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This research explores the dynamic behaviour of horn-shaped single-walled carbon nanotubes (HS-SWCNTs) conveying viscous nanofluid with pulsating the influence of a longitudinal magnetic field. The analysis utilizes Euler–Bernoulli beam model, considering the variable cross section, and incorporating Eringen's nonlocal theory to formulate the governing partial differential equation of motion. The instability domain of HS-SWCNTs is estimated using Galerkin's approach. Numerical analysis is performed using the Haar wavelet method. The critical buckling load obtained in this study is compared with previous research to validate the proposed model. The results highlight the effectiveness of the proposed model in assessing the vibrational characteristics of a complex multi-physics system involving HS-SWCNTs. Dispersion graphs and tables are presented to visualize the numerical findings pertaining to various system parameters, including the nonlocal parameter, magnetic flux, Knudsen number, and viscous factor. [ABSTRACT FROM AUTHOR]

The dynamical motion of a charged symmetrical solid body (SB) about its main symmetric axis is addressed in this work. The body is supposed to have a chamber with a globular shape, in which it contains a mobile mass and filled with a viscous liquid. This mass is assumed to be coupled via a double elastic band at a point that is situated along the dynamical symmetry axis and produces viscous friction. The body's motion is influenced by a gyrostatic moment (GM), whose first two components on the body's main axes are chosen to be zero. Additionally, the body is subject to the effects of an electromagnetic field, owing to a located point charge on the body's dynamic symmetry axis. On the indicated motion, the combined impact of the viscous liquid and the mobile mass is investigated. The achieved outcomes show that, in the presence of internal dissipation, the system's motion tends towards a constant rotation around its axis at the point of highest inertia as time approaches infinity. To demonstrate how the body's parameters affect the motion, the obtained outcomes are graphed. The method of fourth-order Runge-Kutta (4RKM) is employed to generate the governing system's numerical results, which are then displayed in additional diagrams. This work's relevance is concentrated on its considerable potential for usage in the submarine and gyroscope industries. The novelty of this work lies in the intricate interplay of rotational dynamics due to the GM, viscous liquid and electromagnetic effects to achieve new results, besides the gained numerical outcomes. Therefore, these results are considered novel and have significant theoretical and practical relevance. Moreover, it can be used to study the motion of celestial bodies, such as planets or moons, which might have internal cavities filled with fluids or other materials. The charged nature could be relevant for bodies with significant magnetic fields. [ABSTRACT FROM AUTHOR]

The featured problem explores the impact of cross-diffusion on the two-dimensional electrically conducting flow of a viscous liquid over a nonlinearly stretching sheet through a permeable medium. An inclusion of radiative heat energizes the heat transport phenomenon whereas the solutal transfer enriches by the conjunction of the chemical reaction. To justify the behavior of electromagnetic radiation, the Rosseland approximation is used by considering nonlinear thermal radiation. Further, the convective boundary conditions also affect the flow properties. The approachable transformations are employed to get a suitable non-dimensional form of the governing equations for the formulated problem. Due to the complex nature of the distorted equations, the system of equations is solved using an in-built code bvp5c predefined in MATLAB. The computation is carried out for the involvement of the suitable values of contributing parameters on the flow characteristics and along with the simulations of the rate coefficients. Further, the assigned particular parameters present an outcome that validates with a good correlation. Finally, the important outcomes are — enhanced suction due to the permeability of the surface augments the fluid velocity whereas the trend is reversed in the case of injection. The augmentation in the fluid temperature is exhibited for the radiating heat but the reacting species attenuates the fluid concentration. [ABSTRACT FROM AUTHOR]

The dynamics of rotating hydrodynamic systems containing phase inclusions are interesting due to the related widespread occurrence in nature and technology. The influence of external force fields on rotating systems can be used to control the dynamics of inclusions of various types. Controlling inclusions is of current interest for space technologies. In low gravity, even a slight vibration effect can lead to the appearance of a force acting on phase inclusions near a solid boundary. When vibrations are applied to multiphase hydrodynamic systems, the oscillating body intensively interacts with the fluid and introduces changes in the related flow structure. Asymmetries in the fluid flow lead to the appearance of an averaged force. As a result, the body is repelled from the cavity boundary and takes a position at a certain distance from it. The vibrationally-induced movement of phase inclusions in liquids can be used to improve various technological processes (for example, when degassing and cleaning liquids from solid inclusions, mixing various components, etc.). This study presents a relevant methodology to study the averaged vibrational force acting on a pair of free cylindrical bodies near the oscillating wall of a cavity. Attention is paid to the region of moderate and low dimensionless frequencies when the size of the inclusion is consistent with the thickness of the Stokes boundary layer. The dynamics of these bodies is considered in a horizontal cylindrical cavity with a fluid undergoing modulated rotation. The average lift force of a vibrational nature is measured by the method of quasi-stationary suspension of bodies whose density differs from the density of the liquid in a static centrifugal force field. The developed technique makes it possible to determine the dependence of the lift force on vibration parameters and the distance from the oscillating boundary at which solid inclusions are located. It is shown that in the region of moderate dimensionless frequencies, the average lift force acting on an inclusion near the boundary undergoing modulated rotation almost linearly depends on the dimensionless frequency. [ABSTRACT FROM AUTHOR]

Lateral spreading has historically caused extensive pile failure in liquefaction‐prone areas during strong earthquakes. A critical design scenario involves piles embedded in lateral spreading ground composed of a nonliquefied soil crust overlying a liquefied layer; it is critical because both layers can exert loads on the piles. Different thicknesses of the liquefied soil and the upper nonliquefied crust may engender different pile response patterns. Accordingly, to investigate factors influencing the lateral responses of a single pile embedded in liquefied ground with a nonliquefied crust, we conduct parametric analyses. The effects of liquefied and nonliquefied soil thicknesses are analyzed first, followed by those of pile‐head rotational restraint, pile diameter, and lateral spreading displacement. We observe two main pile response patterns for various liquefied soil thicknesses. The ground can be categorized into thin or thick liquefied ground depending on whether its liquefied soil thickness is less or greater than a critical value, namely, critical liquefied soil thickness; this critical thickness is dependent on the pile‐head rotational restraint, pile diameter, and lateral spreading displacement. The difference in the patterns stems from the varying roles of the upper nonliquefied soil layer during lateral spreading. For the thin liquefied ground, the nonliquefied layer contributes to adding lateral spreading force; therefore, the displacement, moment, and shear force responses of the pile increase with the nonliquefied soil thickness. However, for the thick liquefied ground, the nonliquefied layer provides resistance to lateral spreading; therefore, the maximum displacement, moment, and shear force of the pile initially decreases and then gradually increases with the nonliquefied soil thickness. [ABSTRACT FROM AUTHOR]

The dynamical motion of a charged symmetrical solid body (SB) about its main symmetric axis is addressed in this work. The body is supposed to have a chamber with a globular shape, in which it contains a mobile mass and filled with a viscous liquid. This mass is assumed to be coupled via a double elastic band at a point that is situated along the dynamical symmetry axis and produces viscous friction. The body’s motion is influenced by a gyrostatic moment (GM), whose first two components on the body’s main axes are chosen to be zero. Additionally, the body is subject to the effects of an electromagnetic field, owing to a located point charge on the body’s dynamic symmetry axis. On the indicated motion, the combined impact of the viscous liquid and the mobile mass is investigated. The achieved outcomes show that, in the presence of internal dissipation, the system's motion tends towards a constant rotation around its axis at the point of highest inertia as time approaches infinity. To demonstrate how the body’s parameters affect the motion, the obtained outcomes are graphed. The method of fourth-order Runge-Kutta (4RKM) is employed to generate the governing system's numerical results, which are then displayed in additional diagrams. This work's relevance is concentrated on its considerable potential for usage in the submarine and gyroscope industries. The novelty of this work lies in the intricate interplay of rotational dynamics due to the GM, viscous liquid and electromagnetic effects to achieve new results, besides the gained numerical outcomes. Therefore, these results are considered novel and have significant theoretical and practical relevance. Moreover, it can be used to study the motion of celestial bodies, such as planets or moons, which might have internal cavities filled with fluids or other materials. The charged nature could be relevant for bodies with significant magnetic fields.

ABSTRACTAnalysis of 2D magnetohydrodynamic flow of viscous fluid over a magnetized multi-physical curved mechanism is numerically conducted. The flow equations consist of a magnetic field transport, Maxwell’s equations, energy equation and concentration equation. Governing model is generated and establishes the boundary layer equations. Numerical computation by the Keller-Box shooting method is implemented with Jacobi’s iterative technique. The flow behaviours are anticipated against most interesting parameters. The novelty of this study focuses on the mathematical development of the flow problem with significant results. These results are applicable in manufacturing of stretchable materials.

This article surveys some results in the study of Iannelli [Su un modello di Oberbeck-Boussinesq relativo al moto di un fluido viscoso soggetto a riscaldamento, Fisica Matematica, Istituto Lombardo (rend. Sc.) A 121 (1987), 145–191], in which the motion of a viscous, compressible fluid in a two-dimensional domain, subject to heating at the walls, is studied. A global existence and uniqueness theorem for the time-dependent problem is given, and also, under more stringent assumptions, an existence and uniqueness theorem in the stationary case is given. A theorem on the asymptotic behavior for t→∞t\to \infty of the time-dependent solutions is proved.

The aim of the paper is to obtain a system of nonlinear evolution equations for two coaxial cylindrical shells containing viscous fluid between them and in the inner shell, as well as numerical modeling of the propagation processes for nonlinear solitary longitudinal strain waves in these shells. The case when the stress-strain coupling law for the shell material has a hardening combined nonlinearity in the form of a function with fractional exponent and a quadratic function is considered. Methods. To formulate the problem of shell hydroelasticity, the Lagrangian–Eulerian approach for recording the equations of dynamics and boundary conditions is used. The multiscale perturbation method is applied to analyze the formulated problem. As a result of asymptotic analysis, a system of two evolution equations, which are generalized Schamel– Korteweg– de Vries equations, is obtained, and it is shown that, in general, the system requires numerical investigation. The new difference scheme obtained using the Grobner basis technique is proposed to discretize the system of evolution equations. Results. The exact solution of the system of evolution equations for the special case of no fluid in the inner shell is found. Numerical modeling has shown that in the absence of fluid in the inner shell, the solitary deformation waves have supersonic velocity. In addition, for the above case, it was found that the strain waves in the shells retain their velocity and amplitude after interaction, i.e., they are solitons. On the other hand, calculations have shown that in the presence of a viscous fluid in the inner shell, attenuation of strain solitons is observed, and their propagation velocity becomes subsonic.

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature.

This paper introduces an innovative approach for modelling unsteady incompressible natural convection flow over an inclined oscillating plate with an inclined magnetic effect that employs the Atangana-Baleanu time-fractional derivative (having a non-singular and non-local kernel) and the Mittag-Leffler function. The fractional model, which includes Fourier and Fick's equations, investigates memory effects and is solved using the Laplace transform. The Mittag-Leffler function captures power-law relaxation dynamics, which improves our understanding of thermal and fluid behaviour. Graphical examination shows the influence of fractional and physically involved parameters, leading to the conclusion that concentration, temperature, and velocity profiles initially grow and then decrease asymptotically with time. Moreover, the study emphasizes the impact of effective Prandtl and Schmidt numbers on temperature, concentration, and velocity levels in the fluid. [ABSTRACT FROM AUTHOR]

Magnetotactic bacteria (MTB) are promising candidates for use as biomicrorobots in biomedical applications due to their motility, self-propulsion, and the ability to direct their navigation with an applied magnetic field. When in the body, the MTB may encounter non-Newtonian fluids such as blood plasma or mucus. However, their motility and the effectiveness of directed navigation in non-Newtonian fluids has yet to be studied on a single-cell level. In this work, we investigate motility of Magnetospirillum magneticum AMB-1 in three concentrations of polyacrylamide (PAM) solution, a mucus-mimicking fluid. The swimming speeds increase from 44.0 ± 13.6 µm/s in 0 mg/mL of PAM to 52.73 ± 15.6 µm/s in 1 mg/mL then decreases to 24.51 ± 11.7 µm/s in 2 mg/mL and 21.23 ± 10.5 µm/s in 3 mg/mL. This trend of a speed increase in low polymer concentrations followed by a decrease in speed as the concentration increases past a threshold concentration is consistent with other studies of motile, flagellated bacteria. Past this threshold concentration of PAM, there is a higher percentage of cells with an overall trajectory angle deviating from the angle of the magnetic field lines. There is also less linearity in the trajectories and an increase in reversals of swimming direction. Altogether, we show that MTB can be directed in polymer concentrations mimicking biological mucus, demonstrating the influence of the medium viscosity on the linearity of their trajectories which alters the effective path that could be predefined in Newtonian fluids when transport is achieved by magnetotaxis. [ABSTRACT FROM AUTHOR]

This paper proves the existence of R$$ \mathcal{R} $$‐bounded solution operator families of the resolvent problem of Navier–Stokes–Korteweg model in half‐space (R+N)$$ \left({\mathbf{R}}_{+}^N\right) $$ with slip boundary condition. Especially we investigate the model for arbitrary constant viscosity and capillarity. We employ the R$$ \mathcal{R} $$‐bounded solution operators of the model obtained from the whole space cases and partial Fourier transform techniques to analyze the model. [ABSTRACT FROM AUTHOR]

This paper studies the motion of charged test particle, moving in the outermost layer of a heterogeneous body (taken as first primary) filled with incompressible homogeneous viscous fluid and second primary is taken as point mass, whereas both the primaries are assumed to be charged. We compute the equations of motion of test particle (the third body) and stationary points (circular, axial and out-of-plane stationary points). And also, the stability of stationary points is examined utilizing characteristics equations and Routh–Hurwitz criterion. In addition to this, the numerical analysis of stationary points and their stability are worked out for different values of parameters. [ABSTRACT FROM AUTHOR]

We propose an approximation for the functional form of the slip length for two complementary lattice configurations of superhydrophobic texture. The first configuration consists of the square lattice of the superhydrophobic spots employed on the no-slip plane. The second configuration is an 'inverse' of the first one and consists of the same lattice but of the no-slip spots on the superhydrophobic base. We validate our analytical results by a numerical solution of Stokes equation. [ABSTRACT FROM AUTHOR]

Purpose: The steady laminar wall jet flow over a stretching/shrinking surface in the presence of lateral suction or injection with a convective boundary condition is considered. Design/methodology/approach: The partial differential equations for mass, momentum and energy conservation are changed to the system of ordinary differential equations through similarity solution transformations. Solutions, both numerical and asymptotic, to these similarity equations are found in some new ranges of parameters in the governing equations. Findings: The equations are solved both asymptotically and numerically for a range of the transpiration parameter S and the flow parameter λ given in Mahros et al. (2023), thus greatly extending the range of these previous solutions. Asymptotic solutions for both large and small values of the Prandtl number σ are derived, showing good agreement with additional numerical integrations. It should be noted that in Mahros et al. (2023), only the case when σ=1 was treated. A solution for large λ when S=1 is obtained, showing a different asymptotic form to the case when S>0 in Mahros et al. (2023). Multiple solutions were seen by them for S<0 and the nature of the lower solution branch as S→0 from below is discussed. The question as to whether the lower branch solutions join as λ>0 when S<0 is resolved through obtaining an asymptotic solution λ small. Originality/value: The accuracy of the solutions has been checked through a detailed comparison between the solutions obtained numerically and analytically, where excellent agreement has been found. This study is important for scientists working in the area of jet flows to become familiar with the flow properties and behaviour of jets. [ABSTRACT FROM AUTHOR]

In this paper, we investigate conformal η-Ricci–Yamabe soliton on semiconformally flat Kählerian Norden spacetime in conjunction with the Kählerian Norden torse-forming vector field. Furthermore, we examine various physical aspects of such soliton on special fluid spacetime, such as dust fluid, dark fluid, radiation era, viscous fluid, and heat flux. In addition, we light up the harmonic features of conformal η-Ricci-Yamabe soliton on semiconformally flat Kählerian Norden spacetime. Finally, we also deduce the necessary and sufficient conditions for a 1-form η, which is the g-dual of the vector field ξ on such a spacetime, to be a solution of the Schrödinger-Ricci equation. [ABSTRACT FROM AUTHOR]

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature. [ABSTRACT FROM AUTHOR]

In this paper, using interfacial slip on the boundary, the exact solution is obtained for the Stokes flow through a couple stress fluid sphere which is embedded (implanted) in a porous medium with Brinkman's condition. Analytical computations are derived for the stream functions and drag. For the drag force, special conditions are deduced that satisfy the literature's facts. Graphs are created and the numerical results are tabulated. It is noticed that in the external viscous fluid case the porosity parameter and the drag coefficient are directly correlated and for the external couple stress fluid case with raises in slip parameter the coefficient of drag reduces. [ABSTRACT FROM AUTHOR]

The possibilities of simulation of viscous incompressible fluid flows with lattice Boltzmann method are considered. Unlike the traditional discretization approach based on the use of Navier–Stokes equations, the lattice Boltzmann method uses a mesoscopic model to simulate incompressible fluid flows. Macroscopic parameters of a fluid, such as density and velocity, are expressed through the moments of the discrete probability distribution function. Discretization of the lattice Boltzmann equation is carried out using schemes D2Q9 (two-dimensional case) and D3Q19 (three-dimensional case). To simulate collisions between pseudo-particles, the Bhatnaga r–Gross–Crooke approximation with one relaxation time is used. The specification of initial and boundary conditions (no penetration and no-slip conditions, outflow conditions, periodic conditions) is discussed. The patterns of formation and development of vortical flows in a square cavity and cubic cavities are computed. The results of calculations of flow characteristics in a square and cubic cavity at various Reynolds numbers are compared with data available in the literature and obtained based on the finite difference method and the finite volume method. The dependence of the numerical solution and location of critical points on faces of cubic cavity on the lattice size is studied. Computational time is compared with performance of fine difference and finite volume methods. The developed implementation of the lattice Boltzmann method is of interest for the transition to further modeling non-isothermal and high-speed compressible flows.

Since the middle of the 20th century, an understanding of the diversity of the natural magnetohydrodynamic phenomena surrounding us has begun to emerge. Magnetohydrodynamic nature manifests itself in such seemingly heterogeneous processes as the flow of water in the world’s oceans, the movements of Earth’s liquid core, the dynamics of the solar magnetosphere and galactic electromagnetic fields. Their close relationship and multifaceted influence on human life are becoming more and more clearly revealed. The study of these phenomena requires the development of theory both fundamental and analytical, unifying a wide range of phenomena, and specialized areas that describe specific processes. The theory of translational fluid motion is well developed, but for most natural phenomena, this condition leads to a rather limited model. The fluid motion in the cavity of a rotating body such that the Coriolis forces are significant has been studied much less. A distinctive feature of the problems under consideration is their significant nonlinearity, (i.e., the absence of a linear approximation that allows one to obtain nontrivial useful results). From this point of view, the studies presented here were selected. This review presents studies on the movements of ideal and viscous fluids without taking into account electromagnetic phenomena (non-conducting, non-magnetic fluid) and while taking them into account (conducting fluid). Much attention is payed to the macroscopic movements of sea water (conducting liquid) located in Earth’s magnetic field, which spawns electric currents and, as a result, an induced magnetic field. Exploring the processes of generating magnetic fields in the moving turbulent flows of conducting fluid in the frame of dynamic systems with distributed parameters allows better understanding of the origin of cosmic magnetic fields (those of planets, stars, and galaxies). Various approaches are presented for rotational and librational movements. In particular, an analytical solution of three-dimensional unsteady magnetohydrodynamic equations for problems in a plane-parallel configuration is presented.

In this paper, we discussed the chemical reaction influences on the radiating MHD convective flow of an incompressible viscous electrically conducting fluid past an exponentially accelerated perpendicular surface under the influences of slip velocity in the revolving structure taking Hall and ion slip impacts into account. A steady homogeneous magnetic field is applied under the presumption of less magnetic Reynolds number. The ramped wall temperature and time altering concentration at the plate is constructing into consideration. First order consistent chemical reaction and heat absorption are also regarded. Laplace transformation technique is engaged on the non-dimensional governing equations for the closed form solutions. Supporting on these results, the phrases for non-dimensional shear stresses and rate of heat and mass transport are also found. The graphical profiles are represented to examine the impacts of physical parameters on the important physical flow features. The computational quantities of the shear stress and rate of heat and mass transportations near the surface are tabulated by a variety of implanted parameters. The resulting velocity is growing by an increase in heat and solutal buoyancy force, while rotation and slip parameters have reverse outcomes on this. The resulting velocity is falling by an increasing in the Hartmann number while the penetrability parameters and Hall and ion slip effects have overturn impacts on this. The temperatures and the thickness of thermal boundary layer decrease on an enhancing heat source parameter for together ramped wall temperature and uniformed wall temperature. The heat absorptions increase the Nusselt number near the surface. [ABSTRACT FROM AUTHOR]

Details of calculation of the critical Reynolds number that separates two different types of agglomeration of bubbles in a viscous fluid are given. [ABSTRACT FROM AUTHOR]

An alternative analytical model is proposed for hydrodynamics of incompressible Newtonian fluids with suspended solid particles. Unlike existing single-phase models that do not distinguish the velocity field of suspended particles from the velocity field of host fluid, the present model accounts for the relative shift between the two velocity fields and assumes that its effect can be largely captured by substituting the inertia term of Navier-Stokes equations with the acceleration field of the mass center of the representative unit cell. The proposed model enjoys a relatively concise mathematical formulation. The oscillating flow of a particle-fluid suspension between two flat plates is studied with the present model, and detailed results are presented for Stokes' second flow problem on the oscillating flow of a suspension half-space induced by an oscillating plate with specific examples of dusty gases and nanofluids. Remarkably, leading-order asymptotic expressions derived by the present model, for the effect of suspended particles on the decay index and wavenumber of the velocity field, are shown to be identical to known results derived based on the widely adopted Saffman model for dusty gases. It is hoped that the present work could offer a relatively simplified and yet reasonably accurate model for hydrodynamic problems of particle-fluid suspensions. [ABSTRACT FROM AUTHOR]

Hydrodynamic flows induced by translational oscillations of cylindrical bodies of various cross-sectional shapes are studied. The motion of fluid around oscillating bodies is described using the system of Navier–Stokes equations written in a generalized curvilinear coordinate system. Transition to a given body shape is implemented using a conformal mapping. The problem is solved using the method of successive asymptotic expansions under the assumption that the oscillation amplitudes are small. In each asymptotic approximation, the subproblems are solved numerically using the finite-difference method. Based on the results of the work, estimates of the hydrodynamic effect are obtained, the applicability of the high-frequency asymptotic approximation is estimated, and secondary stationary flows near cylinders are studied, in particular, the occurrence of directed stationary flows near an oscillating asymmetric body is considered with reference to the Joukowski airfoil. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem on normal oscillations of a system of bodies partially filled with viscous fluids under the action of elastic and damping forces. It is proven that the nonzero spectrum of the problem is discrete and condenses towards zero and infinity. Asymptotic formulae for the eigenvalues are proved. A theorem on the -basicity of the system of root elements of the problem is proven. [ABSTRACT FROM AUTHOR]

This paper investigates the structural changes in the turbulent motion of an incompressible fluid in the hydrodynamic entrance region of plane-parallel pressure motion. Movement in pressure hydromechanical systems usually occurs in a turbulent regime. Studying the patterns of changes in hydrodynamic parameters under conditions of stationary turbulent pressure motion in the inlet region is a very urgent task. The study was carried out on the basis of boundary layer equations. Taking into account the dependence of changes in the kinematic viscosity coefficient that occur between layers of fluid, a boundary value problem was formed. Analytical solutions have been obtained that make it possible to obtain patterns of changes in velocity and pressure in any effective flow section. Based on the general conclusions of the study, solutions were found for two cases: a) the velocity of the fluid entering the cylindrical pipe is constant; b) the velocity of the incoming fluid has a parabolic distribution. For these cases, using computer analysis of the data obtained, general graphs of velocity changes were constructed in various sections along the hydrodynamic entrance region. These graphs, which display the change in velocity along the entire length of the inlet, make it possible to obtain the velocity of fluid movement at any point along the inlet length and estimate the length of the transition zone. The results obtained are among the least studied issues of classical fluid mechanics and are of important theoretical interest. The results obtained are applicable for the correct construction of the hydrodynamic entrance region of machinery. A calculation formula has been obtained to determine the length of the hydrodynamic inlet region. [ABSTRACT FROM AUTHOR]

Fluid migration in a fracture network plays an important role in the oil accumulation mechanism and hence is key to oil exploration. In this study, we build a model by combining one-dimensional (1D) Navier–Stokes equations, linear elastic equations, and energy equations, and validate the model by reproducing the thickness profile of a fluid-driven crack measured in an experiment. We employ this model to simulate the upward flow of viscous fluid in a single fracture during hydrocarbon migration. The simulation suggests that the parameters of both the fluid and the surrounding rock matrix, as well as the boundary condition imposed on the fracture outlet, affect the upward flow in the fracture. We then extend our model from the single fracture to the bifurcated fracture and the fracture network by maintaining homogeneous pressure and mass conservation at the connection of the channels. We find that the increase in network complexity leads to an increase in the inlet pressure gradient and inlet speed, and a decrease in the outlet pressure gradient and outlet speed. The effective area where the fluid is driven upward from the inlet to the outlet is offset toward the inlet. More importantly, the main novelty of our model is that it allows us to evaluate the effect of inconsistencies in individual branch parameters, such as matrix stiffness, permeability, temperature, and boundary conditions, on the overall upward flow of viscous fluid. Our results suggest that the heterogeneity enforces the greater impact on the closer branches. [ABSTRACT FROM AUTHOR]

A case of underground long-term hot water storage is investigated numerically. The study is based on the unsteady two-dimensional Navier-Stokes equations in Boussinesq approximation applied to a closed cavern with time-dependent temperature boundary conditions on the walls. The problem formulated in a vorticity-stream function statement is solved by finite difference method (FDM) for high values of the Rayleigh number and for the Prandtl number of water. Streamlines, velocity and temperature fields are presented graphically for given moments of time. The evolution of the thermocline thickness in the mid-section of the cavern is slow and illustrates that the hot water zone occupies more than the half of the cavern even after 6 months period. The Nusselt number on the walls shows that the convective thermal losses are small and after certain period of time tend to decrease due to the diminished temperature difference at the walls. The influence of the fluid convection on the thermal losses is evaluated quantitatively, showing high seasonal thermal efficiency of the insulated hot water storage. [ABSTRACT FROM AUTHOR]

Since the middle of the 20th century, an understanding of the diversity of the natural magnetohydrodynamic phenomena surrounding us has begun to emerge. Magnetohydrodynamic nature manifests itself in such seemingly heterogeneous processes as the flow of water in the world's oceans, the movements of Earth's liquid core, the dynamics of the solar magnetosphere and galactic electromagnetic fields. Their close relationship and multifaceted influence on human life are becoming more and more clearly revealed. The study of these phenomena requires the development of theory both fundamental and analytical, unifying a wide range of phenomena, and specialized areas that describe specific processes. The theory of translational fluid motion is well developed, but for most natural phenomena, this condition leads to a rather limited model. The fluid motion in the cavity of a rotating body such that the Coriolis forces are significant has been studied much less. A distinctive feature of the problems under consideration is their significant nonlinearity, (i.e., the absence of a linear approximation that allows one to obtain nontrivial useful results). From this point of view, the studies presented here were selected. This review presents studies on the movements of ideal and viscous fluids without taking into account electromagnetic phenomena (non-conducting, non-magnetic fluid) and while taking them into account (conducting fluid). Much attention is payed to the macroscopic movements of sea water (conducting liquid) located in Earth's magnetic field, which spawns electric currents and, as a result, an induced magnetic field. Exploring the processes of generating magnetic fields in the moving turbulent flows of conducting fluid in the frame of dynamic systems with distributed parameters allows better understanding of the origin of cosmic magnetic fields (those of planets, stars, and galaxies). Various approaches are presented for rotational and librational movements. In particular, an analytical solution of three-dimensional unsteady magnetohydrodynamic equations for problems in a plane-parallel configuration is presented. [ABSTRACT FROM AUTHOR]

IN THIS PAPER, STOKES FLOW PAST A CONTAMINATED FLUID SPHERE embedded in a porous medium is considered using interfacial slip on the boundary. The stream functions and drag are computed analytically. Special cases are deduced for drag force and a satisfactory agreement is reached with available data in the literature. It was observed that in viscous fluid and couple stress fluid cases with an increase in the viscosity ratio, the slip parameter, the porous parameter there is an increase in the values of the drag coefficient for varying different parameters, respectively. Also noticed that coefficient of drag values for a uniform flow of the viscous fluid flow over a contaminated viscous fluid sphere in a porous medium with the slip condition are superior to those of a couple stress fluid (CSF) flow. [ABSTRACT FROM AUTHOR]

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes (CNTs) are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems. Therefore, the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscous fluid and supported on a nonlinear elastic foundation. The proposed model is based on nonlocal Euler–Bernoulli beam theory. The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation, respectively. A detailed parametric study is reported into how the nonlocal parameter, foundation coefficients, fluid viscosity, and amplitude and frequency of the external force influence the nonlinear dynamics of the system. Subharmonic, quasi-periodic, and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories, frequency-response curves, bifurcation diagrams, phase portraits, power spectra, and Poincaré maps. Also, the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters. ARTICLE HIGHLIGHTS: HIGHLIGHTS • A nonlocal model of an embedded CNT conveying viscous fluid is developed. • The simply supported CNT is subjected to an external harmonic force. • The amplitude of the external harmonic force is used as the bifurcation parameter. • The effects of key parameters on the bifurcation behavior of the CNT are studied. • Bifurcation behaviors of the CNT and routes to chaos are detected. [ABSTRACT FROM AUTHOR]

Background: Extensive numerical calculations are usually requested with existing models for acoustic waves in fiber-filled viscous fluids and different models often give different results for attenuation and phase velocity even with considerable relative errors. Objective: Develop a novel (two-dimensional) acoustic model for acoustic wave propagation of unidirectional fiber-filled composite viscous fluids with conceptual and mathematical simplicity and reasonable accuracy. Methodology and Novelty: The novelty of the present model is presented by the idea to modify classical acoustic equations by substituting the inertia term with the acceleration field of the mass centre of the representative unit cell, supplied with a derived simple differential relation between the mass centre's velocity field and the velocity field of fiber-filled composite viscous fluid. Results: Under the widely adopted long-wavelength assumption, explicit formulas are obtained for attenuation coefficient and effective phase velocity of compression waves and shear waves, and efficiency and accuracy of the present model are demonstrated by good agreement between predicted results and recent known data on unidirectional fiber-filled viscous fluids. Conclusion: The proposed model offers a relatively simple method and easy-to-use formulas to study acoustic waves in a viscous fluid filled with randomly distributed unidirectional solid fibers. [ABSTRACT FROM AUTHOR]

Magnetotactic bacteria (MTB) are promising candidates for use as biomicrorobots in biomedical applications due to their motility, self-propulsion, and the ability to direct their navigation with an applied magnetic field. When in the body, the MTB may encounter non-Newtonian fluids such as blood plasma or mucus. However, their motility and the effectiveness of directed navigation in non-Newtonian fluids has yet to be studied on a single-cell level. In this work, we investigate motility of Magnetospirillum magneticum AMB-1 in three concentrations of polyacrylamide (PAM) solution, a mucus-mimicking fluid. The swimming speeds increase from 44.0 ± 13.6 μm/s in 0 mg/mL of PAM to 52.73 ± 15.6 μm/s in 1 mg/mL then decreases to 24.51 ± 11.7 μm/s in 2 mg/mL and 21.23 ± 10.5 μm/s in 3 mg/mL. This trend of a speed increase in low polymer concentrations followed by a decrease in speed as the concentration increases past a threshold concentration is consistent with other studies of motile, flagellated bacteria. Past this threshold concentration of PAM, there is a higher percentage of cells with an overall trajectory angle deviating from the angle of the magnetic field lines. There is also less linearity in the trajectories and an increase in reversals of swimming direction. Altogether, we show that MTB can be directed in polymer concentrations mimicking biological mucus, demonstrating the influence of the medium viscosity on the linearity of their trajectories which alters the effective path that could be predefined in Newtonian fluids when transport is achieved by magnetotaxis.

Strong impact does serious harm to the military industries so it is necessary to choose reasonable cushioning material and design effective buffers to prevent the impact of equipment. Based on the capillary property entangled porous metallic wire materials (EPMWM), this paper designed a composite buffer which uses EPMWM and viscous fluid as cushioning materials under the low-speed impact of the recoil force device of weapon equipment (such as artillery, mortar, etc.). Combined with the capillary model, porosity, hydraulic diameter, maximum pore diameter and pore distribution were used to characterize the pore structure characteristics of EPMWM. The calculation model of the damping force of the composite buffer was established. The low-speed impact test of the composite buffer was conducted. The parameters of the buffer under low-speed impact were identified according to the model, and the nonlinear model of damping force was obtained. The test results show that the composite buffer with EPMWM and viscous fluid can absorb the impact energy from the recoil movement effectively, and provide a new method for the buffer design of weapon equipment (such as artillery, mortar, etc.).

Nonclassical problems in mathematical hydrodynamics arise when studying the motion of rheologically complex media, as well as under boundary conditions different from classical ones. In this paper, existence and uniqueness theorems are established for the classical solution to the problem of a stationary boundary layer of a liquid with the rheological law of Ladyzhenskaya near a solid wall with given conditions characterizing the force of surface tension and the phenomenon of slipping near this wall. [ABSTRACT FROM AUTHOR]

AbstractThis article explores the influence of joule heating and viscous dissipation on the unsteady three-dimensional squeezing flow of Newtonian fluid. The Squeezing flow refers to the fluid flow through a constriction or a narrow opening. The fluid with some external/internal forces compelled to pass through the constriction which results a change in fluid velocity and a decrease in pressure. It can occur in various natural and man-made systems such as rivers flowing through canyons or fluids flowing through pipes or valves. The Pumping of heart, Synovial fluid in the knee joints, and Blood flow in vein and arteries are also include in the physical domain of squeezing flow. Keeping in view these applications, the goals of this article is to explore the viscous fluid flow behavior in a three dimensional system between two rotating plates that are being vertically squeezed together. The flow in a rotating channel with a lower stretched permeable wall is observed under the influence of a uniform magnetic field. The thermal radiation influence is also considered. The mass and heat transfer effect is investigated for Newtonian fluids in a squeezing phenomenon and the mathematical equations are modeled using the four fundamental governing equations of fluid flow, that is, the mass equation, momentum equation, concentration equation, and energy equation. By introducing the suitable transformations (similarity), the modeled highly non-linear partial differential equations are transformed to ordinary differential equations. The solution methodology is developed using the homotopy analysis method though which we obtained the series solution. The influence of several physical parameters including the squeezing parameter, the suction parameter, the magnetic number, the rotation parameter, the Eckert number, the Prandtl number, the Dufour number, the Soret number, the radiation parameter, and the Schmidt number on the velocity profile, energy, and concentration are also discussed with the help of graphs. Additionally, it is observed that enhancing the top plate’s squeezing impact causes a rise in the velocity profile while lowering the temperature and concentration distribution. It is also obtained that for the velocity field, increasing the magnetic number shows a decrease in the value of the velocity field along the y- and z axes, whereas the velocity field along the x-axes exhibits dual behavior, such that it initially falls as the magnetic number intensifies but starts to rise in the upper region of the channel. The impact of the Dufour, Soret, and Eckert numbers on temperature and concentration distribution is also studied. It is found that while these numbers directly affect the temperature distribution, the mass distribution follows the opposite trend. Also, it is noticed that the thermal radiation parameter is an increasing function of temperature and mass distribution. [ABSTRACT FROM AUTHOR]

In this paper, we study obliquely propagating of small amplitude ion acoustic waves (IAWs) in non-relativistic cold plasma in which the ions are viscous fluid, electrons distribution is Maxwellian and external magnetic field varies in space. Using the reductive perturbation method, a nonlinear equation which complies with Korteweg–de Vries–Burgers (KdVB) equation is derived for this model. It is shown that a new effective dissipative which depends on the ion kinematic viscosity and varying in the magnetic field is appeared in the plasma. We show that the complete set of equations, by considering the varying magnetic field and viscosity effect, create IA waves which radiate energy as oscillatory shock wave during their travelling in the medium. [ABSTRACT FROM AUTHOR]

In this work, the authors examine the dynamics of viscous Universe in the Sáez–Ballester theory of gravity. The solutions of the Friedmann–Robertson–Walker field equations have been derived within the framework of full causal theories presented by Israel and Stewart using simple parametrization of scale factor a(t), i.e., power law relation a(t) = a0tα and exponential law a(t) = b0eβt. The power law cosmological model shows that the Universe transitioned from early cosmic deceleration to the present cosmic acceleration, and the exponential cosmological model shows the accelerated expansion of the Universe. It has been discovered that as time passes, energy density and viscosity decrease while temperature rises. Energy conditions are also investigated in which the strong energy condition is violated. The behaviour of the cosmological parameters such as the Hubble parameter, energy density, pressure, coefficient of viscosity, and state-finder parameter has been presented graphically. [ABSTRACT FROM AUTHOR]

This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are useful for describing viscous fluid motion in long pipes, thus considering geometric parameters like pipe diameter and characteristic length. This study provides a representation for the vorticity vector and energy dissipation in the flow problem for a curved channel, thereby determining the magnitude of vorticity and energy dissipation depending on the channel's central line curvature and torsion. The accuracy of the asymptotic formulas are estimated in terms of small parameter powers. Numerical calculations for helical tubes demonstrate the effectiveness of the asymptotic formulas. [ABSTRACT FROM AUTHOR]

The work is a survey of the author's results with modifications and preliminary information on the use of stochastic analysis on Sobolev groups of diffeomorphisms of a flat n-dimensional torus to describe the motion of viscous fluids (nonrandom ones). The main idea is to replace the covariant derivatives on the groups of diffeomorphisms in the equations introduced by Ebin and Marsden to describe ideal fluids by the so-called mean derivatives of random processes. [ABSTRACT FROM AUTHOR]

This paper focuses on studying structural changes in the viscous fluid during turbulent unsteady plane-parallel pressure flow. This investigation analyzes how hydrodynamic parameters change in viscous fluid unsteady motion, particularly by calculating the turbulent viscosity coefficient. The study addresses the boundary problem that arises when there are axisymmetric changes in the flow. The selection of boundary conditions aligns with the patterns associated with the arbitrary distribution of pressure gradients and velocities within the section. Based on the initial and boundary conditions, the boundary value problem is formulated. The method for solving this boundary value problem was developed, and the regularities of the instantaneous speed change along the cross-section were obtained. The solution to the boundary value problem is derived by integrating partial differential equations, ensuring the satisfaction of all boundary conditions. Analytical solutions have been derived, enabling the determination of velocity patterns at any given moment. On the basis of the general solutions to the problem, solutions were obtained for the accelerating motion under the influence of a constant pressure gradient on a fluid at rest. The computer analysis generated composite graphs displaying average velocities across various time intervals. The provided solutions enable the visualization of average velocity changes within conditions of plane-parallel turbulent flow. These findings allow for the conclusion of the design of individual units within hydro-mechanical equipment. [ABSTRACT FROM AUTHOR]

AbstractMany scientific and technological disciplines in the specialization of chemical and petroleum sectors are related to multilayer fluid flow systems. In light of this perspective, the current article focuses on the steady, laminar flow of mono nanofluid saturated with porous media sandwiched between a viscous fluid filled in a vertical channel to develop a new model. The main subject of this scientifical research is to explore the prediction analysis through machine learning algorithm for the physical quantities across the entire region of the proposed fluid. This present physical phenomenon is witnessed in the mathematical form of nonlinear PDEs through the conservation principles and Darcy’s law. The system of governing PDEs are nondimensionalized by treating the suitable fundamental variables to facilitate the simulation process. After that, the dimension-free form of momentum and temperature equations is numerically simulated by utilizing the Wolfram language algorithm. In addition, the comparison analysis is accounted to find the higher heat transfer performance for the particles Ag, MgO, and Fe3O4. After ensuring the numerical computation for the specific flow scenarios, an innovative machine learning-based multiple linear regression technique is employed to anticipate the flow and heat transfer rate for the inclusion of Ag nanoparticle. The validation of the present study is highlighted by comparing with the existing literature. The current findings exhibit that the region of single-phase nanosized particles suspended in water affects the momentum and thermal behavior of the clear viscous fluid regions. Silver Ag nanosized particles exhibit better performance in heat transfer than the MgO and Fe3O4. Also, the MLR approach offers a new viewpoint on flow control with higher accuracy 99.59% and lower error 10−2. The outcomes of the suggested techniques enrich the application of the multilayer fluid flow model, specifically fire suppression systems, petroleum sectors, agricultural sprays, and oil recovery. [ABSTRACT FROM AUTHOR]

This article explores the influence of variable viscosity on the peristaltic movement of viscous fluid through a tapered microfluidic vessel having sinusoidal walls. The aspect of slip velocity has been considered on the channel walls. Furthermore, the heat transfer phenomenon is explored under the effectiveness of thermal radiation and viscous dissipation. The nonlinearity of the problem is scrutinized by the lubrication approximation hypothesis. Analytic outcomes have been acquired for liquid velocity, temperature, pressure rise, and streamlines. The impact of dissimilar physical parameters influencing the liquid flow features is revealed and deliberated through graphs. The study revealed that the velocity at the central region diminishes with increasing values of the velocity slip parameter. The number of boluses in the streamlines pattern is enhanced by enhancing the viscosity parameter. The current model has been used in bio‐engineering processes, industrial fluid mechanics, thermal processing, and cooling systems. [ABSTRACT FROM AUTHOR]

This paper focuses on studying structural changes in the viscous fluid during turbulent unsteady plane-parallel pressure flow. This investigation analyzes how hydrodynamic parameters change in viscous fluid unsteady motion, particularly by calculating the turbulent viscosity coefficient. The study addresses the boundary problem that arises when there are axisymmetric changes in the flow. The selection of boundary conditions aligns with the patterns associated with the arbitrary distribution of pressure gradients and velocities within the section. Based on the initial and boundary conditions, the boundary value problem is formulated. The method for solving this boundary value problem was developed, and the regularities of the instantaneous speed change along the cross-section were obtained. The solution to the boundary value problem is derived by integrating partial differential equations, ensuring the satisfaction of all boundary conditions. Analytical solutions have been derived, enabling the determination of velocity patterns at any given moment. On the basis of the general solutions to the problem, solutions were obtained for the accelerating motion under the influence of a constant pressure gradient on a fluid at rest. The computer analysis generated composite graphs displaying average velocities across various time intervals. The provided solutions enable the visualization of average velocity changes within conditions of plane-parallel turbulent flow. These findings allow for the conclusion of the design of individual units within hydro-mechanical equipment.