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Ranque-Hilsch vortex tube has been well known as a fluidic device to separate gas stream into low and high temperature, and has been employed in a variety of engineering applications. Although it is composed of the simple structure such as a vortex chamber, a long vortex tube, a hot exit and cold exit, the flow field involved is quite complicate, being subject to unsteady, 3-dimensional, viscous, compressible behaviors. Till now, many flow models have been developed to analyze the flow characteristics inside the vortex chamber and vortex tube, which are specified by a forced vortex flow and a viscous swirling flow, respectively. However, these flow models have never been proven by reliable experimental data and elaborate computational fluid dynamics predictions. Thus, the optimal design of the vortex tube has relied largely on trial and error and empirical data. In the present study, an integrated theoretical model has been developed for the whole flow field through the vortex tube system and the results of the theoretical predictions were well validated with existing experimental data. Thus, the present flow model can be used for the purpose of convenient design of the vortex tube with a specific application. [ABSTRACT FROM AUTHOR]

At 308 K, using a 9.37 GHz dielectric relaxation setup, dielectric investigations of H-bonded complexes of Propanamide and Butanamide with 4-bromophenol, 4-chlorophenol, 4-iodophenol and 4-fluorophenol in benzene were performed. Various parameters of dielectric like (ε′), (ε″), (ε0) and (ε∞) have been tested. The group rotation relaxation time τ(2) is a function of the steric interactions of the proton donor, while the significance of Higasi et al. single frequency equation used for few relaxation times τ(1) is creates towards a role of the hydrogen bonding power of the phenolic hydrogen. The dielectric relaxation process like the viscous flow process may be defined as a rate process. Higasi's approach yields the maximum relaxation time values at 1:1 molar ratio for the complicated system under consideration. The system under investigation illustrates that the relaxation time value increases as the concentration of solute increases. [ABSTRACT FROM AUTHOR]

In practice, there are many works dedicated to the drastic simplification of the Navier-Stokes equations and to finding their particular solutions that are very relevant for practice. These studies are usually based either on symmetry considerations or on the theory of concreteness and dimensions. In this article, a mathematical model of the motion of an incompressible fluid in a diffusion nozzle was created and numerical results were obtained. For this, the Nave-Stokes equation was reduced to a parabolic equation with Mises substitutions. Using the obtained numerical results, the longitudinal and transverse velocities of the fluid were determined [ABSTRACT FROM AUTHOR]

The current research focuses on the heterogeneity of fluid when it is allowed to flow over two parallel porous plates, as well as considering the flow to be viscous oscillatory in the presence of an angled magnetic field, as well as a radiative heat flux and heat source. The fluid is hypothesized to have an extremely low electrical conductivity, and the electromagnetic forces are measured in nanometers. Analytical solutions are provided for the consequences of various elements influencing the problem on velocity and temperature profiles, local skin friction coefficient, and local Nusselt number. [ABSTRACT FROM AUTHOR]

Research on the flow behavior of unplasticized PVC compounds remains rather limited even if rigid PVC is widely processed in the polymer processing industry. One major hurdle is that the shear viscosity of PVC is highly influenced by the thermomechanical history during processing. Within the conical double screw extruder, PVC's hierarchical grain structure is broken down and the flow profile is evolving dependent on its gelation degree. For standard thermoplastic polymer melts, shear viscosities are measured using standard rheometers assuming isothermal conditions. While for industrial processing of rigid PVC, viscous dissipation is high and can not be neglected at high shear rate regimes. Besides the remarkable viscous heating effect, rigid PVC also exhibits pronounced wall slippage as a result of the affluent presence of lubricants. A highly instrumented slit die on the extrusion line allows to measure pressure along the die during processing. Due to the non-isothermal manner of PVC processing, a model describing the pressure drop in the dies of different thicknesses requires 2D viscous flow simulations with slip boundary conditions. In this research, power-law and slip parameters (consistency index, power law coefficient, slip coefficients,...) on commercial rigid PVC compounds are estimated. An optimization is set up to minimize the pressure difference between slit die data and the 2D simulation. With the addition of lubricants, we noticed a reduction in extrusion load during slit die measurement, declined viscosity through the plate-plate rheometer test, and enhanced slip velocity from the capillary rheometer test. Such an inverse method, based on slit die experiments, provides a quantitative comparison of viscosity parameters before and after the addition of internal (fatty acid ester) or external lubricants (PE wax), which paves the path for future investigation on the prediction of rheological performance on PVC recyclates boosted with additives. [ABSTRACT FROM AUTHOR]

The use of high-performance single screws, such as barrier and wave-dispersion screws, is steadily increasing in polymer processing operations. In these screw types, regions with deep channels are found, where the polymer melt flow is markedly affected by channel curvature. Aiming for an accurate prediction of the flow rate and viscous dissipation rate, the governing equations for three-dimensional viscous fluid flow were developed in a helical reference frame. In contrast to previous modeling approaches, two helical coordinates in down-and cross-channel direction were introduced, which allows a more direct comparison with the flat plate theory. To reduce the complexity of the problem, focus was placed on an isothermal and fully developed flow of a power law fluid in fully confined channels of unit length. After conversion into a dimensionless form, the equations reveal five influencing parameters on the flow: (i) the channel depth ratio, (ii) the screw pitch ratio, (iii) the channel aspect ratio, (iv) the power law index, and (v) the dimensionless down-channel pressure gradient. The effect of channel curvature is described by the channel depth ratio and appears threefold: (i) net forces and deformations due to the locally changing orientation of the channel, (ii) additional flow coupling due to the twisted channel cross-section, and (iii) variable curvature radius and down-channel arc length across the channel depth. The resulting mathematical framework can be implemented into various numerical solution techniques to investigate and optimize the melt conveying behavior of single screw pumps. [ABSTRACT FROM AUTHOR]

In the present work, the hjgh viscous oil-water multiphase flows have been simulated using the Interfacial Area Density (AIAD) model, while the turbulence model was performed using the SST k-ω. The oil (Uso) and water (Usw) superficial velocities were set at 0.06 - 0.12 m/s and 0.23 - I m/s, respectively. The computational domain was adjusted on a horizontal pipe with 26mm in diameter and 1000mm in length for the primary pipe, while the oil and water inlets diameter were set to 12mm. A comparison between the volume of fluid (VOF) model and previous experimental was carried out. A comparison with experimental data showed relatively good agreement, both qualitative and quantitative. The AIAD model exhibited a better simulation result than the VOF model, whereby wavy and droplet were clearly revealed. The flow characteristics were obtained with satisfactory predictions in different flow regimes and the quantitative results of oil volume fraction were also investigated. Moreover, the numerical simulation appeared to be a reliable tool for predicting oil-water flow patterns on high viscous oil-water flow. These results show that the AIAD model run on commercial Fluent was able to investigate the practical case of oil-water flow. [ABSTRACT FROM AUTHOR]

In this article it is pointed out the issue of a pulsating flow of a viscous incompressible fluid in a flat channel for a given harmonic fluctuation of the fluid flow rate. The transfer function of the amplitude-phase rate response is determined, with the help of these functions the ratio of the tangential shear pressure on the channel fence to the average acceleration over the channel section is determined. Calculations determine that the non-stationary shear pressure on the channel fence increases non-monotonically with the acceleration of the liquid particle, at low oscillation frequencies. The shear pressure reaches its maximum value, then decreases with increasing dimensionless oscillation rate and asymptotically approaches the values without accelerated flow. [ABSTRACT FROM AUTHOR]

Large amounts of heavy oil are readily available all over the world, but their high viscosity makes the extraction and transportation very challenging. Typically, the flow of a high viscosity fluid (such as heavy oil) in a pipeline while being lubricated by a low viscosity fluid (such as water) is called Core-Annular Flow (CAF). In CAF, the more viscous liquid takes up the region close to the pipe center, and the less viscous liquid flows alongside the pipe wall where significant wall shear stresses are present. The CAF arrangement is governed by several parameters including fluid properties, flow characteristics, and piping arrangements. The stability of CAF is primarily governed by viscous forces, inertial forces, and buoyancy forces, and also influenced by the relative flow rates of the two liquids as well as the geometric configuration of the piping system. The key parameters of interest in a CAF arrangement are pressure drop and hold-up. In the present work, we review various correlations available in the literature on predicting pressure drop as well as hold-up in a water lubricated transportation of heavy oil in a CAF arrangement. [ABSTRACT FROM AUTHOR]

Quartz is a very common constituent of the materials of traditional ceramics – natural clays. These clays frequently contain illite as the main mineralogical phase. The effect of quartz amount and particle size in the illite-quartz system without impurities has not yet been studied systematically. This study aims to fill this gap using samples made of purified illite and quartz sand in amounts ranging from 5 wt.% to 40 wt.% and in three size fractions: (0 – 50) µm, (50 – 100) µm, and (100 – 200) µm. The influence of quartz amount on firing shrinkage was small until at least 20 wt.% of quartz was used. Above this amount, the total firing shrinkage decreased due to the retardant effect of quartz on the viscous flow sintering. This was found to be less pronounced if the finest fraction (0 – 50) μm of quartz was used. With the addition of at least 30 wt.% of quartz, dimension changes around 570 °C during heating were affected. The influence of quartz β – α transition during cooling on the rate and extent of shrinkage was linear in terms of quartz amount. The extent and rate of shrinkage due to β – α quartz transition on cooling were not influenced by particle size. [ABSTRACT FROM AUTHOR]

Simulations need to be validated by experiments to develop robust, accurate hypersonic flow-simulation methods to predict the wide range of flight regimes including highly rarefied hypersonic gas flows. We have developed and used a unified flow model for compressible flows (called RNS), based on the Generalized Hydrodynamic Equations (GHE) by Alexeev (1994), derived from generalized Boltzmann transport equation (GBE). The model is supposed to account for kinetic effects (intermediate Knudsen number, fluctuations) in the continuum approximation. This model has been explored for simulations of incompressible viscous flows for a wide range of problems and flow parameters, demonstrating good agreement with experimental data, Fedoseyev (2012). Simulations of hypersonic flows is a very challenging problem as those can exhibit both continuum and non continuum flow regimes. Typically, the flow can be continuous to transitional in the near field flow structure, and free molecular flow in the far field. The bow shock can be detached from the vehicle at high-altitude, and near boundary slip-flow is typical for such regimes. First results of RNS model for hypersonic flows have been reported in Fedoseyev (2020), Fedoseyev and Griaznov (2021). In this paper we continue a comparison of simulation results of our RNS model with the experimental data for rarefied hypersonic flows by Allegre et al (1997) and several other works. Simulations by Direct Simulation Monte Carlo (DSMC) method are provided for comparisons. The comparisons show good agreements of both RNS and DSMC with the experiment, or each other, confirming that RNS model can be used for simulation of hypersonic rarefied flows. [ABSTRACT FROM AUTHOR]

The cylindrical Pirani gauge sensitivity under different conditions is studied in our previous paper. We are modeled the Pirani gauge as cylindrical Couette flow – one dimensional axis symmetrical problem by using a statistical method – Direct Simulation Monte Carlo (DSMC) and the Navier-Stokes-Fourier equations numerical solving. The purpose of this article is to study the cylindrical two-dimensional Taylor-Couette flow with finite length of rarefied gas. The suddenly temperature change of the inner cylinder wall (the fiber) is used to modeling the boundary conditions. The finite volume method and statistical modeling is used to study this problem. This paper is a continuation of our previous work which we extend the study using the NSF model and its numerical solution to assess the applicability of the obtained results. The state of the gas is studied over a long time period close to establishing a steady state in the previous work, while in this paper is studied the initial moment of occurrence and reflection of the wave from the other cylinder. The realization of such conditions is difficult technically feasible in some cases, but their set in mathematical model gives more opportunities to study the stability in the gaseous medium between the cylinders. [ABSTRACT FROM AUTHOR]

The task of the spots chain dynamics with initial intervals of mixed liquid in stratified environment, and viscous flow is considered. To solve the problem, the splitting method for studying incompressible fluid flows (SMIF method) is used. The finite-different scheme of SMIF has such properties as the second order of approximation on spatial variables, minimal scheme dissipation and dispersion. The results of the formation of a streak depending on the Reynolds and Froude numbers values and the initial interval between spots are presented. Two characteristic variants were identified among the calculating variants. There are four stages of horizontal banding dynamics of spots chain with intervals. [ABSTRACT FROM AUTHOR]

Various commercial proppants originally produced for fracking industry were examined as candidate materials to be used in concentrating solar power (CSP) plants as heat transfer and storage medium. Material properties as well as application related functional properties have been elucidated in a comparative manner. Despite their similar chemical composition, varying microstructures resulted in distinct application related functional properties. Carboceramics proppants are determined as the most promising candidate with highest viscous flow temperature, heat capacity, solar absorptance after thermal aging and abrasion resistance owing to well crystallized microstructure without glassy components. Moreover, the importance of the microstructure to achieve desired application related properties is revealed, in the scope of this study. [ABSTRACT FROM AUTHOR]

This work explores fundamental numerical and physical issues associated with the flow around flows different bluff bodies configurations at a Reynolds number of 200. The strategy to solve incompressible viscous fluid flow problems around solid geometries is based on a combination of a narrow-band accurate conservative level set method and ghost-fluid framework. In this strategy, the interface is defined as the isocontour of a hyperbolic tangent function, which is advected by the fluid, and then periodically reshaped to enforce the degraded level set function being a signed distance function using a reinitialization equation based on an improved form. The latter approach takes advantage of a mapping onto a classical distance level set while much better preserving the interface shape. Simulations were performed for two circular cylinders in tandem and side-by-side arrangements. [ABSTRACT FROM AUTHOR]

The estimates obtained in [1] for compact operators are used to evaluate the accuracy of calculating normal modes when studying the stability of a flow of a viscous incompressible fluid on a rotating sphere. [ABSTRACT FROM AUTHOR]

Dry sliding of model samples (steel AISI steel 1020 and tungsten) against quenched AISI steel 1045 or molybdenum under electric current was carried out according to the "pin-on-ring" scheme. It was shown that the steel/steel contact exhibits higher wear resistance compared to the W/steel contact. It was assumed that the electrical conductivity of such contact will increase in sliding against molybdenum counterbody. In reality, samples of AISI steel 1020 and tungsten showed low wear resistance in sliding against Mo. A morphological feature of the samples sliding surfaces was found namely the formation of two sectors on the sliding surface. The sector directed towards the counterbody movement was deformed and deteriorated due to the plowing mechanism. The deformation of another sector of specimens sliding surfaces was carried out due to viscous plastic flow. This morphological feature was observed on the sliding surface of all considered specimens that did not allow us to indicate the reason for the difference in the contact characteristics. The formation of FeO on the surface layer of AISI steel 1020 was found by X-ray phase analysis. The FeO absence or its low content on the surface layers of molybdenum or tungsten corresponds to unsatisfactory contact characteristics. [ABSTRACT FROM AUTHOR]

In the present study, conductance and viscosity values have been measured for aliphatic amino acids; glycine and L-alanine in aqueous solutions of 1-Butyl-3-propyl imidazolium bromide, ([BPim][Br]) (mIL=0.01, 0.03 and 0.05 mol kg−1) at different temperatures and atmospheric pressure. Using conductance as well as viscosity data, various thermodynamic parameters have been investigated which in turn assisted to infer the molecular interactions occurring in the (glycine/L-alanine + water + ([BPim][Br])). From conductance values, limiting molar conductivities have been determined using Onsager equation and further, Walden product have been computed. Joules-Dole equation have been analyzed using viscosity data. A and B-coefficients of Joules-Dole equation and temperature derivative of B-coefficient have also been calculated. Moreover, Eyring transition state theory utilized to compute different viscous flow's activation parameters. [ABSTRACT FROM AUTHOR]

When studying problems of axisymmetric fluid flows, a scalar function, is usually employed, namely a stream function through which, the vector velocity function can be derived. The governing equation in the case of a creeping flow at steady state is then given by the fourth-order partial differential equation E4=ψ0, where E2 is the Stokes irrotational operator and =EE42oE2 is the Stokes bistream operator. As it is already known, E2=ψ0 separates variables in some axisymmetric coordinate systems, such as the cylindrical, spherical, and spheroidal ones, but in some others, such as the toroidal coordinate system) ψθ,η, (the general solution is given in R-separable form. In the present manuscript we combine the R-separation method and an Almansi-type methodology to derive the analytical solution of E4=ψ0, in toroidal coordinates. This is of fundamental importance when solving flow problems involving toroidal surfaces. [ABSTRACT FROM AUTHOR]

Flow through a turbine is one of the most geometricaly complex problems used in many engineering applications. Therefore in many theoretical and computational problems the appropriate 2D model is used, but the proper justification is missing. The aim of this work is to bridge this gap. Here the 3D problem of a flow of a viscous incompressible fluid through a rotating turbine wheel is step by step reduced to an appropriate 2D problem. We describe the reduction and provide arguments for its justification. We also comment on the used simplifications and dimensional analysis (of similar type used in other model reduction problems). [ABSTRACT FROM AUTHOR]

The present analysis deals with the time-independent magnetohydrodynamic flow of viscous fluid past a thin slit embedding with a preamble medium affected by the transverse magnetic field. Further, the role of dissipative heat, in particular, viscous dissipationon the fluid temperature profile enhances the thermophysical properties. Additionally, radiative heat for the consideration of Roseland approximation also enriches the flow phenomena significantly. The previously mentioned physical properties are important because of the rising industrial applications likely controlling temperature used in better shape of the final product, emission of electromagnetic radiation, etc. The renovation of governing equation into nonlinear ODEs are obtained by the use of suitable similarity transformations. The exact solution of the velocity profile is obtained and further, the same solution is used in the temperature profile to get the solution numerically. Extensive discussion on the various profiles is presented by implementing the characteristic of several parameters on the profiles through graphs. However, the computation of the rate coefficients is pondered in tabular form. Further, the validation with the earlier study is presented, showing a good correlation. [ABSTRACT FROM AUTHOR]

The discussion of dielectric relaxation properties of Paracetamol has been made at a fixed frequency of 8.73 GHz when it get dissolved in Carbon Tetrachloride solution. Different dielectric parameters are observed at four different temperatures and for five different mole fractions to estimate the values of relaxation time (τ1, τ2 and τ0) and dipole moment (μ). The present study suggests there is more than one relaxation process exist in the solution since the values of τ2 are found higher than τ1. The studies of different thermodynamic parameter for dielectric relaxation process and viscous flow process help to study different long and short-range interactions between dipoles. I have determined these thermodynamic parameters at different temperatures and found that we may treat both the method as a rate method. [ABSTRACT FROM AUTHOR]

An analytical study is performed to analyze the effects of thermal radiation and mass diffusion on MHD flow of a viscous incompressible fluid past an infinite vertical porous plate embedded in a porous medium with time dependent permeability subjected to oscillatory suction normal to the plate. The flow is also subjected to oscillatory suction and transverse magnetic field. The present analysis undergoes a resisting buoyancy mechanism due to same sign of buoyant terms in momentum equation. The novelty of the present work is to investigate the combined effects of the thermal radiation and the Soret effect in the presence of chemical reaction. Solutions for the velocity field, temperature and concentration distributions are obtained using perturbation technique. The validation of the present work has been made by comparing the result of the present work as a particular case with the previous work reported earlier. The important outcomes of the present analysis are reported here in as: flow reversal occurs for negative values of mass buoyancy parameter, suggesting a remedial measure to avoid back flow; the primary fluid motion is retarded due to interaction of the applied transverse magnetic field with conducting fluid; the flow gets accelerated due to coupling effect of temperature and concentration ratio (Soret number), which is a control measure suggested for reducing thermal buoyancy and applied magnetic field strength to ensuring stream line flow; surface concentration level (Sherwood number) gets depleted due to high thermal diffusivity and diffusion of heavier species, an useful guideline for thinning of surface coating in chemical industry. [ABSTRACT FROM AUTHOR]

This work deals with the 1-dimensional modeling and simulation of the viscous flow of polymers in flat film, round hole and circular ring dies considering realistic constitutive equations like that of Carreau, Cross or Yasuda, the pressure and temperature dependence of the polymeric melt and difficult boundary conditions like moving wall conditions (e. g. coating of sheets or cables). Furthermore, viscoplastic models like that of Bingham, Herschel-Bulkley [9], Casson as well as a new viscoplastic model published be Kneidinger et al. in 2021. The work shows how this simulation can be done using standard spreadsheet software. Furthermore, an easy-to-use spreadsheet file will be provided. This file can be used to determine both the throughput as a function of pressure and the pressure required to achieve a predefined throughput and helps to fit model parameters. [ABSTRACT FROM AUTHOR]

This work deals with two-dimensional flow of viscous compressible gas from a source in an apex of wedge. In case of adiabatic walls and transfer coefficients arbitrarily depending on temperature, the possibility of self-similar solutions is established. New analytical solutions are compared with the previous solutions for a gas with power-law transfer coefficients. Making use of small perturbation method gas flow in a slender wedge is considered analytically. [ABSTRACT FROM AUTHOR]

The 3D structure of the wake behind a circular cylinder in a cross-flow is studied experimentally using stereo PIV technique, Reynolds number was around 5 thousands. The statistical characteristics along the cylinder axis are effectively constant and thus 2D, however instantaneous flow-field in the wake is fully 3D. Within the wake dynamical flow, the streamwise vortices and spots of streamwise velocity component pulsations are detected. [ABSTRACT FROM AUTHOR]

Soret and Dufour effect with hall current of a magneto hydro dynamic flow of a viscous fluid through vertical porous channel is studied here. Also studied the impacts of ramped wall temperature on the incompressible fluid. Using regular perturbation technique with boundary conditions the velocity, temperature and concentration of the fluid are calculated and it shows the velocity of the fluid increases when Soret number increases and velocity decreases with the increasing values of Dufour number. Also the variations in temperature and concentration also studied with the help of graphs. [ABSTRACT FROM AUTHOR]

More difficult fluctuation of rectangular flat element is the fluctuation when two of the opposite edges are hinge-supported, and two other edges have different types of fixing or they are free from tension. This class of tasks leads to the transcendental equations for determination of frequencies of own fluctuations which can be solved both numerically and analytically. The transcendental frequency equations can be reduced to algebraic ones and to investigate the influence of both boundary conditions at the edges of rectangular plate or rectangular flat element and parameters of geometrical and mechanical character on the frequencies of own fluctuations of rectangular flat elements. In the study of oscillations and wave processes in a deformable solid body core of a viscoelastic operators it is advisable to take regular, so as soon as such statements describe the instantaneous elasticity, and then viscous flow, which is typical for deformable bodies. Integra-differential equations with regular kernels, as you know, the equivalent differential equations. [ABSTRACT FROM AUTHOR]

High fidelity modeling and simulations methods need to be anchored to data collected from selected flight tests or experiments to develop robust, accurate and validated supersonic flow-simulation methods to predict the behavior of flowfield throughout the wide range flight regimes including highly rarefied supersonic gas flows. We have developed a unified flow model for compressible flows (called RNS model), based on the Generalized Hydrodynamic Equations (GHE) by Alexeev (1994), derived from generalized Boltzmann transport equation. The model is supposed to account for kinetic effects (intermediate Knudsen number, fluctuations) in the continuum approximation. This model has been explored for simulations of incompressible viscous flows for a wide range of problems and flow parameters, including high Reynolds numbers flows with thin boundary layers, demonstrating good agreement with experimental data, Fedoseyev (2012). Simulations of compressible supersonic flows is a very challenging problem as such flows can exhibit both continuum and non-continuum flow regimes. Typically, the flow can be continuous to transitional in the near field flow structure, and free molecular flow in the far field. The shock wave (bow shock) is detached from the vehicle at high altitude, and near boundary slip-flow is typical for such regimes. First results for this model has been reported in Fedoseyev (2020). In this paper we provide a comparison of simulation results of our model (called RNS, the Regularized Navier-Stokes) with the experimental data for rarefied hypersonic flows by Allegre et al. (1997). Simulations by DSMC method are also provided for comparison, the DSMC results obtained using the open source SPARTA DSMC code. The comparisons show good agreements of both RNS and DSMC with the experiment, and proove that SPARTA DSMC results can be used as a good approximation for experimental data, in cases where those are not available. [ABSTRACT FROM AUTHOR]

During the eruption of the Kizimen volcano in 2010-2013 there was a uniform squeezing of the viscous lava flow. Simultaneously with its movement, earthquakes with an unusual quasi-periodicity were recorded, the "drumbeats" mode. In this work, we show that these earthquakes were generated by the movement of the flow front, which was observed for the first time in the practice of volcanological research. We represent the movement of the flow as an intermittent slip with the inclusion of the "stick-slip" mechanism with the initiation of a self-oscillating process. The plausibility of the phenomenological model at the qualitative level is confirmed by the mathematical model of a fractional nonlinear oscillator. [ABSTRACT FROM AUTHOR]

In metallurgical production, it is often necessary to deal with moving liquid and gaseous media. These are melts in smelting furnaces, electrolytes in electrolysis tanks, products of fuel combustion in the working space of furnaces, various liquids and gases moving through pipes and channels. One of the flow methods studied in theoretical and applied hydromechanics is the Couette flow. Under the Couette flow, there is a laminar stream of a viscous liquid between two walls, one of which moves relative to the other. In this article, we find an approximate analytical solution of this problem is approximated taking into account the heat of friction (energy dissipation). Taking into account internal friction is especially important in the flow of highly viscous liquids, since the power of dissipative sources is determined by the velocity gradient in the flow. The use of the additional sought-for function (heat flow on the channel wall) makes it possible to get a solution to the formulated problem in a simple analytical form. For example, in the first approximation, the solution is represented as an algebraic polynomial of the second degree of the spatial modified. It is momentous to mark that the solutions are obtained in a parametric (dimensionless) form. Such solutions are more effective, they allow drawing the most general conclusions about the universal processes of the flow of the investigated. It is revealed that the accurateness of the solutions obtained depends on the degree of the approximating polynomial. Unknown polynomial coefficients using additional physically based conditions of the boundary of the study area. In the algorithm for providing additional boundary characteristics, which makes it possible to receive solutions to the formulated problem using the capabilities for engineering problems. [ABSTRACT FROM AUTHOR]

The paper presents the solution of problems generalizing Nusselt classical solution, which describes the steady flow of viscous liquid on an inclined plane. First, it is a stationary two-layer flow. Secondly, these are analogous unsteady motions. In the latter case, the solutions are found by the Laplace transform method. It is proved that with increasing time, these solutions tend to stationary. It has been established that all new solutions uniquely determined by the initial and boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, the viscous flow theory is used to investigate the coupled effect of the magnetic field and swirling on the vapor/liquid interface in cylindrical geometry. The liquid, as well as vapor, are confined in an annular region enclosed by two rigid cylinders, and the phenomenon of heat/mass transport at the interface is also considered in this analysis. The outer cylinder is swirling in the anticlockwise with constant angular velocity and the magnetic field is applied in the axial direction of the cylindrical flow. The perturbed flow is taken as irrotational meanwhile fluids are taken to be viscous having different dynamic viscosities. A quadratic equation is achieved in terms of growth of perturbations which is depending upon various flow variables such as magnetic field, viscosity, density, swirl, heat transfer coefficient, etc. The magnetic field in the axial direction is found to have stabilizing nature in the stability analysis. [ABSTRACT FROM AUTHOR]

It is well known that numerical simulations of high-speed reacting viscous flows, in the framework of state-to-state (STS) formulations, are often prohibitively computationally expensive. In this work, we investigate the possibility of using machine learning algorithms (MLAs) for STS approaches in order to alleviate such issue. As a first step in this direction, we assessed the potential of data-driven regression models based on machine learning to predict the relaxation terms which appear in the r.h.s. of the Euler system of equations for a one-dimensional reacting shock flow in the STS approach for a N2/N binary mixture. Results show that by appropriately choosing the MLA regressor and opportunely tuning the hyperparameters it is possible to achieve accurate predictions compared to the full-scale STS simulation in significantly shorter times. [ABSTRACT FROM AUTHOR]

The derivation of asymptotic equations describing the processes of heat and mass transfer in axisymmetric swirling laminar flows of a viscous incompressible fluid. Self-similar solutions of these equations are obtained, on the basis of which steady hydrodynamic fields (velocities, pressures) and a temperature field in swirling jets are constructed. The plane and axisymmetric heat and mass transfer problems for unsteady laminar layered flows of a viscous incompressible fluid in channels are also considered. [ABSTRACT FROM AUTHOR]

In the paper, we consider stationary, linearized by Picard's iterations, Navier-Stokes equations governing the flow of a incompressible viscous fluid in the convection form in non-convex polygonal domain. An Rν -generalized solution of the problem is defined. A weighted finite element method for finding an approximate Rν-generalized solution is constructed. Numerically shown that the convergence rate does not depend on a value of the reentrant corner in the norm of the weighted Sobolev space. [ABSTRACT FROM AUTHOR]

Flow past a stationary circular cylinder is the fundamental problem of interest in fluid mechanics. Numerical simulations were performed for two dimensional viscous incompressible flow past a circular cylinder at Reynolds number (Re) 100. The objective is to show the detailed way of grid convergence study for CFD beginners in ANSYS Fluent using the basic problem. The minimum domain size and the minimum number of nodes on the body required to achieve convergence was found. The numerical results obtained was validated with existing researches. The mesh convergence test was performed on the grid. The optimal grid that helps to achieve accurate results with minimal computational time was concluded. [ABSTRACT FROM AUTHOR]

The paper studies the large-scale convective flow of viscous incompressible fluid in the equatorial zone, taking into account two components of the Coriolis force. Temperature gradients are set at the flow boundaries. The Marangoni effect works on the free boundary. The existence and position of stagnation points is analyzed. The parameter values at which stagnation points can appear are determined. The possibility of a double stagnation point is shown. [ABSTRACT FROM AUTHOR]

An inhomogeneous solution describing the laminar large-scale isothermal Poiseuille-Ekman flow of the viscous incompressible fluid in the equatorial zone is constructed. At the free boundary, tangent stresses are set to simulate the effect of wind. The slip conditions for the Navier fluid are set on the solid surface. The condition of compatibility of the redefined system of equations describing the laminar flow is obtained. The compatibility condition imposes restrictions on the boundary conditions. The solution is constructed in the form of polynomials. [ABSTRACT FROM AUTHOR]

An analytical solution describing the stationary isobaric flow of a viscous incompressible slowly rotating fluid in an infinitely extended layer is obtained, with inhomogeneous velocity distribution. The fluid flow is considered at constant pressure, in accordance with the generalization of the classical Ekman flow. The allowance made for velocity gradients can both increase and decrease the number of stagnation points in the fluid layer as compared to the homogeneous Ekman flow. It is shown that the new exact solution allows us to construct new classes of exact solutions of the Navier-Stokes equations describing fluid flow in an inertial coordinate system and in a rotating one. [ABSTRACT FROM AUTHOR]

An exact solution of the Oberbeck-Boussinesq equations system is shown. This solution describes the flow of a viscous incompressible fluid in a flat channel, which is heated by a quadratic point source. A nonzero vertical velocity is taken into account in the fluid layer. The temperature and pressure fields are specified by quadratic forms of longitudinal coordinates. For the proposed exact solution, a boundary value problem is considered which takes into account the no-slip conditions on the lower solid boundary of the fluid layer and the heating and parabolic wind on the upper free surface. The obtained solutions are analyzed for various cases of the parameters of the boundary conditions. [ABSTRACT FROM AUTHOR]

The paper discusses a new exact solution of the Oberbeck-Boussinesq system describing the three-dimensional flow of a viscous incompressible fluid layer. Quadratic heating is determined at one of the boundaries of the fluid layer, along two mutually perpendicular horizontal directions. A particular exact solution of the boundary value problem is analyzed for the obtained velocity and temperature fields. The possibility of the occurrence of counterflow regions inside the fluid layer is reported. [ABSTRACT FROM AUTHOR]

Depending on the reasons causing changes in the density of a fluid, it is customary to distinguish between thermal convection and concentration-induced convection. The phenomenon of concentration-induced convection often accompanies the flow of a working fluid in devices working, for example, with fluid coolants. When modeling such flows, the consideration of the generalization of the Boussinesq hypothesis assuming the dependence of the fluid density on the impurity concentration and on the temperature of the fluid itself leads to the situation that the flow velocity field and the concentration field affect each other. The paper investigates the features of the shear convective flow of a viscous incompressible fluid with an admixture in the horizontal layer. The system of concentration-induced convection equations consisting of the equation of motion of a viscous fluid, the concentration change equation, and the incompressibility condition is taken as a system of defining relations. The solution is sought in the class of functions linear in two coordinates (x and y). As the boundary conditions, it is assumed that the no-slip condition is met at the lower impermeable boundary, that the upper boundary of the layer is immobile, and that the distribution of salinity and pressure is specified on it. A complete solution of the boundary value problem is given. The attention is focused on the analysis of the distribution of the concentration field inside the fluid layer. It is shown that, according to the solution of the boundary value problem for the concentration field, its homogeneous (with respect to the horizontal coordinates) component does not vanish inside the layer. The components of the concentration field, linearly dependent on the horizontal coordinates, take a constant value everywhere inside the layer. The change in the mutual arrangement of the isolines of the concentration field at the transition from one section of the fluid layer to another is studied. Relevant findings are illustrated. [ABSTRACT FROM AUTHOR]

The Ekman angle is the angle between the tangential stress vector on the free surface and the flow velocity vector in the upper layer. Ekman showed that, for an isobaric flow in an ocean with an infinitely great depth (fluid flow in half-space), the angle is equal to 45°. The paper studies the Ekman angle occurring in an isothermal laminar flow with the Navier slip boundary condition. In order to determine the Ekman angle, an analytical solution of the Oberbeck-Boussinesq equations is constructed; the solution describes the laminar Ekman-Poiseuille isothermal flow with allowance made for two components of the Coriolis force and the Navier condition at the lower (solid) boundary. The components of the tangential stress vector are set at the upper boundary. The velocity representation in the form of linear functions of the horizontal coordinates is used. The paper studies the dependence of the Ekman angle on the pressure gradient and on the friction coefficient on the solid surface, the depth of the ocean being finite. It is shown that at a sufficiently large depth there is no friction effect, and the Ekman angle is 45°. [ABSTRACT FROM AUTHOR]

A layered steady-state convective flow of a viscous incompressible fluid in an infinite horizontal layer induced by an inhomogeneous pressure distribution at one of the layer boundaries and by the presence of an impurity (salinity) in the fluid is considered. In addition to the equation of motion of a viscous fluid and to the law of conservation of mass for an incompressible fluid, the determining system of relations also includes an equation describing the distribution of the volume fraction of the impurity (salinity) over the entire region of the flow of the fluid under consideration. The solution of the determining system of equations is sought with the use of the class of generalized solutions, in which the velocities depend only on the vertical (transverse) coordinate, and the impurity concentration and pressure are linearly distributed along the horizontal (longitudinal) coordinates. A general solution for the determining system of equations within the chosen class is presented, and the corresponding number of boundary conditions necessary to find the values of the integration constants that appear in this general solution is formulated. A complete solution for the boundary value problem is also given. The features of the velocity field, the concentration field, and the pressure field are analyzed. The dependences of the properties of these fields on the values of parameters determining the distribution of the pressure field and the concentration field at the upper boundary of the layer are studied. It is shown that the constructed exact solution is able to describe multiple stratifications of the above-mentioned hydrodynamic. All the results obtained during the study are illustrated. [ABSTRACT FROM AUTHOR]

The paper studies the properties of steady layered unidirectional convective flows of a viscous incompressible fluid in a closed horizontal layer. At the upper boundary of the layer, the distribution of the temperature and pressure fields linearly dependent on the longitudinal (horizontal) coordinates, are assumed to be specified. At the lower boundary, a special case of the Navier slip condition (the perfect slip condition) is implemented. In terms of physical implementation, this boundary condition holds at the contact between a fluid and a hydrophobic solid surface. An exact solution to the system of thermal convection equations is given. The solution is obtained within a class of generalized solutions linearly dependent on a part of coordinates. It is shown that this solution is able to describe counterflows in the fluid and the stratification of physical fields. The field of flow velocities is investigated in detail. It is demonstrated that, for a certain combination of parameters characterizing the inhomogeneity of heating (cooling) of the boundaries and the inhomogeneity of pressure distribution at the upper boundary of the fluid layer, velocity can have zero points. Thus, the velocity field can be stratified into zones; in each zone the velocity takes values of a certain sign. The tangential stress field corresponding to this velocity field can also be stratified into zones, in one of which stresses are either tensile or compressive. All the results obtained during the study and presented in the paper are illustrated. [ABSTRACT FROM AUTHOR]

It is known that convection contributes to the natural mixing of melts due to the uneven distribution of their density. This mixing can be enhanced by various devices and by changing the conditions surrounding the flow region of the medium, e.g. by changing the pressure at the boundaries of the flow region of such fluid media. A pressure difference inside the region filled with a viscous fluid can induce its flow. A classic example of such a flow is the Poiseuille flow. Moreover, if the pressure distribution depends also on horizontal coordinates (i.e., there is a pressure difference not only in the vertical direction), then longitudinal pressure gradients also generate additional flows, which are superimposed on the classical flow. The paper studies the effect of pressure on the shear convective flow of a viscous incompressible binary fluid in a horizontal layer. To describe such flows, we use a system of equations of concentration convection, which includes the equation of motion of a viscous binary fluid, the equation of a concentration change, and the incompressibility equation. The solution of the system of constitutive equations is sought with the use of the class of generalized solutions, in which the velocities depend only on the vertical coordinate, the pressure and concentration being also linearly dependent on the longitudinal (horizontal) coordinates. As the boundary conditions, it is assumed that the no-slip condition is met at the lower impermeable boundary, that the upper boundary of the layer is motionless, and that the distribution of salinity and pressure is specified on it. The solution of the formulated boundary value problem is a set of polynomial functions. The highest-degree polynomial describes background pressure. The study of the properties of background pressure and the longitudinal pressure gradients is in the focus of attention. It is shown that background pressure decreases strictly monotonically with moving away from the lower boundary of the layer, regardless of the control parameters of the boundary value problem. In this case, the longitudinal pressure gradients are also described by strictly monotonic functions, but the nature of the monotonicity is determined by the values of the longitudinal concentration gradients specified at the upper boundary of the fluid layer. The relevant findings are illustrated. [ABSTRACT FROM AUTHOR]