Ordinary Fluid Research Articles

Quantum kinetic theory of flux-carrying Brownian particles

We develop the kinetic theory of the flux-carrying Brownian motion recently introduced in the context of open quantum systems. This model constitutes an effective description of two-dimensional dissipative particles violating both time-reversal and parity that is consistent with standard thermodynamics. By making use of an appropriate Breit–Wigner approximation, we derive the general form of its quantum kinetic equation for weak system-environment coupling. This encompasses the well-known Kramers equation of conventional Brownian motion as a particular instance. The influence of the underlying chiral symmetry is essentially twofold: the anomalous diffusive tensor picks up antisymmetric components, and the drift term has an additional contribution which plays the role of an environmental torque acting upon the system particles. These yield an unconventional fluid dynamics that is absent in the standard (two-dimensional) Brownian motion subject to an external magnetic field or an active torque. For instance, the quantum single-particle system displays a dissipationless vortex flow in sharp contrast with ordinary diffusive fluids. We also provide preliminary results concerning the relevant hydrodynamics quantities, including the fluid vorticity and the vorticity flux, for the dilute scenario near thermal equilibrium. In particular, the flux-carrying effects manifest as vorticity sources in the Kelvin’s circulation equation. Conversely, the energy kinetic density remains unchanged and the usual Boyle’s law is recovered up to a reformulation of the kinetic temperature.

Analysis of natural convection flows of Jeffrey fluid with Prabhakar-like thermal transport

The free convection flow of Prabhakar fractional Jeffrey fluid on an oscillated vertical plate with homogenous heat flux is investigated. With the help of the Laplace transform and the Boussinesq's approximation, precise solutions for dimensionless momentum may be found. The temperature and velocity of Prabhakar fractional time free convection flows are compared to conventional thermal transport, as shown by Fourier's law. They met all of the requirements and recovered Newtonian and ordinary Jeffrey fluid solutions from fractional Jeffrey fluid. Finally, graphs show the effect of various physical parameters such as fractional parameters, Grashof number, Prandtl number and Jeffrey parameters on both temperature and velocity.

On the Yield Stress of Magnetorheological Fluids

• Effect of magnetic field and particle volume fraction are investigated experimentally. • MRFs with different particle concentration are tested through steady stress sweep test. • A nonlinear model is proposed for the yield stress of MRFs. • Model includes two parameters, covers a wide field range and captures magnetic saturation. • A modified form of the magnetic dipole model is also proposed. Magnetorheological fluids (MRFs) are a category of functional materials that exhibit magneto-mechanical coupling. These materials exhibit a reversible and instantaneous change from a free-flowing Newtonian fluid to a semi-solid state upon application of a magnetic field. In contrast to ordinary fluids, MRFs can tolerate shear stresses up to a yield value in the presence of a magnetic field. The yield stress strongly depends on intensity of the applied magnetic field and volume fraction of magnetic particles. As the yield stress is the most important parameter of an MRF and must be considered in the design of MR devices, in this work, effects of magnetic field and volume fraction of particles are investigated both experimentally and theoretically. MRF samples with the same carrier fluid but different particle concentrations are analyzed, and an empirical model is proposed for the yield stress of MRFs that covers a wide field strength range and also captures magnetic saturation of the MR fluids. Though the model is mathematically simple, it also includes the effect of particle concentration such that once calibrated, it can be utilized for different particle concentrations as well. Moreover, a modified form of the magnetic dipole model is proposed to model the yield stress of MRFs where an exponential distribution function is utilized to describe the arrangement of particle chains in the presence of a magnetic field. It is shown that, though the model has a simple mathematical formulation, it leads to a reasonable distribution of chains compared to previous similar models.

Thermal Instability and Chaos in a Hybrid Nanofluid Flow

In this work, the linear and nonlinear dynamics of thermal convection in an incompressible Newtonian (alumina-copper)/water hybrid nanofluid each confined in an infinite rectangular cavity and heated from below via the Cattaneo–Christov heat flux model are studied for volume fractions fixed between 0 and 0.05. Firstly, using the governed flow equations and free boundary conditions, we proceed to the classical theory of stationary and oscillatory convection which help us to find the expressions of critical Rayleigh numbers, Cattaneo numbers and wavenumber of base fluid as a function of mono or hybrid nanofluid thermophysical properties. The results show that when the Cattaneo number increases, the critical Rayleigh number is constant in the case of stationary convection but decreases in the case of oscillatory convection for pure base fluid and hybrid nanofluids. It is noted that beyond the threshold Cattaneo number, the critical Rayleigh number of stationary convection is greater than those of oscillatory convection and the critical wavenumber shifts discontinuously from stationary to oscillatory convection. Secondly, the use of the truncated Galerkin approximation made it possible to find a five low-dimensional system in order to study numerically the transition from natural convection to chaotic behavior of nanofluid. We noticed that the addition of hybrid nanoparticle in the heat fluid transfer increases the domain of stationary convection by delaying the oscillatory convection with increasing normalized Rayleigh number. Also, the bifurcation diagrams show that the use of hybrid nanoparticles allows further control of the chaos in base fluid by expanding the convective flow. Furthermore, in the presence of thermal relaxation time, the chaos in the hybrid nanofluid lasts longer compared to the ordinary fluid.

Heat transfer analysis of hybrid nano-fluid through porous medium


 
 
 The main focus of this paper is to use water based hybrid nanofluid in place of ordinary fluid in porous medium to improve thermal properties. This paper deals with the effect of MHD and chemical reaction on a hybrid nanofluid through porous medium with suction/injection. We also studied the effects of MHD, heat source, suction/injection and chemical reaction influences on a hybrid nanofluid. Two types of nano particles namely copper (Cu) and Aluminum oxide (Al2O3) are suspended in base fluid (water) to form the hybrid nanofluid. Similarity transformations are used to change ordinary differential equations to partial equations, and then solved solved by perturbation method. Numerical investigation is carried out to test Skin friction, heat and mass transfer coefficient for different geometrical parameters.
 
 

Study on the flow and heat transfer characteristics of liquid sodium in a hexagonal 7-rod bundle

The flow and heat transfer characteristics of liquid metal sodium are different from the ordinary fluids, which brings great challenges to the CFD simulation in the sodium-cooled fast reactor (SFR). Therefore, the accurate flow and heat transfer models are particularly significant in the high fidelity three dimensional analysis of liquid metal reactors. In this paper, the OpenFOAM solver implemented with k – ε – kθ – εθ turbulent heat transfer model was developed and used to study the flow and heat transfer characteristics of liquid metal sodium. Firstly, the proposed thermal hydraulic models were validated against the thermal hydraulic experiment of single-phase liquid sodium in a 7-rod bundle. The key thermal hydraulic parameters, such as the Nusselt number, pressure drop and frictional coefficient, were compared with the experimental data. Results show that the developed OpenFOAM solver with new implemented model performs well and the simulated results were in good agreement with the experimental data. Then the thermal–hydraulic characteristics of liquid sodium in the bend rod bundle were investigated. The effects of bending angle, Reynolds number on peak wall temperature and Nusselt number were investigated. CFD results suggest that the heat transfer in the bend rod bundle is highly sensitive to the bending angle but not to Reynolds number. Two opposite-direction cross flows were formed in the sections before and after the maximum bend position, which reveals the formation and disappearance of hot spot in the narrow gap.

Experimental Study on the Pressure Transfer Mechanism of Embedded Magnetic Fluid Seals

Although the sealing mechanism of the embedded magnetic fluid seal is unclear, it is an effective way to improve the performance of the ordinary magnetic fluid seal. Embedded magnetic seals can be divided into diverging and converging embedded magnetic fluid seals, according to the direction of leakage of the sealed medium. This article mainly focuses on presenting a sealing device that can observe the change in the shape of the magnetic fluid film and investigate the mechanism of diverging and converging embedded magnetic fluid seals. The pressure transfer mechanism of the embedded magnetic fluid seal with a large gap was studied through experiments. Numerical analysis of the magnetic field distribution in the seal gap and calculation of the theoretical pressure capacity of the embedded magnetic fluid seal are produced on the basis of embedded magnetic fluid seal theory. The experimental pressure capacity is compared with the theoretical pressure capacity to verify the correctness of the embedded magnetic fluid seal pressure capacity theory. The research has investigated the effect of the number of magnetic fluid film ruptures on the self-restoring capacity of embedded magnetic fluid seals, compared with the self-restoring capacity of diverging and converging embedded magnetic fluid seals, and analyzed the data. The results illustrated that the experimental pressure capacity of the embedded magnetic fluid seal matched well with the theoretical pressure capacity, which verifies the correctness of the embedded magnetic fluid seal theory. The pressure transfers from one chamber to another when the pressure difference between the two sides of the magnetic fluid film under the pole tooth is larger than the pressure capacity of the magnetic fluid seal, and the air will enter from the high-pressure side seal chamber to the low-pressure side seal chamber, in turn. As the inlet pressure increases, the pressure trend in the radial chamber of the embedded magnetic fluid seal differs from that in the axial chamber. When the seal fails, the magnetic fluid shows microleakage and complete leakage. As the number of magnetic fluid film ruptures increases, the self-restoring capacity first decreases and then increases. The self-restoring capacity of the converging embedded magnetic fluid seals is better than that of the diverging embedded magnetic fluid seals.

A time fractional model of Brinkman-type nanofluid with ramped wall temperature and concentration

Nanofluid is an innovative heat transfer fluid with the potential to significantly enhance the heat transfer performance of traditional fluids. By adding various types of nanoparticles to ordinary base fluids, several attempts have been made to boost the rate of heat transfer and thermal conductivity. The unsteady electrically conducting flow of Brinkman-type nanofluid over an infinite vertical plate with ramping wall temperature and concentration is investigated in this article. Water is taken as the base fluid, and multi-walled carbon nanotubes are distributed equally throughout it. The Caputo-Fabrizio fractional derivative, which has a non-singular kernel, is used to generalize the classical model. The Laplace transform technique has been utilized to achieve exact solutions. Furthermore, various graphs for fractional and physical parameters are used to represent the solutions. All figures are drawn for both conditions, that is, ramped and isothermal wall temperature and concentration. The velocity field increases for greater values of thermal and mass Grashof numbers while the reverse effect is observed for Hartman number, Brinkman parameter and volume fraction. Moreover, the obtained results are also reduced to the already published results in order to show the validation of the present results. The results are used to calculate the skin friction, Nusselt number, and Sherwood number. The heat transfer of pure water is increased by 17.03% when 4% of nanoparticles are added to it which will of course increase the efficiency of solar collectors and solar pools. Moreover, the mass transfer decreases by 3.18% when 4% of nanoparticles which are dispersed in it.

How an Oxide Layer Influences the Impact Dynamics of Galinstan Droplets on a Superhydrophobic Surface.

When exposed to air, gallium-based alloys rapidly form a thin oxide layer with viscoelasticity and high adhesion. Although previous work demonstrated that an oxide layer inhibits liquid metal droplet rebound, there is still a lack of a quantitative study to elaborate how an oxide layer affects the impact dynamics. To address this issue, we experimentally investigate Galinstan droplet impingement on a superhydrophobic CuO nanoblade surface and physically explain the difference in the dynamic characteristics of oxidized and unoxidized droplets. Experimental results show that the effect of an oxide layer becomes prominent during the retraction phase. The high adhesion significantly suppresses retraction and rebound, while the elastic response prevents a droplet from sufficiently stretching and maintains the stability of the morphology. More importantly, we systematically and quantitatively explore the influence of an oxide layer on several critical impact parameters, which contributes to a comprehensive understanding of the impact dynamics of liquid metal droplets. It is indicated that an oxide layer has little effect on the maximum spreading factor and spreading time, whereas it causes a 45% reduction of the restitution coefficient and a 36% increase in contact time. Notably, the scaling laws that describe the critical impact parameters of unoxidized droplets show good agreement with the ones known from ordinary Newtonian fluids.

Numerical simulation of a low Prandtl number flow with a four-parameters turbulence model through an explicit algebraic definition of Reynolds stress and turbulent heat flux

Computational Fluid Dynamics codes usually adopt the Reynolds analogy in order to simulate dynamic and thermal flow fields for ordinary fluids like water and air. On the other hand, in low Prandtl fluids, such as heavy liquid metals like Lead-Bismuth Eutectic (LBE), the time scales of temperature and velocity fields are rather different and therefore similarity hypothesis cannot be used. Furthermore, to properly predict a complex flow field characterized by anisotropic behavior, it is necessary to overcome eddy-viscosity models and move to more advanced turbulence models. In the present work, we propose a nonlinear method for the computation of the Reynolds stress tensor and of the turbulent heat flux. Explicit algebraic models (EAM) and new time scales have been implemented using a logarithmic four parameters turbulence model (i.e. K-Ω-K θ -Ω θ ). This new model is validated through the simulation of plane channel and cylinder flows and results are compared with DNS data.

Experimental Study on Divergent Magnetic Fluid Seal with Small Clearance and Double Magnetic Source

In order to solve the problem of poor sealing performance of rotating machinery under the condition of small clearance, a new type of divergent magnetic fluid seal device with small clearance and double magnetic source is designed in this paper. The effect of magnetic fluid injection, tooth number and sealing clearance on the sealing pressure resistance of dual magnetic source divergence were studied and compared with the experimental value of ordinary magnetic fluid seal. The experiment results show that the pressure resistance ability of divergent magnetic fluid seal is at least 3 times that of ordinary magnetic fluid seal, which verifies the correctness of divergent magnetic seal with small clearance and double magnetic source pressure resistance theory, and has important theoretical guiding significance for solving the problem of poor magnetic fluid seal performance under small clearance.

Entropy analysis of radiative [MgZn6Zr-Cu/EO] Casson hybrid nanoliquid with variant thermal conductivity along a stretching surface: Implementing Keller box method

Heat transfer is critical due to its broad application in a variety of industries. New hybrid nanofluids are being used to improve the heat transfer competencies of ordinary fluids and have an enormous exponent heat than nanofluids. Hybrid nanofluids, a novel form of nanofluid, are being utilized to improve the heat transfer capacities of regular fluids and have a more outstanding heat exponent than nanofluids. Two-element nanoparticles submerged in a base fluid make up the hybrid nanofluids. Flow and heat transport properties of a hybrid nanofluid across a slick surface are studied in this study. Nanoparticle shape analysis, porous media, thermal conductance variations, and thermal radiative effects are all part of the process. A numerical approach called the Keller box method is used to solve the governing equations numerically. EO-Engine Oil has been used as a rich, viscous base fluid in this study, and a Cason hybrid nanofluid was examined. This fluid contains two diverse forms of nanoparticles: Copper (Cu) and Magnesium Zinc Zirconium alloy (MgZn6Zr). Compared to standard Cu-EO nanofluids, the heat transmission level of such a fluid (MgZn6Zr-Cu/EO) has steadily increased, which is an important finding from this study. The boundary-lamina-shaped layer's components have the highest thermal conductivity, while sphere-shaped nanoparticles have the lowest. When nanoparticles are assimilated, the entropy of the system increases by a factor of three: their ratio by fractional size, their radiative properties, and their thermal conductivity variations.

Pulsatile Darcy flow of water‐based thermally radiative carbon nanotubes between two concentric cylinders

AbstractIt is perceived that the addition of nanoparticles has increased the heat transfer capabilities of ordinary fluids significantly for both turbulent and laminar flow regimes. The current investigation analyzes the effects of carbon nanotubes (CNTs) on the pulsatile flow and heat transfer characteristics of viscous fluid between two concentric cylinders in the presence of thermal radiation effects. The flow of Magneto‐hydrodynamic (MHD) viscous fluid in a Darcy type porous medium is driven by the pressure gradient, assumed as a periodic function of time. The fluid is taken as optically thick and radiations can travel only a short distance within the fluid. The magnetic field is applied perpendicular to the direction of flow and the induced magnetic field is considered negligible. The conventional governing equations are based upon partial differential equations affected by the viscosity of the base fluid, effective thermal conductivity, and thermophysical characteristics of CNTs nanoparticles. The exact solutions are obtained in the form of the modified Bessel functions of the first and second kind. The effect of the flow control parameters like thermal radiation parameter , nanoparticles volume fraction , and Darcy number are illustrated through graphs. Based on a comprehensive analysis, it is concluded that the addition of single‐walled carbon nanotubes provides higher velocity and temperature distribution of nanofluid when compared with the multi‐walled carbon nanotubes.

An improved thermal model for predicting wellbore temperature distribution in deep-water gas well

Accurate prediction of wellbore temperature plays an extremely important role in the production design of deep-water gas wells. This study overcomes the shortcomings of the previous literature in temperature calculations, comprehensively studies the heat transfer mechanism in the annulus and tubing, and an improved thermal model for predicting wellbore temperature in deep-water gas well is established. This model includes two important innovations: the natural convection heat transfer model in the annulus and the gas–liquid two-phase heat transfer model in the tubing. Firstly, the mechanism of heat transfer through natural convection in annulus is revealed by a numerical study, and a new calculation method for the annulus convective-heat-transfer coefficient, which can be applied to non-Newtonian fluids, is proposed. Secondly, considering that the two-phase flow in the tubing often presents an annular-mist flow in water-bearing gas well, a heat transfer model of the annular-mist flow in the tubing is developed considering the gas–liquid distribution characteristics and droplet dynamics. The results obtained using this improved thermal model are in good agreement with the field data of deep-water gas well, and the model prediction error is within 10%. Further, the sensitivity analysis is carried out on the parameters of annulus testing fluid that affect the wellbore temperature, and a novel solution for the annular insulation testing fluid was designed. Compared with ordinary annulus testing fluids, the wellbore temperature are more than doubled after adopting the new solution, thereby providing effective guidance for the development of insulation testing fluid system during deep-water gas well testing.

Transverse oscillations of the incompressible MHD mode in the visco-resistive plasmas: an explanation of Alfvénic to Landau-type characteristics

ABSTRACT In this paper, we characterize transverse oscillations as either Alfvénic or Landau-type in an incompressible non-ideal magnetohydrodynamic (MHD) fluid. We consider shear viscosity and magnetic diffusivity as dissipation mechanisms to derive a general dispersion relation for the incompressible MHD waves. The solutions of this dispersion relation for k as a function of ω – denoting by the source for any value of θ up to which magnetic tension acts as restoring force and dominates over internal friction forces – result in four roots, as follows. Two roots, which have a high phase velocity $c_{\rm A}\cos\theta $ are identified as almost undamped propagating Alfvén waves. The other two roots, which have a phase velocity $(2c_{\rm A}\cos\theta)/(\sqrt{\eta/\nu} + \sqrt{\nu/\eta})$, result in Alfvénic-type disturbances of a much shorter decay length than the wavelength. In contrast, when internal frictional forces start dominating over magnetic tension (i.e. for the propagation perpendicular to the background magnetic field, where the tension in the magnetic field becomes zero), the solutions of the dispersion are akin to Landau-type transverse oscillations. Transverse waves of this type were initially reported by Landau in an ordinary viscous fluid. However, our study corresponds to MHD visco-resistive fluid. The prediction for these lateral propagating transverse waves to be of Landau type may be very useful to explain the heating of observed filamentary structures across the magnetic field on a very small spatial scale in the solar coronal plasma, wherein the heating rate is directly proportional to the operating frequency of the driver, while its damping length is inversely proportional to the square root of the frequency.

Thermal flow analysis of self-driven temperature-sensitive magnetic fluid between partially heated parallel plates

To develop a heat transfer device based on a temperature-sensitive magnetic fluid (TSMF), it is necessary to investigate its flow and heat transfer characteristics. This study used the fractional step method to numerically investigate the flow and heat transfer characteristics of TSMF between parallel plates with small spacing when the solenoidal magnetic field is applied. Due to the influence of the magnetic field and temperature, the flow characteristics of the TSMF between the plates are significantly different from ordinary working fluids such as oil, and the fluid near the plate flows faster than the fluid near the center. We used numerical analysis to analyze the formation of this phenomenon and investigated the influence of dimensionless Prandtl number and magnetic effect parameter on this phenomenon. As the result, the heat transfer increased with the increase of the magnetic effect parameter which is affected by the magnetic field or the distance between the plates. The center between the two plates in the heating region formed a vortex under high Prandtl number conditions, and the generation of the vortex enhanced the heat transfer.

Design and Experimental Study on Divergent Magnetic Fluid Seal with Large Clearance and Dual Magnetic Sources

In order to solve the leakage problem of rotating machinery under the condition of large clearance, a new type of divergent magnetic fluid sealing device with secondary magnetic source was designed. The magnetic field distribution in the clearance of the magnetic fluid seal was simulated by the finite element method of magnetic field, and the theoretical value of the sealing pressure resistance was calculated according to the pressure resistance theory of the divergent magnetic fluid seal. The influences of the volume of magnetic fluid injection, the number of teeth, the clearance, and the eccentricity of the rotating shaft on the pressure resistance abilities of divergent magnetic fluid seal were studied by experimental method and compared with the pressure resistance experimental value of ordinary magnetic fluid seal. The results showed that when the injection volume of magnetic fluid is more than 3 ml, the sealing pressure resistance ability of the magnetic fluid does increase greatly and tends to be stable gradually. The saturated magnetic fluid injection volume of divergent magnetic fluid seal with large clearance is 3 ml. With the increase of radial teeth, the pressure resistance ability of magnetic fluid seal first increases and then decreases. With the increase of axial teeth, the pressure resistance ability of magnetic fluid seal also increases. With the increase of radial clearance, the pressure resistance value of magnetic fluid seal first increases and then decreases. With the increase of axial clearance, the pressure resistance value of magnetic fluid seal decreases. The pressure resistance ability of divergent magnetic fluid seal is significantly higher than that of ordinary magnetic fluid seal.

English

Two isothermal motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are investigated when gravity effects are taken into account. The fluid motion, between two infinite horizontal parallel plates, is generated by the lower plate that applies a time-dependent shear stress to the fluid. Exact expressions are established for the steady-state components of the dimensionless start-up velocity, shear stress, and normal stress. They are used to find the needed time to touch the steady-state and to provide corresponding solutions for the motion of the same fluids induced by an exponential shear stress on the boundary. This time is useful for experimentalists who want to eliminate transients from their experiments. It is higher for motions of ordinary fluids as compared to fluids with pressure-dependent viscosity. The variation of starting solutions (numerical solutions) in time and space is graphically represented and some characteristics of the fluid motion are brought to light.

Analytical Solution of Fractional Oldroyd-B Fluid via Fluctuating Duct

This investigation focuses on the mixed initial boundary value problem with Caputo fractional derivatives. The studied pour an incompressible fractionalized Oldroyd-B fluid prompted by fluctuating rectangular tube. The explicit expression of the velocity field and shear stresses for the fractional model are obtained by utilizing the integral transforms, i.e., double finite Fourier sine transform and Laplace transform. Furthermore, the confirmation of the analytical solutions is also analyzed by utilizing the Tzou’s and Stehfest’s algorithms in the tabular form. In limited cases, ordinary Oldroyd-B fluid similar solutions and classical Maxwell and fractional Maxwell fluid are derived. The flow field’s graphs with the influences of relevant parameters are also mentioned.

Entropy Amplified solitary phase relative probe on engine oil based hybrid nanofluid

Heat transfer is of vital importance because of its application in industries. A new nanofluid class called "hybrid nanofluid" is being used to boost ordinary fluids' heat transfer capabilities and has a higher heat exponent than nanofluids. The hybrid nanofluids (HNFs) are associated with two-element nanoparticles immersed in a base fluid. The steady hybrid nanofluid flowing and thermal transport characteristics passed overhead a slippery surface are investigated in this research. The impact of nanosolid particle shapes, Porosity material, heat source, viscous dissipative flow, and radiative flux are also involved in this examination. In a regime of partial-differential equations (PDEs), the predominant flow equations are formulated. Keller-box's computational technique is the utilized method to detect the self-similar solution for formulas transformed into ordinary-differential equations (ODEs) through appropriate transmutations. Williamson hybrid nanofluid has been considered for this work, which consists of double diverse kinds of nanoparticle, Copper (Cu) and Silicon dioxide (SiO2) in the rich viscous based fluid of kind EO (Engine Oil). The noteworthy result of this analysis is that the comparing thermal transmission level of such kind of fluid (SiO2Cu/EO) which has progressively more upsurges as compared to traditional nanofluids (Cu-EO). The lamina-shaped elements cause the utmost important thermal conductivity in the boundary- layer, whilst the lowermost thermal conductivity is detected in sphere shaped nanoparticles.