Effects of multiple shapes for steady flow with transformer oil+Fe_(3)O_(4)+TiO_(2) between two stretchable rotating disks

In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.

Finite deformation analysis of the rotating cylindrical hollow disk composed of functionally-graded incompressible hyper-elastic material

The deformations and stresses of a rotating cylindrical hollow disk made of incompressible functionally-graded hyper-elastic material are theoretically analyzed based on the finite elasticity theory.The hyper-elastic material is described by a new micro-macro transition model.Specially,the material shear modulus and density are assumed to be a function with a power law form through the radial direction,while the material inhomogeneity is thus reflected on the power index m.The integral forms of the stretches and stress components are obtained.With the obtained complicated integral forms,the composite trapezoidal rule is utilized to derive the analytical solutions,and the explicit solutions for both the stretches and the stress components are numerically obtained.By comparing the results with two classic models,the superiority of the model in our work is demonstrated.Then,the distributions of the stretches and normalized stress components are discussed in detail under the effects of m.The results indicate that the material inhomogeneity and the rotating angular velocity have significant effects on the distributions of the normalized radial and hoop stress components and the stretches.We believe that by appropriately choosing the material inhomogeneity and configuration parameters,the functionally-graded material(FGM)hyper-elastic hollow cylindrical disk can be designed to meet some unique requirements in the application fields,e.g.,soft robotics,medical devices,and conventional aerospace and mechanical industries.

Dynamic analysis of rotating flexible disk subjected to double slider loading systems

Rotating disk subjected to stationary slider loading system is a very common mechanical structure. This paper investigates the multibody dynamics of a rotating flexible annular thin disk subjected to double slider loading systems. Along the rotating disk radial and circumferential directions, two stationary slider loading systems are distributed. System dynamic model is solved by Galerkin＇s method, and then natural frequency, dynamic stability and mode shape are determined with a quadratic eigenvalue problem. Effects of the distributing positions and interaction mechanism of the double slider loading systems on natural frequency, dynamic stability and mode shape are discussed and investigated.

Prediction of mass transfer coefficients in an asymmetric rotating disk contactor using effective diffusivity

Mass transfer characteristics have been investigated in a 113 mm diameter asymmetric rotating disk contactor of the pilot plant scale for two different liquid–liquid systems. The effects of operating parameters including rotor speed and continuous and dispersed phase velocities on the volumetric overall mass transfer coefficients are investigated. The results show that the mass transfer performance is strongly dependent on agitation rate and interfacial tension, but only slightly dependent on phase flow rates. In this study, effective diffusivity is used instead of molecular diffusivity in the Grober equation for estimation of dispersed phase overall mass transfer coefficient.The enhancement factor is determined experimentally and there from an empirical expression is derived for prediction of the enhancement factor as a function of Reynolds number. The predicted results compared to the experimental data show that the proposed correlation can efficiently predict the overall mass transfer coefficients in asymmetric rotating disk contactors.

Chemically reactive and radiative von Kármán swirling flow due to a rotating disk

A new mathematical model is presented to study the heat and mass transfer characteristics of magnetohydrodynamic(MHD) Maxwell fluid flow over a convectively heated stretchable rotating disk. To regulate the fluid temperature at the surface, a simple isothermal model of homogeneous-heterogeneous reactions is employed. The impact of nonlinear thermal radiative heat flux on thermal transport features is studied. The transformed nonlinear system of ordinary differential equations is solved numerically with an efficient method, namely, the Runge-Kutta-Felberg fourth-order and fifth-order(RKF45)integration scheme using the MAPLE software. Achieved results are validated with previous studies in an excellent way. Major outcomes reveal that the magnetic flux reduces the velocity components in the radial, angular, and axial directions, and enhances the fluid temperature. Also, the presence of radiative heat flux is to raise the temperature of fluid. Further, the strength of homogeneous-heterogeneous reactions is useful to diminish the concentration of reaction.

Recovery of Hg(Ⅱ)from aqueous solution by complexation-ultrafiltration using rotating disk membrane and shear stability of PMA-Hg complex

Copolymer of acrylic acid and maleic acid(PMA)was used to remove Hg^2+from aqueous solution by complexation-ultrafiltration(C-UF)through rotating disk membrane(RDM).The effects of P/M(mass ratio of PMA to metal ions),pH and rotation speed(N)on the interception of Hg^2+were investigated.The interception could reach 99.7%at pH 7.0,P/M 6 and N less than 1890 r/min.The shear stability of PMA-Hg complex was studied by RDM.The critical rotation speed,at which the interception starts to decrease,was 1890 r/min,and the critical shear rate,the smallest shear rate at which PMA-Hg complex begins to dissociate,was 2.50×10^5s^-1 at pH 7.0.Furthermore,the critical radii were obtained at different rotation speeds and pHs.The results showed that the critical radius decreased with the rotation speed and increased with pH.Shear induced dissociation coupling with ultra?ltration(SID-UF)was efficiently used to recover Hg^2+and PMA.

An Evaluation of Metronidazole Degradation in a Plasma-Assisted Rotating Disk Reactor Coupled with TiO2 in Aqueous Solution

Pollution involving pharmaceutical components in bodies of water is an increasingly serious environmental issue.Plasma discharge for the degradation of antibiotics is an emerging technology that may be relevant toward addressing this issue.In this work,a plasma-assisted rotating disk reactor(plasma-RDR)and a photocatalyst—namely,titanium dioxide(TiO_(2))—were coupled for the treatment of metronidazole(MNZ).Discharge uniformity was improved by the use of a rotating electrode in the plasma-RDR,which contributed to the utilization of ultraviolet(UV)light radiation in the presence of TiO_(2).The experimental results showed that the degradation efficiency of MNZ and the concentration of generated hydroxyl radicals respectively increased by 41%and 2.954 mg∙L^(-1) as the rotational speed increased from 0 to 500 r∙min^(-1).The synergistic effect of plasma-RDR plus TiO_(2) on the generation of hydroxyl radicals was evaluated.Major intermediate products were identified using three-dimensional(3D)excitation emission fluorescence matrices(EEFMs)and liquid chromatography-mass spectrometry(LC-MS),and a possible degradation pathway is proposed herein.This plasma-catalytic process has bright prospects in the field of antibiotics degradation.

Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors （SIFs） in rotating disks containing three-dimensional （3D） semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop- erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen- trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.

INTELLIGENT INTEGRATION CONTROL OF ROTATING DISK VIBRATION

The rotating disk is a basic machine part that is u sed widely in industry. The motion equation is transformed into the dynamic equa tion in real modal space. The personating intelligent integration is introduced to improve the existing control method. These modes that affect the transverse vibration mainly are included to simulate the vibration of rotating disk, and two methods are applied separately on condition that the sensor and the ac tuator are collocated and non collocated. The results obtained by all sided si mulations show that the new method can obtain better control effect, especially when the sensor and the actuator are non collocated.

Darcy-Forchheimer flows of copper and silver water nanofluids between two rotating stretchable disks

This investigation describes the nanofluid flow in a non-Darcy porous medium between two stretching and rotating disks. A nanofluid comprises of nanoparticles of silver and copper. Water is used as a base fluid. Heat is being transferred with thermal radiation and the Joule heating. A system of ordinary differential equations is obtained by appropriate transformations. Convergent series solutions are obtained. Effects of various parameters are analyzed for the velocity and temperature. Numerical values of the skin friction coefficient and the Nusselt number are tabulated and examined. It can be seen that the radial velocity is affected in the same manner with both porous and local inertial parameters. A skin friction coefficient depicts the same impact on both disks for both nanofluids with larger stretching parameters.

Numerical Simulation of Reiner–Rivlin Nanofluid Flow under the Influence of Thermal Radiation and Activation Energy over a Rotating Disk

In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical situations,the motile microorganisms are incorporated too.The multiple slip effects are considered in the boundary conditions.The bioconvection of motile microorganism is utilized alongside nanofluids to provide stability to enhanced thermal transportation.The Bioconvection pattern in various nanoparticles accredits novel applications of biotechnology like the synthesis of biological polymers,biosensors,fuel cells,petroleum engineering,and the natural environment.By deploying some suitable similarity transformation functions,the governing partial differential equations(PDEs)of the flow problem are rehabilitated into dimensionless forms.The accomplished ordinary differential equations(ODEs)are solved numerically through the bvp4c scheme via a built-in function in computational MATLAB software.The upshots of some prominent physical and bioconvection parameters including wall slip parameters,thermophoresis parameter,Brownian motion parameter,Reiner–Revlin nanofluid parameter,Prandtl number,Peclet number,Lewis number,bioconvection Lewis number,and the mixed convection parameter against velocity,temperature,nanoparticles concentration,and density of motile microorganism profiles are dichotomized and pondered through graphs and tables.The presented computations show that the velocity profiles are de-escalated by the wall slip parameters while the thermal and solutal fields are upgraded with augmentation in thermophoresis number and wall slip parameters.The presence of thermal radiation enhances the temperature profile of nanofluid.The concentration profile of nanoparticles is boosted by intensification in activation energy.Furthermore,the increasing values of bioconvection Lewis number and Peclet number decay the motile microorganisms’field.

Mathematical and numerical modelling of large creep deformations for annular rotating disks

A simulation model is presented for the creep process of the rotating disks under the radial pressure in the presence of body forces. The finite strain theory is applied. The material is described by the Norton-Bailey law generalized for true stresses and logarithmic strains. A mathematical model is formulated in the form of a set of four partial differential equations with respect to the radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, a numerical procedure is proposed. The given example shows the effectiveness of this procedure. The results show that the classical finite element method cannot be used here because both the geometry and the loading （body forces） change with the time in the creep process, and the finite elements need to be redefined at each time step.

Investigations of Thallium(Ⅰ) Underpotential Deposition on the Silver Rotating Disk Electrode and Its Analytical Application

The cyclic voltammetry(CV) and the square wave technique were used for the investigations of thallium(Ⅰ) underpotential deposition(UPD) on the silver electrode. A solution of 10 \{mmol/L\} HClO 4+10 mmol/L NaCl was selected as the supporting electrolyte. The calibration plots for Tl(Ⅰ) concentration in the range of 2×10 -9 -1×10 -7 mol/L were obtained. The detection limit was 5×10 -10 mol/L. For the solutions of 4 0×10 -9 mol/L thallium added before the urine sample pretreatment procedure, the average recovery was 105 6% with a relative standard deviation(RSD) of 15 5%.

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensionM axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter β and the rotating parameter Ω. However, the lower branch solution breaks down at some moderate values of β The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β. The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.

Flow of a Viscoplastic Fluid on a Rotating Disk

The equations describing the flow of a viscoplastic fluid on a rotating disk are de-rived and are solved by perturbation technique and nurmerical computation respectivelyfor 2 cases. This makes it possible to calculate the thickness distribution of film. Twokinds of distribution of thickness have been found. For the viscoplastic fluid for whichboth viscosity and yield stress are independent of radial coordinate r, the thickness hdecreases with increasing r. For a Bingham fluid for which both viscosity and yieldstress are function of time and r. the thickness h increases with increasing r.

Effect of Axial Clearance on the Flow Structure around a Rotating Disk Enclosed in a Cylindrical Casing

Numerical study is performed to investigate the swirling flow around a rotating disk in a cylindrical casing. The disk is supported by a thin driving shaft and it is settled at the center of the casing. The flow develops in the radial clearance between the disk tip and the side wall of the casing as well as in the axial clearance between the disk surfaces and the stationary circular end walls of the casing. Keeping the geometry of the casing and the size of the radial clearance constant, we compared the flows developing in the fields with small, medium and large axial clearances at the Reynolds number from 6000 to 30,000. When the rotation rate of the disk is small, steady Taylor vortices appear in the radial clearance. As the flow is accelerated, several tens of small vortices emerge around the disk tip. The axial position of these small vortices is near the end wall or the axial midplane of the casing. When the small vortices appear on one side of the end walls, the flow is not permanent but transitory, and a polygonal flow with larger several vortices appears. With further increase of the rotation rate, spiral structures emerge. The Reynolds number for the onset of the spiral structures is much smaller than that for the onset of the spiral rolls in rotor-stator disk flows with no radial clearance. The spiral structures in the present study are formed by the disturbances that are driven by a centrifugal instability in the radial clearance and they are penetrated radially inward along the circular end walls of the casing.

Experimental Study on Vortex Growth during the Early Development of Rotating Disks

In previous studies, the effects of radial clearance on the flow of a rotating disk in a cylindrical vessel have been investigated by using rotating disks of different shapes. As a result, different flow phases were observed in each disk due to the difference in disk dimensions. In this study, we focus on the end-face effect and conduct experiments to visualize the vortex growth process and elucidate the generation mechanism of the vortex structure. From the experiment results, at Re = 4000, 7000, and 9000, four types of vortex flow modes appeared in the vortex development process. However, at Re = 4000, only regular 2-cells and regular 4-cells appeared, and at Re = 9000, only mutated 2-cells and mutated 3-cells appeared. In addition, it was found that only one type appeared depending on the rotational ascent time ts. When Re = 4000, the rotational ascent time ts = 0, 2, 7, and 8 was stable at regular 4-cells, while the others were finally stable in regular 2-cells. This study revealed the influence of the acceleration of the rotating disk on the non-unique flows in the cylindrical casing.

Separation of La(Ⅲ),Ce(Ⅳ)and Ca(Ⅱ)from bastnaesite using acidic phosphonic chitosan and rotating disk membrane

The separation of rare earths is difficult due to their similar properties and the complex characteristics of associated vein o res.Complexation-ultrafiltration(CUF)and shear induced o rderly dissociation coupling with ultrafiltration(SIODUF)were used to separate metal ions(M,M=La(Ⅲ),Ce(Ⅳ)and Ca(Ⅱ))from simulated bastnaesite leaching solution using acidic phosphonic chitosan(aPCS)and rotating disk membrane.Effect of simultaneous removal of metallic ions was investigated by CUF,and suitable conditions were obtained for C/M 10.0(mass ratio of complexant to metal ions)and pH 5.0.The shear stabilities of aPCS-M complexes were explored at different pH values and the results show that the complexes can dissociate at a certain rotational speed,the critical one.The critical s hear rates of aPCS-La,aPCS-Ce and aPCS-Ca complexes at pH 5.0 were calculated as 1.42×10^(5).1.69×10^(5) and 9.75×10^(4) s^(-1),respectively.The order of complexes shear stability is aPCS-Ca aPCS-La<aPCS-Ce.The high selective separation of M and regeneration of aPCS were achieved by SIODUF in the light of the difference of aPCSM complexes shear stabilities.The separation coefficientsβLa/Ce andβCa/La reach 31.2 and 53.9,respectively.

Unsteady squeezing flow and heat transport of SiO_(2)/kerosene oil nanofluid around radially stretchable parallel rotating disks with upper disk oscillating

In this study,we have analyzedfluid mobility and thermal transport of the SiO_(2)/kerosene nanofluid within two rotating stretchable disks.The top disk is simulated to be oscil-lating with a periodic velocity and squeezing continuously the nanofluid within a porous me-dium and making thefluid toflow perpendicularly to the situated magneticfield.Thermal radiation effects are considered in the heat transfer model.The non-linear(NL)PDEs that describe the nanofluid mobility structure and thermal transport are transformed into system of NL-ODEs by introducing adequately suitable non-dimensional variables after which the NL-ODEs were numerically solved via spectral quasi-linearization method(SQLM)on over-lapping grids.The consequences of several pertinent parameters of the model on pressure,tem-perature,velocity,skin drag coefficient and thermal transport rate are examined and elucidated in detail with the aid offigures and tables.It was found that theflow structure with prescribing conditions develops negative pressure situation which has vast applications in modern day medical engineering,especially in the construction of air pressure stabilizers used in medical isolation and wound therapy physiology.

Comprehensive evaluations of heat transfer performance with conjugate heat dissipation effect in high-speed rotating free-disk modeling of aero-engines

Thermal boundary conditions of the turbine disk cavity system are of great importance in the design of secondary air systems in aero-engines.This study aims to investigate the complex heat transfer mechanisms of a rotating turbine disk under high-speed conditions.A high-speed rotating free-disk model with Dorfman empirical solutions is developed to evaluate the heat transfer performance considering various factors.Specifically,the influence of compressibility,variable properties,and heat dissipation is determined using theoretical and numerical analyses.In particular,a novel combined solution method is proposed to simplify the complex heat transfer problem.The results indicate that the heat transfer performance of a free disk is primarily influenced by the rotating Mach number,rotating Reynolds number,Rossby number,and wall temperature ratio.The heat transfer temperature and Nusselt number of the free disk are strongly correlated with the rotating Mach number and rotating Reynolds number.Analysis reveals that heat dissipation is a critical factor affecting the accurate evaluation of the heat transfer performance of the turbine disk.Thus,the combined solution method can serve as a reference for future investigations of flow and heat transfer in high-speed rotating turbine disk cavity systems in aero-engines.