Viscous Fluid Model Research Articles

Numerical simulation of heat-transfer fluid warm-up in heating facilities with heat transfer augmentation achieved with swirling flow

Swirling flow of heat transfer fluid in heating facilities is a compelling way to intensify heat transfer augmentation. The paper considers the process of passive swirling flow in heating pipes by way of application of special design pipe connectors. Numerical simulation has been accomplished on the basis of viscous incompressible fluid model represented by Navier-Stokes equations complemented with temperature transfer equation. Numerical experiments has been completed with the help of applied software OpenFOAM based on finite volume method.

Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids

The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory’s strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique.

Numerical investigation of the MHD suction–injection model of viscous fluid using a kernel-based method

Numerical investigation of the MHD suction–injection model of viscous fluid using a kernel-based method

MHD Flow of a Newtonian Fluid in Symmetric Channel with ABC Fractional Model Containing Hybrid Nanoparticles.

The nanofluid is the novelty of nanotechnology to overcome the difficulties of heat transfer in several manufacturing and engineering areas. Fractional calculus has many applications in nearly all fields of science and engineering, which include electrochemistry, dispersion and viscoelasticity. This paper focused on the heat transfer of a hybrid nanofluid in two vertical parallel plates and presented a comparison between fractional operators. In this paper, the fractional viscous fluid model is considered along with physical initial and boundary conditions for the movement occurrences. The analytical solutions have been obtained via the Laplace transform method for the concentration, temperature and velocity fields. After that, we have presented a comparison between Atangana-Baleanu (ABC), Caputo (C) and Caputo-Fabrizio (CF) fractional operators. The comparison of different base fluids (Water, kerosene, Engine Oil) is discussed graphically with respect to temperature and velocity. The results show that due to the high thermal conductivity of water, temperature and velocity are high. While engine oil has maximum viscosity than water and kerosene, thus temperature and velocity are very low. However, due to the improvement in the thermal conductivity with the enrichment of hybrid nanoparticles, the temperature increased, and since the viscosity also increased, the velocity got reduced. Atangana-Baleanu (ABC) fractional operator provided better memory effect of concentration, temperature and velocity fields than Caputo (C) and Caputo-Fabrizio (CF). Temperature and velocity of water with hybridized nanoparticles were high in comparison to kerosene and engine oil.

Application of novel fractional derivative to heat and mass transfer analysis for the slippage flow of viscous fluid with single‐wall carbon nanotube subject to Newtonian heating

The single‐walled carbon nanotubes are the solid tiny materials in nature with efficient thermal conductivity and has many useful applications in biological domain specifically in the formation of biological nanofluid. The physical effects of single‐wall carbon nanotube (SWCNT) are considered in this study for free convection slippage flow of fractional viscous fluid by considering the thermal radiation, heat generation, chemical reaction of order first, and Newtonian heating through a porous medium. The fractional flow model of viscous fluid with SWCNT is constructed by inserting most recent approach of non‐integer derivative (constant proportional Caputo fractional derivative). Non‐dimensional boundary layer equations which govern the flow are solved analytically via integral transform, namely, the Laplace transform, and explicit transformed results for field variables, temperature, concentration, and velocity are established. Thermal and mass fluxes are also obtained numerically and presented in tabular form. The parametric study is carried out by plotting some graphs of thermal, concentration, and momentum profiles. In the light of paramedic study, it is noted that from the plots of field variables with slip condition are higher than that with the no‐slip condition. The constant proportional Caputo (CPC) fractional derivative is a best choice to get more stable temperature, concentration, and velocity fields than that of ordinary fields. More precisely, fractional parameter controls the boundary thickness of temperature, concentration, and velocity fields.

On the characterization of constitutive equations for third-grade viscous Korteweg fluids

We consider a model of a third-grade viscous Korteweg-type fluid in three space dimensions and apply the extended Liu procedure in order to explicitly solve the constraints imposed by the entropy principle on the nonlocal constitutive relations. We detail the algorithm we use and are able to characterize the material functions involved in the constitutive equations. In a natural way, the application of the extended Liu procedure allows us to recover an extra-term in the entropy flux, preserving all the features of third-grade viscous Korteweg-type fluids. Moreover, a further constraint, in order to avoid that at equilibrium only very special phase boundaries are admissible, is investigated.

Modified shallow water model for viscous fluids and positivity preserving numerical approximation

Shallow water equations are widely used in the simulation of those geophysical flows for which the flow horizontal length scale is much greater than the vertical one. Inspired by the example of lava flows, we consider here a modified model with an additional transport equation for a scalar quantity (e.g., temperature), and the derivation of the shallow water equations from depth-averaging the Navier-Stokes equations is presented. The assumption of constant vertical profiles for some of the model variables is relaxed allowing the presence of vertical profiles, and it follows that the non-linearity of the flux terms results in the introduction of appropriate shape coefficients.The space discretization of the resulting system of hyperbolic partial differential equations is obtained with a modified version of the finite volume central-upwind scheme introduced by Kurganov and Petrova in 2007. The time discretization is based on an implicit-explicit Runge-Kutta method which couples properly the hyperbolic part and the stiff source terms, avoiding the use of a very small time step; the use of complex arithmetic increases accuracy in the implicit treatment of stiff terms. The whole scheme is proved to preserve the positivity of flow thickness and the stationary steady-states.Some numerical experiments are performed to validate the proposed method and to show the incidence on the numerical solutions of shape coefficients introduced in the model.

Hydrodynamic attractor of a hybrid viscous fluid in Bjorken flow

The nonequilibrium evolution in a boost-invariant Bjorken flow of a hybrid viscous fluid model containing two interacting components with different viscosities, such that they represent strongly and weakly self-coupled sectors, is shown to be characterized by a hydrodynamic attractor which has an early-time behavior that is reminiscent of the so-called bottom-up thermalization scenario in heavy-ion collisions. The hydrodynamization times for the two sectors can differ strongly, with details depending on the curve realized on the two-dimensional attractor surface, which might account for different scenarios for small and large systems in nuclear collisions. The total system behaves like a single viscous fluid with a dynamically determined effective shear viscosity.

Global Dynamics of 3-D Compressible Micropolar Fluids with Vacuum and Large Oscillations

This paper deals with the Cauchy problem to three-dimensional compressible viscous and heat-conducting micropolar fluid model. We establish the global existence and uniqueness of classical solution to this specific system with small initial energy. In particular, the small initial energy allows the solution to have large oscillations and initial density may contain a vacuum.

Flow analysis of conical spiral mandrel dies

Spiral dies are divided into three categories, namely: Flat Spiral Die (FSD), Cylindrical Spiral Mandrel Die (SMD), and Conical Spiral Mandrel Die (CSD). These dies are used to produce films via blown film extrusion and multilayer films via co-extrusion. The goal is to improve the flow distribution and to decrease the pressure drop which will result in uniform film thickness and reduced energy dissipation. A viscous power-law fluid model shows that low-pressure drop and proper flow distribution can be achieved in a CSD simultaneously. As the number of grooves and the initial channel depth increases, the flow distribution becomes more uniform and the pressure drop decreases. Also, there is an optimum initial clearance and clearance increment angle. The model results show that the pseudo-plastic fluid has more appropriate performance than the Newtonian and dilatant fluids in improving the flow distribution and reducing the pressure drop.

Numerical Solution of a Two Dimensional Tumour Growth Model with Moving Boundary

We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls the birth and death rate of the tumour cells. The cell volume fraction, cell velocity--fluid pressure system, and nutrient concentration are the model variables. A coupled system of a hyperbolic conservation law, \cred{a viscous fluid model}, and a parabolic diffusion equation governs the dynamics of the model variables. The tumour boundary moves with the normal velocity of the outermost layer of cells, and this time--dependence is a challenge in designing and implementing a stable and fast numerical scheme. We recast the model into a form where the hyperbolic equation is defined on a fixed extended domain and retrieve the tumour boundary as the interface at which the cell volume fraction decreases below a threshold value. This procedure eliminates the need to track the tumour boundary explicitly and the computationally expensive re--meshing of the time--dependent domains. A numerical scheme based on finite volume methods for the hyperbolic conservation law, Lagrange $\mathbb{P}_2 - \mathbb{P}_1$ Taylor--Hood finite element method for the \cred{viscous} system, and mass--lumped finite element method for the parabolic equations is implemented in two spatial dimensions, and several cases are studied. We demonstrate the versatility of the numerical scheme in catering for irregular and asymmetric initial tumour geometries. We present numerical simulations for both cases and the results are consistent with theoretical and heuristic expectations such as early linear growth rate and preservation of radial symmetry when the boundary conditions are symmetric.

Unified thixotropic fluid model for soil liquefaction

The geotechnical earthquake engineering profession has struggled with the inherent complexity of the multiphase soil response to cyclic loading owing to the progressive nature of the generation of excess pore pressure (EPP) and degradation of soil stiffness and strength. One approach to improve understanding of the cyclic response and correlate the transition from a two-phase saturated soil to a single, fluid-phase liquefied soil is to treat the soil as a non-Newtonian viscous liquid. However, the work to date suggests that the viscous fluid model approach can only be implemented following the onset of sustained soil liquefaction. This paper presents a unified thixotropic fluid model and framework that effectively links the pre-shear soil fabric and its progressive cyclic response to the onset and maintained state of soil liquefaction. The framework treats the soil fabric as a fluid net-type structure proposed for use with thixotropic fluids, and presents the constitutive state and rate equations describing the deconstruction of the liquefiable soil fabric in response to cyclic loading. The unified framework uses physically meaningful soil parameters that can be obtained from common cyclic laboratory tests to seamlessly link the state-dependent and shear-strain-rate-dependent nature of soils to the generation of EPP, the latter of which is shown to increase in significance as EPP accumulates. The proposed thixotropic-induced excess pore pressure model should prove advantageous for use in forward modelling of the stress–strain rate response of liquefiable soil and generation of EPP.

The Effect of Draft Ratio of Side-By-Side Barges on Fluid Oscillation in Narrow Gap

In the present study, the effects of the draft ratio of the floating body on the fluid oscillation in the gap are investigated by using the viscous fluid model. Numerical simulations are implemented by coupling wave2Foam and OpenFOAM. The Volume of Fluid (VOF) model is used to capture the free surface waves. It is verified that the numerical results agree well with the experimental and other results. It is firstly found that, within the water depth range investigated in the present study, the depth of the wave tank has a significant effect on the numerical results. As the depth of the wave tank increases, the oscillation amplitude of the narrow-gap fluid largely decreases and the resonant frequency of the fluid oscillation in the narrow gap increases. The results also reveal that the draft ratio of floating bodies has a significant nonlinear influence on the resonant frequency and on the oscillation amplitude of the fluid in the narrow gap. With an increase in the draft of either the floating body on the wave side or the one on the back wave side, the resonant frequency decreases. The increase in the draft of the floating body on the wave side causes an increase in the reflection wave coefficient and leads to a drop in the fluid oscillation amplitude, and the increase in the draft of the floating body on the back wave side triggers a decrease in the reflection wave coefficient and results in an increase in the fluid oscillation amplitude. Meanwhile, the viscous dissipation induced by the fluid viscosity synchronously increases with the oscillation amplitude of the fluid in the increasing gap. Moreover, it is found that the draft ratio mainly affects the horizontal force of the floating body on the back wave side and that the highest calculated force increases with the draft ratio.

Cosmological viscous fluid models describing infinite time singularities in f(T) gravity

In this paper we explore the state parameter behaviour of the interacting viscous dark energy in f(T) gravity. Using constant deceleration parameter we investigate the cosmological implications of the viscosity and interaction between the dark components (energy and matter) in terms of Redshift. So doing, the viscosity and the interaction between the two fluids are parameterized by constants delta and xi respectively. In the later part of the paper, we explore some bulk viscosity models describing Little Rip and Pseudo Rip future singularities within f(T) modified gravity. We obtain gravitational equations of motion for viscous dark energy coupled with dark matter. Solving these equations, we found analytic expressions for characteristic properties of these cosmological models.

Utilization of hall current and ions slip effects for the dynamic simulation of peristalsis in a compliant channel

The recent hypothetical analysis is to explore the effect of hall current and ion's slip for a peristaltic mechanism of non-Newtonian Rabinowitsch fluid model (lubricant blended with the viscosity index reformer) with the dynamic damping and stiffness features. The mathematical model is examined by considering the assumptions of low Reynold's number and long wavelength, the governing system of non-linear differential equations are solved with the help of the perturbation technique. The impact of numerous parameters associated with a fluid flow such as viscous damping, stiffness, rigidity, Hall parameter and Brickman number are intrigued for velocity profile, temperature distribution, and concentration profile. Results are strategized and deliberated for shear thickening, shear-thinning, and a viscous fluid model. It is observed that the momentum distribution is enhanced for larger values of stiffness, rigidity and viscous damping force parameters, but quite reverse nature is depicted for thermal distribution. The variations of streamline are presented graphically for the Hartman number and elastic parameters. Brinkman number is related to the viscous dissipation effects, so it contributes to enhancing the thermal distribution of fluid for all cases.

A STUDY OF TRANSIENT FLOWS WITH INTERFACES USING NUMERICAL SOLUTION OF NAVIER–STOKES EQUATIONS

Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier–Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh–Taylor instability, and a film flowing down a vertical wall in an extended region.

Attractors of an Autonomous Model of Nonlinear Viscous Fluid

For an autonomous model of the motion of a nonlinear viscous fluid, we study the limiting behavior of its weak solutions as time tends to infinity. Namely, the existence of weak solutions on the positive half-axis is established, the trajectory space corresponding to the solutions of this model is determined, and the existence of a minimum trajectory attractor and, then, a global attractor in the phase space is proved using the theory of trajectory spaces. Thus, it turns out that whatever the initial state of the system describing the model is, it is “forgotten” over time and the global attractor is infinitely approached.

On the correct use of mathematical constructions in physical models

The physical limitations of the mathematical constructions used in developing or modifying mathematical models are discussed. All reasonings are illustrated by examples from fluid mechanics. The following topics are considered: means of description; correct approach to model modification and the physical meaning of model development stages. In the first case, the method of describing physical objects using numbers as well as corresponding restrictions are investigated, followed by developing general recommendations on procedures for modifying mathematical models of fluid dynamics. The well-known procedure of averaging the viscous fluid model equations to obtain the turbulent fluid model is used as an illustration. Since we are considering the models of physical phenomena, it is natural to provide physical interpretation for each stage of model development. Unfortunately, some of the transformations used are often treated as purely technical tricks, therefore denoting the lack of the physical meaning in such cases, which does not make a mathematical procedure unacceptable, but does mark out the model's place which requires reasonable interpretation. In this paper, we are considering two variants of this kind of interpretation, namely the case of using imaginary quantities, and the case of applying integral transformations. Meanwhile, all the above-mentioned restrictions are not always given due attention. Sometimes this leads to various undesirable consequences, including excessive task complication, implicit substitution of a declared problem with another one, or, finally, lack of solution to the formulated problem.

Modeling the gravitational flows of a viscoplastic fluid on a conical surface

рідка плівка,The problem of a stationary waveless gravitational flow of a viscoplastic fluid over the surface of a cone with an arbitrary smooth cross section is considered. It is assumed that the axis of the body is located at a certain angle to the vertical, and the film of liquid flows down from its top. A curvilinear orthogonal coordinate system (ξ, η, ζ) associated with the body surface is introduced: ξ is the coordinate along the generatrix of the body, η is the polar angle in the plane perpendicular to the axis of the body of revolution, ζ is the distance along the normal to the surface. To describe the flow of a liquid film, a viscous incompressible fluid model is used, which is based on partial differential equations - the equations of motion and continuity. The following boundary conditions are used: sticking conditions on the solid surface; on the surface separating liquid and gas, the conditions for continuity of stresses and normal component of the velocity vector. To close the system of differential equations, the Shvedov-Bingham rheological model is used. To simplify the system of differential equations, the small parameter method is used. The small parameter is the relative film thickness. It is assumed that the generalized Reynolds number has an order equal to one. The solution of the equations of continuity and motion (taking into account the principal terms of the expansion) was obtained in an analytical form. The obtained formulas for the components of the velocity and pressure vector generalize the known relations for flat surfaces. To determine the unknown film thickness, an initial-boundary value problem was formulated for a first-order partial differential equation. The solution to this problem is found with the help of the finite difference method. The results of calculations by the proposed method for cones with a cross section in the form of a circle and a square with rounded corners are presented. Calculations show that the plasticity parameter and the cross-sectional shape significantly affect the velocity and distribution profiles of the thickness of the viscous layer over the surface of the body.

Analysis of mathematical model of fractional viscous fluid through a vertical rectangular channel

Unsteady motion of a viscous fluid passing through a vertical channel with MHD (magnetohydrodynamics) effect has been analyzed in this manuscript. Fractional model is developed by two approaches, namely; Caputo fractional time derivatives with singular kernel and Caputo–Fabrizio fractional time derivatives with non-singular kernel. Analytical solutions have been obtained via Laplace transform method after converting the governing equations into dimensionless form and presented graphical analysis of the obtained results in terms of comparison. The effect of fractional and other flow parameters on temperature, concentration and velocity fields is seen, respectively. As a result, we have found that for the physical model with fractional derivative of Caputo–Fabrizio, temperature, concentration and velocity have greater values in comparison with Caputo one. It is also noted that velocity has shown dual nature for large and small time. Further, rates of heat and mass transfer and skin friction can also be enhanced for the small values of non-integer order parameter and are presented in Table 1.