained by applying a new difference scheme developed using the Gröbner basis technique. Computational experiments are performed to investigate the effect of fluid viscosity and the inertia of fluid motion in the shells on the wave process. In the absence of fluids in the inner shell, the results of calculations demonstrate that the strain waves in the shells during elastic interactions do not change their shape and amplitude, i.e., they are solitons. The presence of viscous fluid in the inner shell leads to attenuation of the wave process.