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This analysis deals the steady and the incompressible MHD fluid flow by sinusoidal walls of a hexagonal cavity with a cylindrical obstacle at the center. Finite element method (FEM), a numerical modeling method is used to examine the heat transfer and fluid flow controlled by the energy equation, the continuity equation and Navier-Stokes equations, which are converted to dimensionless form through suitable parameterization, which are tackled by finite element method. The temperature distribution and velocity fields are displayed for various parameters which are Richardson number, Hartmann number, Reynolds number, velocities’ amplitudes ratio, temperatures’ amplitudes ratio and phase deviation. This graphical study shows good convergent results of temperature and velocity for variation of involved parameters. At the end, the significant effects of the heat transfer rate are discussed in terms of the Nusselt number.

In this study, a numerical solution of the velocity and heat transfer on the magnetohydrodynamic suction–injection model of viscous fluid flow has been studied. We use the differential transformation method and Bernoulli wavelet method to solve the highly nonlinear governing equations; applying appropriate similarity transformations and reducing governing equations to highly nonlinear coupled ordinary differential equations. The objective of this analysis is to determine how the suction parameter, Hartmann number, squeeze number, thermophoresis parameter, and Prandtl number affect the velocity and temperature profiles. When the current findings are compared with those that have already been published in the literature, confident suppositions are made, and it is discovered that there is considerable agreement. Graphs have been used to discuss the influence of nondimensional characteristics on velocity and temperature. [ABSTRACT FROM AUTHOR]

In this paper, we reconstruct an f(T) function from ΛCDM model and obtained field equations for this function f(T) = T 2 + c1(−T)1 2 − 2Λ in a flat FLRW viscous-fluid dusty universe, where T is the torsion scalar, c1 is an arbitrary constant and Λ is the cosmological constant. We have solved the field equations and obtained an scale factor a(t) = c2sinh 2Λ 9(1−ξ0)2 t + c1Λ 3(1−ξ0)3(1−ξ0) 2,ξ0≠1 with c2 as an integrating constant and ξ0 is an arbitrary constant generated from viscous fluid, and this type of scale factor gives a time-dependent deceleration parameter. We have made observational constraints on Hubble parameter H(z) and apparent magnitude m(z) with observational datasets H(z) data and SNe Ia data by applying χ2-test, to obtain the best-fit values of model parameters. Using these values of cosmological parameters, we have discussed our model results. We have obtained a transit phase accelerating quintessence dark energy model in viscous-fluid universe with effective equation of state ( − 1.65 ≤ ωeff ≤−0.79). [ABSTRACT FROM AUTHOR]

This paper depicts the fully developed natural convective flow on a conducting viscous fluid towards a nonlinearly stretching sheet. Furthermore, the porous dissipation, thermal radiation and heating parameter effects are implemented on both the vertical walls of the stretchy channel. To model the stretchy flow equations, the Cartesian coordinates' system is utilized. Through the utilization of similarity variables, the nonlinear partial differential equations that describe the flow (mass, momentum and energy conservation) are converted into nonlinear ordinary differential equations. With the help of the MAPLE, a well-known fourth-order Runge–Kutta procedure is used to do a numerical evaluation of the stated nonlinear and non-dimensional set of equations. For each of the several nonlinear radiative parameters regulating the flow regime, the velocity and temperature distribution functions are determined, viz the nonlinear heating parameter θ R , Eckert number E c , Prandtl number Pr , porosity variable P m and thermal radiation parameter N R . Graphic representations are provided for every outcome. Furthermore, skin friction and Nusselt number are also computed to give an approximation of the surface shear stress and cooling rate, respectively. A remarkable compaction is obtained between computed numerical data and published results. It has been demonstrated that an increase in the value of the nonlinear parameter P m outcomes creates a reduction in the dimensionless translational velocity g ′ of both viscous and Newtonian fluids. Dimensionless temperature mostly upsurges with growth in nonlinear parameters E c , P m , θ R and decreases with an intensification in convective parameters, Pr , N R . There is a detailed discussion on the implications of all embedded stretching sheet variables on the flow. The flow regime is extremely useful in the technology of polymer processing as well as in the field of materials science. [ABSTRACT FROM AUTHOR]

We investigate in this work the inflationary scenario in viscous f(R,T) gravity formalism with mimetic potential and Lagrange multiplier. Considering that our universe contains beside a perfect fluid, a dark energy and a bulk viscous fluid, we obtain through the modified Friedmann equations a main differential equation that may describe the cosmological evolution in viscous mimetic f(R,T) gravity. For particular choice of the model f(R,T) = R + αR2 + βTγ and for two forms of bulk viscosity coefficient, one as function of the Hubbe parameter H(t) and the other, as density-dependent viscosity, we present a numerical results of the inflationary parameters such as the tensor-to-scalar ratio r and the scalar spectral index ns. A comparison of these results with observational data shows that our model can be used to describe the accelerated expansion of the universe. [ABSTRACT FROM AUTHOR]

We investigate in this work, the inflationary scenario in viscous f(R, T) gravity formalism with mimetic potential and Lagrange multiplier. Considering that our universe contains beside a perfect fluid, a dark energy and a bulk viscous fluid, we obtain through the modified Friedmann equations a main differential equation that may describe the cosmological evolution in viscous mimetic f(R, T) gravity. For particular choice of the model f (R , T) = R + α R 2 + β T γ and for two forms of bulk viscosity coefficient, one as function of the Hubbe parameter H(t) and the other, as density dependent viscosity, we present a numerical results of the inflationary parameters such as the tensor-to-scalar ratio r and the scalar spectral index n s . A comparison of these results with observational data shows that our model can be used to describe the accelerated expansion of the universe. [ABSTRACT FROM AUTHOR]

Purpose of this paper is to study the evolution of longitudinal strain waves in the walls of an annular channel filled with a viscous incompressible fluid. The walls of the channel were represented as coaxial shells with fractional physical nonlinearity. The viscosity of the fluid and its influence on the wave process was taken into account within the study. Metods. The system of two evolutionary equations, which are generalized Schamel equations, was obtained by the two-scale asymptotic expansion method. The fractional nonlinearity of the channel wall material leads to the necessity to use a computational experiment to study the wave dynamics in them. The computational experiment was conducted based on obtaining new difference schemes for the governing equations. These schemes are analogous to the Crank–Nicholson scheme for modeling heat propagation. Results. Numerical simulation showed that over time, the velocity and amplitude of the deformation waves remain unchanged, and the wave propagation direction concurs with the positive direction of the longitudinal axis. The latter specifies that the velocity of the waves is supersonic. For a particular case, the coincidence of the computational experiment with the exact solution is shown. This substantiates the adequacy of the proposed difference scheme for the generalized Schamel equations. In addition, it was shown that solitary deformation waves in the channel walls are solitons.

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.

The generalized Langevin equation (GLE) for a Brownian particle (BP) in a bath under the influence of a moving external harmonic potential is derived. It is assumed that the friction coefficients of the bath particles depend on time. The found GLE has the usual form but its memory kernel is a generalization of the expression known as a Prony series used to approximate a number of memory functions from the literature. Analytical solutions are obtained for the mean and mean squared displacements assuming the overdamped character of motion of the BP.

The results of a theoretical study on Benjamin–Ono (BO) soliton evolution are presented in a simple model of a two-layer ocean with a shear flow and viscosity. The upper layer is assumed to move with a constant speed relative to the lower layer with a tangential discontinuity in the flow profile. It is shown that in the long-wave approximation, such a model can be appropriate. If the flow is supercritical, i.e., its speed (U) exceeds the speed of long linear waves ( c 1 ), then BO solitons experience "explosive-type" enhancement due to viscosity, such that their amplitudes increase to infinity in a finite time. In the subcritical regime, when U < c 1 , BO solitons experience very slow decay due to viscosity. Soliton amplitude decays with time as A ∼ t − 1 / 2 or A ∼ t − 1 / 3 , depending on whether both layers are weakly viscous (the former case) or only the lower layer is viscous (the latter case). Estimates of "explosion time" are presented for real oceanic parameters. [ABSTRACT FROM AUTHOR]

The dynamics of spherical and cylindrical bodies in the vicinity of the cylindrical wall of the cavity filled with fluid under rotational oscillations is experimentally studied. We consider (i) the motion of a light spherical body inside a cylinder under rotational oscillations and (ii) the motion of the heavy cylindrical body in a horizontal cavity under modulated rotation. In the absence of the oscillations, the bodies are pressed against the cavity walls due to the action of (i) the buoyant force and (ii) the centrifugal force. The tangential and rotational body oscillations are studied by means of video registration. It is found that the body oscillations induce the averaged lift force that is responsible for the detachment of the body from the wall at the critical value of the amplitude of the body oscillations. The oscillation-induced repulsive force is measured by the method of the body suspension in a static field of (i) gravitational force or (ii) centrifugal force. It is found that the dimensionless lift force decreases with the distance from the wall according to the exponential law. The magnitude of the lift force is determined only by the amplitude of the velocity of the tangential body oscillation relative to the surrounding fluid while the intensity of the rotational body oscillations is of no importance. Also, the lift force does not depend on the distance to the wall and increases with the dimensionless frequency ω in the studied range ω = 10 – 90. The phenomenon of the oscillation-induced repulsion of the solid from the cavity wall is of interest for the development of an effective method for the control of multiphase media under microgravity conditions. [ABSTRACT FROM AUTHOR]

Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of incompressible fluids is nowadays available not only for Navier–Stokes fluids but also for various fluid models where the relation between the Cauchy stress tensor and the symmetric part of the velocity gradient is nonlinear. The majority of such studies however concerns models where such a dependence is explicit (the stress is a function of the velocity gradient), which makes the class of studied models unduly restrictive. The same concerns boundary conditions, or more precisely the slipping mechanisms on the boundary, where the no-slip is still the most preferred condition considered in the literature. Our main objective is to develop a robust mathematical theory for unsteady internal flows of implicitly constituted incompressible fluids with implicit relations between the tangential projections of the velocity and the normal traction on the boundary. The theory covers numerous rheological models used in chemistry, biorheology, polymer and food industry as well as in geomechanics. It also includes, as special cases, nonlinear slip as well as stick–slip boundary conditions. Unlike earlier studies, the conditions characterizing admissible classes of constitutive equations are expressed by means of tools of elementary calculus. In addition, a fully constructive proof (approximation scheme) is incorporated. Finally, we focus on the question of uniqueness of such weak solutions. [ABSTRACT FROM AUTHOR]

This investigation aims to explain the study of heat transfer and entropy generation of Magnetohydrodynamics (MHD) viscous fluid flowing through a ciliated tube. Heat transfer study has massive importance in various biomedical and biological industry problems. The metachronal wave propagation is the leading cause behind this viscous creeping flow. A low Reynolds number is used as the inertial forces are weaker than viscous forces, and also, creeping flow limitations are fulfilled. For the cilia movement, a very large wavelength of a metachronal wave is taken into account. Entropy generation is used to examine the heat transfer through the flow. Numerical solutions are calculated by using MATHEMATICA. Exact mathematical solutions are calculated and analyzed with the help of graphs. Streamlines are also plotted. An axially symmetric flow as well as temperature profile is revealed through the graphical solutions. Both velocity and temperature profiles attain maximum value in the center of this ciliated tube that eventually declines toward the boundaries. [ABSTRACT FROM AUTHOR]

Directed motion of a sphere immersed in a viscous fluid and subjected solely to a nonlinear drag force and zero-average biharmonic forces is studied in the absence of any periodic substrate potential. We consider the case of two mutually perpendicular sinusoidal forces of periods T and T/2, respectively, which cannot yield any ratchet effect when acting separately, while inducing directed motion by acting simultaneously. Remarkably and unexpectedly, the dependence on the relative amplitude of the two sinusoidal forces of the average terminal velocity is theoretically explained from the theory of ratchet universality, while extensive numerical simulations confirmed its predictions in the adiabatic limit. Additionally, the dependence on the dimensionless driving frequency of the dimensionless average terminal velocity far from the adiabatic limit is qualitatively explained with the aid of the vibrational mechanics approach. [ABSTRACT FROM AUTHOR]

A model of the transport of magnetic particles by a uniform magnetic field in a nonuniformly heated nonmagnetic liquid is proposed. The mechanism of transfer is based on taking into account the collective perturbation of the distribution of temperature and of the magnetic field strength by nonuniformly heated particles in the surrounding liquid. The change in the magnetic permeability of particles with temperature is taken into account. The interaction of particles leads to the appearance of a thermomagnetic force acting on particles in an external uniform magnetic field. The direction of movement of particles under the action of such a force depends on the mutual orientation of the vectors of the magnetic field strength and temperature gradient and can be either in the direction of an increasing or a decreasing temperature. The speed and magnitude of particle displacement in these cases are different, which means the anisotropy of the thermomagnetophoresis coefficient. The results obtained agree with the experimental data. [ABSTRACT FROM AUTHOR]

Accurate prediction of the dynamic behavior of coupled shafts in a fluid medium is crucial to accurately estimate equipment life and enable safe operation. However, this task is far from trivial due to the vibrations induced by the highly nonlinear nature of the machine system. This paper presents an experimental analysis of a cardan shaft under the influence of viscous hydrodynamic forces. An experimental setup was created using a cardan shaft rig installed in a plexiglas tank, with a self-aligned crack simulator supporting the driveshaft for crack extraction. Adequate instrumentation was used to measure the rotor's fluctuation under industrial viscous fluid at various motor speeds. By analyzing the changes of unwanted high vibration, the obtained results demonstrated that the characteristics of the cracks in the fluid medium can be efficiently extracted from multiple tests using the wavelet synchrosqueezing transform and energy spectrum. This latter aspect, in particular, implies that the responses that can be observed in practice are highly sensitive to the values of the system parameters: average flow velocity, mass eccentricity, and shaft stiffness, among others. Finally, the study provides conclusions on practical applications for the reliable identification of cracks in a viscous fluid to validate the recently published theoretical study. [ABSTRACT FROM AUTHOR]

The objective of current communication is to study heat transfer phenomenon for slip flow of viscous fluid due to wavy channel with general cosine function boundaries and fixed amplitude. The walls along with slip boundary constraints are kept at different temperatures. The flow is incompressible and Newtonian with AIS as a predicting material being used to check the fluids and thermal properties. The Navier–Stokes expressions with 2D flow regime subject to heat transfer due to convection are used to develop the simulations. A parametric theoretical assumptions analysis is performed for specified range of Reynolds number (100–1000) with upper and lower surface vibration periods of 1 to 6. The results are displayed with graphs, surface and contours plots and first, ever a novel work was done to represent the percentage change in velocity magnitude and local Nusselt number as surface plots and contours, respectively. The results are authentic due to mesh independent study and verification with the experimental correlation. A periodic flow at the lower wall was deducted. The maximum and average rotation rates attain a linear relationship with Reynolds number and their correlation was found. The simulations show the strict relationship of Reynolds number and the geometry of the channel with shear rate. The pressure gradient in y -direction was found minimum in trough and maximum in the crest region. It has been observed that the boundary friction is reduced due to periodic variation of walls surface. [ABSTRACT FROM AUTHOR]

An effective boundary condition on a porous wall is derived, starting from basic principles of mechanics. Stokes system, governing the viscous flow through a reservoir with an array of small pores on the boundary, was studied, and the corresponding macroscopic model via rigorous asymptotic analysis is found. Under the assumption of periodicity of the pores, the effective boundary condition of the Darcy type is derived, using homogenization and boundary layer techniques. Further asymptotic analysis with respect to the porosity yields a recursive sequence of boundary value problems showing that the large pressure jump occurs on the boundary. [ABSTRACT FROM AUTHOR]

In current paper, we have elaborated the mathematical results found by exact solutions for electro-osmotic and thermal effects in the ciliary-oriented flow pattern of a viscous fluid through an elliptical duct connected with an external battery. The model for heat transfer is also presented to investigate temperature distribution during the procedure of flow period. The governing equations have been derived by incorporating electric double layer effects through Boltzmann relation. By following wave frame and dimensionless phenomena, the governing equations have been transformed into more concise form under the light of lubrication approach. A series solution (fourth degree polynomial) technique is employed to obtain the exact solutions. Effects of various parameters are discussed simultaneously through graphical aspect. From the detailed discussion, it is noted that eccentricity of the elliptical shape and the electro-kinetic energy are responsible for the enhancement in the flow attributes and thermal distribution but Helmholtz velocity factor causes a reduction there. Such studies can be useful in industrial and medical field where an elliptical conduit is designed for the electrically conducting thermal flow. [ABSTRACT FROM AUTHOR]

We present the theoretical description of plane Couette flow based on the previously proposed equations of vortex fluid, which take into account both the longitudinal flow and the vortex tubes rotation. It is shown that the considered equations have several stationary solutions describing different types of laminar flow. We also discuss the simple model of turbulent flow consisting of vortex tubes, which are moving chaotically and simultaneously rotating with different phases. Using the Boussinesq approximation, we obtain an analytical expression for the stationary profile of mean velocity in turbulent Couette flow, which is in good agreement with experimental data and results of direct numerical simulations. Our model demonstrates that near-wall turbulence can be described by a coordinates-independent coefficient of eddy viscosity. In contrast to the viscosity of the fluid itself, this parameter characterizes the turbulent flow and depends on Reynolds number and roughness of the channel walls. Potentially, the proposed model can be considered as a theoretical basis for the experimental measurement of the eddy viscosity coefficient. [ABSTRACT FROM AUTHOR]

The buckling of a nanoplate at the bottom of a channel over which the fluid passes with a one‐dimensional flow is investigated in this article. Navier–Stokes equations were used to obtain the applied force from the fluid to the nanoplate. Non‐local elasticity theories and surface effects were used to consider nanoscale effects. By solving this problem using Galerkin's weighted residual method, interesting results were obtained. Applying non‐locality increases the fluid's impact on the buckling of a nanoplate. The lower modes are more noticeably affected by being placed in a fluid environment. Also, the presence of fluid and surface effects both increase the buckling capacity of the system. The obtained results are very helpful for developing and improving the performance of fluid‐coupled nanostructures that have buckling potential. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann method (LBM) is employed in the current work to simulate two-phase flows of immiscible fluids over a square obstacle in a 2D computational domain using the Rothman-Keller color gradient model. This model is based on the multiphase Rothman-Keller description, it is used to separate two fluids in flow and to assess its efficacy when treating two fluids in flow over a square obstacle with the objective of reducing turbulence by adjusting the viscosities of the two fluids. This turbulence can cause major problems such as interface tracking techniques in gas-liquid flow and upward or downward co-current flows in pipes. So, the purpose of the study is to replace a single fluid with two fluids of different viscosities by varying these viscosities in order to reduce or completely eliminate the turbulence. The results show that to have stable, parallel and non-overlapping flows behind the obstacle, it is necessary that the difference between the viscosities of the fluids be significant. Also, showing that the increase in the viscosity ratio decreases the time corresponding to the disappearance of the vortices behind the obstacle. The results presented in this work have some general conclusions: For M≥2, the increase in the viscosity difference leads to an increasing of friction between fluids, reducing of average velocity of flow and decreasing the time corresponding to the disappearance of the vortices behind the obstacle. However, for M≤1/2, the opposite occurs.

Although several methods are known to calculate pump performance with highly viscous and non-Newtonian fluids, research has not yet determined all the key parameters of these predictions. It is unclear how these parameters depend on the pump geometry and the delivered fluid rheology, which can vary widely in the chemical industry. In our study, the performance curves of a radial centrifugal pump with a viscous Newtonian glycerol solution and a non-Newtonian power-law fluid were experimentally compared. The head degradation of the pump was also presumed with the ANSI/HI and the Ofuchi methods, which are evident and commonly used for viscous Newtonian fluids, but not for non-Newtonians. The required constants were estimated based on experimental data for both models, and the Ofuchi method was adapted to power-law fluid. Based on our results, the Ofuchi method proved to apply for head degradation prediction with the examined power-law fluid.

In this paper, we investigate the linearized two-dimensional problem on small motions of a system of rigid bodies partially filled with viscous incompressible fluids and connected in series by springs. The first and last bodies are attached by springs to two supports with a given law of motion. The trajectory of the system is perpendicular to the direction of gravity, and the damping forces acting on the hydrodynamical system are generated by the friction of bodies against a stationary horizontal support. For the described system, the law of total energy balance is formulated. Using the orthogonal projection method and a number of auxiliary boundary problems, the original initial-boundary value problem is reduced to the Cauchy problem for a first-order differential-operator equation in the orthogonal sum of some Hilbert spaces. The properties of operator matrices, which are coefficients of the obtained differential equation, are investigated. A theorem on the unique solvability of the resulting Cauchy problem on the positive semi-axis is proved. On the basis of the proved theorem, sufficient conditions for the existence of a strong with respect to time solution of an initial-boundary value problem describing the evolution of a hydrodynamical system, are found. From a mathematical point of view, the system under consideration is a finite-dimensional perturbation of the well-known S.G. Krein’s problem on small motions of a viscous fluid in an open vessel.

The relevance. Diffusers, either as nozzles or constituent elements, are frequently used in many mechanisms and machines. In this regard, the study of viscous fluid flow in diffusers aims to discover patterns of changes in the flow's hydrodynamic parameters, allowing better understanding of the nature of flow as a function of Reynolds number. Following the results of the analysis of the study, conditions for the proper construction of the mechanism unit, ensuring its reliable and durable operation will be revealed. The main aim of this study is to determine the velocity profiles in the flat diffuser for a viscous incompressible fluid by integrating the simplified Navier–Stokes differential equations under the established initial and boundary conditions, as well as the bifurcation point's dependence on the opening angle and Reynolds number of the diffuser. Objects: a flat diffuser in which viscous incompressible fluid moves. At the same time, revealing the patterns of changes of the hydrodynamic parameters of the flow is of defining value when choosing the structural dimension of devices and mechanisms, the main part of which is the flat diffuser. Methods. To reveal the patterns of changes of the hydrodynamic parameters of the flow in a flat diffuser, the study is based on the fundamental nonlinear differential equations of viscous fluid mechanics, which in a general case are not subject to an exact mathematical solution. For integration in the nonlinear differential equations, due to the smallness, the nonlinear-convective terms are neglected, and the inertial terms are also partially simplified. Such a simplification is justified if the velocities are very small or if the dynamic coefficient of viscosity of the fluid is very large. A method for solving the boundary value problem was developed, and regularities for changing the flow parameters were obtained. According to the derived regularities, graphs of the change in velocity, pressure and shear stresses on the wall of the fixed channel were plotted and the coordinates of the separation point were determined. Results. Depending on the angle of the diffuser opening and the Reynolds number, a general solution of the approximating Navier–Stokes equations was given. In accordance with the nature of the motion, the boundary conditions of the problem were established and the boundary value problem was stated. A method for integrating a boundary value problem was developed, and regularities for the change in velocities along the length of the diffuser were obtained for a parabolic distribution of velocities in the inlet sections. Graphs of the change in radial velocities along the length and at a fixed value of the opening angle were constructed, a flow pattern and the transition of a single-mode flow to multimode operation were obtained. For a fixed opening angle and Reynolds number, the conditions for flow separation from a fixed wall were derived, where the flow velocity changes the sign.

Viscous fluid can micro-rotate due to collisions between particles that affect viscous fluid's velocity and temperature.This study aims to determine the effect of viscosity parameters, micro-rotation materials, and heat sources on fluid velocity and temperature. The model of the laminar flow equation for viscous fluid in this study uses the laws of physics, namely, the law of conservation of mass, Newton II, and Thermodynamics I. The formed dimensional equations are converted into non-dimensional equations by using non-dimensional variables. Then, the non-dimensional equations are converted into similarity equations using stream function and similarity variables. The formed similarity equation was solved numerically by using the Gauss-Seidel method. The results of this study indicate that the velocity and temperature of the viscous fluid flow can be influenced by the parameters of viscosity, micro-rotation material, and heat source. The presence of collisions between particles causes heat to cause an increase in the variance of viscosity parameters, micro-rotation materials, and heat sources. Therefore, the viscous fluid's velocity decreases and its temperature increases.

The primary determination of this study is a numerical investigation of the entropy generation (EG) in the steady two-region flow of viscous fluid and hybrid nanofluid (NF) in a long-infinite vertical annulus having a clear region as well as porous media. Stoke’s and single-phase NF models are used to study the viscous fluid and hybrid nanofluid (HNF) heat transfer developments, respectively. Two types of nanoparticles are taken, such as copper (Cu) and silver (Ag) within base fluid water to make it a HNF. Darcy-Brinkman law is also used to examine the flow through the porous zone in the annulus. Necessary quantities have been used in the system of equations to transfer them into non-dimensional forms. For momentum and energy transport, the numerical results are evaluated for various model parameters and are examined via the shooting method in MATHEMATICA. It is noted that the momentum and energy transport are more significant when two immiscible fluids in a clear vertical annulus are taken. The findings also indicate that two-phase momentum and heat flow are greater when a NF is used in Region-II and lower when a HNF is used. The temperature (in Region-II) falls with a high nanomaterials volume fraction (see Figure 4) while it is increased when the Hartman number is increased. Moreover, velocity declines with increment in nanomaterials volume fraction. Thus, higher thermal conductivity can be accomplished by using a magnetic field.

The laminar flow around two side-by-side circular cylinders was numerically investigated using a vortex-in-cell method combined with a continuous-forcing immersed boundary method. The Reynolds number (Re) of the flow was examined in the range from 40 to 200, and the distance between the cylinders varies from 1.2 D to 6 D, where D is the cylinder diameter. Simulation results show that the vortex wake is classified into eight patterns, such as single-bluff-body, meandering-motion, steady, deflected-in-one-direction, flip-flopping, anti-phase-synchronization, in-phase-synchronization, and phase-difference-synchronization, significantly depending on the Re, the cylinder distance, and the initial external disturbance effects. The anti-phase-synchronization, in-phase-synchronization, and phase-difference-synchronization vortex patterns can be switched at a low Re after a long time evolution of the flow. In particular, the single-bluff-body and flip-flopping vortex patterns excite the oscillation amplitude of the drag and lift coefficients exerted on the cylinders.

In this paper, we consider a compressible fluid model of the Korteweg type on general domains in the N-dimensional Euclidean space for N ≥ 2 . The Korteweg-type model is employed to describe fluid capillarity effects or liquid–vapor two-phase flows with phase transition as a diffuse interface model. In the Korteweg-type model, the stress tensor is given by the sum of the standard viscous stress tensor and the so-called Korteweg stress tensor, including higher order derivatives of the fluid density. The local existence of strong solutions is proved in an L p -in-time and L q -in-space setting, p ∈ (1 , ∞) and q ∈ (N , ∞) , with additional regularity of the initial density on the basis of maximal regularity for the linearized system. [ABSTRACT FROM AUTHOR]

The study of the patterns of change in the hydrodynamic parameters under the conditions of non-stationary flow at the entry of the cylindrical pipe and the initial arbitrary distribution of velocities in the entry section was conducted based on the boundary layer equations. A boundary problem was formed under the axisymmetric change conditions in the flow. The boundary conditions were chosen in accordance with the pattern of an arbitrary distribution of velocities in the entry section. A general solution of the approximating Navier-Stokes equations is presented depending on the initial conditions and the Reynolds number. In accordance with the type of flow, the boundary conditions of the problem are established, and the boundary-value problem is formulated. Regularities for the change in velocities lengthwise in the entrance region have been obtained for a constant and parabolic velocity distribution in the inlet cross-sections. Analytical solutions have been obtained, allowing to obtain patterns of changes in velocities and pressures toward flow at any section and at any time. For the mentioned cases, the composite graphs of velocity changes in different sections along the length of the entrance transition area were constructed by computer analysis, for different time conditions. With the obtained composite graphs, the patterns of change over the entire length of the transition area of the entrance region were constructed, enabling to obtain fluid flow velocity at any point of the section. The length of the transition zone can be estimated based on the condition of reaching a certain percentage (99 %) of the maximum velocity of the flow. The proposed solutions create the conditions for correctly constructing separate units of hydromechanical equipment [ABSTRACT FROM AUTHOR]

This article is devoted to the investigation of gaseous bubble dynamics in oscillating viscous liquids of different density values. The study is conducted numerically using the level-set method with a non-stationary approach. The bubble is initially located near the upper wall of the container. The effects of the inclusion and host liquid viscosities on interaction of the bubble with the wall are analysed. The calculations show that in the absence of gravity, for low-viscosity fluids the bubble is attracted to the nearest wall, which is consistent with previous analytical and experimental results. With increasing viscosity, the vibrational attraction to the wall becomes weaker and is then replaced by repulsion, which can be explained by the decelerative effect of viscosity in the boundary layer near the rigid surface, where the average flow becomes less intensive. The dependencies of the repulsion force on the parameter values are obtained by using the balance method (investigation of the gravity level needed to attain the quasi-equilibrium state at a certain distance between the bubble and the wall). The calculations show that the repulsion force grows with decreasing Reynolds number (increase of the viscosity). This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'. [ABSTRACT FROM AUTHOR]

We studied the radiation magnetohydrodynamic flow of an incompressible viscous electrically conducting fluid past an exponentially accelerated perpendicular surface under the influence of slip velocity in the revolving structure. A steady homogeneous magnetic strength is applied under the assumption of low magnetic Reynolds quantity. The ramped heat and time‐altering concentration near the plate are taken into consideration. First‐order consistent chemical reactions and thermal absorption were also studied. The Laplace transformation technique is used for the non‐dimensional governing equations to get the closed‐form solutions. Supporting these results, the phases for nondimensional shear stress, rate of thermal as well as accumulation transport are also found. Graphical profiles are represented to examine the impact of physical parameters on the important physical flow features. The computational quantities of shear stress and rate of thermal and mass transportation near the surface are tabulated with a variety of implanted parameters. The resulting velocity is growing with an increase in heat and solutal buoyancy forces, while revolution and slip parameters have reverse effects on this. The resulting velocity is falling due to an increase in the Hartmann quantity, while the penetrability parameters have the opposite impacts on this. The species concentration of fluid is reduced by an increase in Schmidt number and chemical reacting parameter. [ABSTRACT FROM AUTHOR]

The free convective flow of an incompressible viscous fluid over an isothermal vertical cone with variable viscosity and variable thermal conductivity is examined in the presence of the Soret and Dufour effects. As thermal and solutal boundary conditions at the cone's surface, the constant temperature and concentration (WTC) and constant heat and mass flux (HMF) cases are taken into account. The successive linearization method is applied to linearize a system of nonlinear differential equations that describes the flow under investigation. The numerical solution for the resulting linear equations is attained by means of the Chebyshev spectral method. The obtained numerical results are compared and found to be in good agreement with previously published results. The impact of significant parameters on the heat and mass transfer rates is evaluated and presented graphically for the WTC and HMF situations. In both cases, the Soret number increases the skin friction coefficient and rate of heat transfer while decreasing the Sherwood number. With an increase in the Dufour parameter, the coefficient of skin friction and Sherwood numbers increase while the heat transmission rate decreases. [ABSTRACT FROM AUTHOR]

Mass, energy, and momentum transfer processes between fluid-saturated porous media and the adjacent free flow occur in many natural and technical systems. The flow dynamics in the porous region and the adjacent free flow is strongly controlled by the mechanisms at the common interface and conditions on the outer surface of the free-flow. The present paper considers unsteady axisymmetric flows of viscous fluids through an annular domain with a porous layer covering a cylindrical solid core. Fluid flow in the domain filled with porous material and in transparent domain is described by Brinkman model and Navier Stokes equations, respectively. Analytical solutions for the dimensionless velocity fields in the Laplace domain are determined using Bessel functions, Laplace transform, and the appropriate interface and boundary conditions. The inversion of the Laplace transforms is done with the help of a numerical algorithm. In addition, the hydrodynamic permeability is determined. The dependence of the dimensionless velocity fields and of hydrodynamic permeability on characteristic parameters of the porous layer is numerically and graphically discussed. Since the velocity on the outer surface is given by an arbitrary function of time, the results in this paper could be used to study various filtration problems. [ABSTRACT FROM AUTHOR]

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Abstract The buckling of a nanoplate at the bottom of a channel over which the fluid passes with a one‐dimensional flow is investigated in this article. Navier–Stokes equations were used to obtain the applied force from the fluid to the nanoplate. Non‐local elasticity theories and surface effects were used to consider nanoscale effects. By solving this problem using Galerkin's weighted residual method, interesting results were obtained. Applying non‐locality increases the fluid's impact on the buckling of a nanoplate. The lower modes are more noticeably affected by being placed in a fluid environment. Also, the presence of fluid and surface effects both increase the buckling capacity of the system. The obtained results are very helpful for developing and improving the performance of fluid‐coupled nanostructures that have buckling potential.

A study was conducted to analyze how hydrodynamic parameters change in the entrance region of plane-parallel flow under stationary flow conditions, with an initial arbitrary distribution of velocities in the entrance section. This study was based on boundary layer equations, and a boundary problem was formed under the conditions of plane-parallel flow. The boundary conditions were chosen to reflect the pattern of arbitrary velocity distribution in the entrance section. A general solution of the approximating Navier-Stokes equations is provided, which depends on the initial conditions and the Reynolds number. The boundary conditions are established based on the nature of the motion, and the boundary value problem is described. A method for integrating the boundary value problem has been developed, and regularities for the change in velocities along the length of the inlet section have been obtained for both constant and parabolic velocity distributions in the entrance sections. Analytical solutions have been derived to obtain patterns of velocity and pressure changes in any given flow direction. Through computer analysis, velocity change patterns in various sections along the inlet transition area have been constructed, allowing for the determination of fluid velocity at any point on the section and an estimation of the length of the transition area. These proposed solutions provide a framework for accurately constructing individual units of hydromechanical equipment.

In this article, the buckling of a nanoplate at the bottom of a tank over which the fluid passes with a one-dimensional flow was investigated. Navier-Stokes equations were used to obtain the applied force from the fluid to the nanoplate. Surface effects theory was used to consider nanoscale effects. By solving this problem using Galerkin's weighted residual method, the effect of fluid viscosity and flow velocity was studied, and also the way surface effects change the critical buckling load of the nanoplates placed in the fluid was investigated. The results reported in this research are very helpful for developing and improving the performance of fluid-coupled nanostructures that have buckling potential.

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.

For the first time, bicompact schemes have been generalized to nonstationary Navier–Stokes equations for a compressible heat-conducting fluid. The proposed schemes have an approximation of the fourth order in space and the second order in time, and they are absolutely stable (in the frozen-coefficients sense), conservative, and efficient. One of the new schemes is tested on several two-dimensional problems. It is shown that when the mesh is refined, the scheme converges with an increased third order. A comparison is made with the WENO5-MR scheme. The superiority of the chosen bicompact scheme in resolving vortices and shock waves, as well as their interaction, is demonstrated. [ABSTRACT FROM AUTHOR]

The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion, vicious, and Darcy dissipation is studied. The first region consists of a clear fluid, and the second one is filled with a nanofluid saturated with a porous medium. The behaviors of Cu-H2O, In-H2O, and Au-H2O nanofluids are analyzed. The transport properties are assumed to be constant. The coupled non-linear equations of the flow model are transformed into the dimensionless form, and the solutions for the velocity, temperature, and concentration are obtained by the regular perturbation technique. Investigations are carried out on the flow characteristics for various values of the material parameters. The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number, solutal Grashof number, and Brinkman number while decrease with the porosity parameter and solid volume fraction. [ABSTRACT FROM AUTHOR]

A viscous fluid is confined between two smooth horizontal walls, in a vertical channel. The upper wall may move with constant speed, but the lower wall is stationary and a portion of it is heated. A plume of heated fluid develops, and may also be swept downstream by the motion of the upper wall. When the heating effect is small and the upper plate does not move, a closed-form solution for the temperature profile is presented. A numerical spectral method is then presented, and allows highly accurate nonlinear solutions to be obtained, for the temperature and the fluid motion. These are compared against the closed-form solution in the linearized case, and the effects of nonlinearity on temperature and velocity are revealed. The results also show that periodic plume shedding from the heated region can occur in the nonlinear case. [ABSTRACT FROM AUTHOR]

Flagellated bacteria propel themselves by rotating flexible flagella driven by independent motors. Depending on the rotation direction of the motors and the handedness of the helical filaments, the flagella either pull or push the cell body. Motivated by experimental observations of Magnetococcus marinus, we develop an elastohydrodynamic model to study the locomotion of a bi-flagellated bacterium with one puller flagellum and one pusher flagellum. In this model, the boundary integral technique and Kirchhoff rod model are employed respectively to calculate the hydrodynamic forces on the swimmer and model the elastic deformations of the flagella. Our numerical results demonstrate that the model bacterium travels along a double helical trajectory, which is consistent with the experimental observations. Varying the stiffness, orientations or positions of the flagella significantly changes the swimming characteristics. Notably, when either the applied torque is higher than a critical value or the flagellum stiffness is lower than a critical stiffness, the pusher flagellum exhibits overwhirling motion, resulting in a more complicated swimming style and a lower swimming speed. For a moderate flagellum stiffness, the swimming speed is insensitive to the rest configuration orientation over a wide range of orientation angles as the flagella deform to maintain alignment with the swimming direction. [ABSTRACT FROM AUTHOR]