Effects of Hall current and heat transfer on flow due to a pull of eccentric rotating disks

The influence of Hall current and heat transfer on the magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid is investigated. The fluid is between two infinite disks rotating about non-coaxial axes normal to the disks in the presence of a uniform transverse magnetic field. The flow is due to a constant velocities of eccentric rotating disks. Exact solutions are derived for the velocity, force and torque exerted by the fluid on one of the disk and temperature distribution.     

Entropy optimization analysis of Marangoni convective flow over a rotating disk moving vertically with an inclined magnetic field and nonuniform heat source

The present study investigates the Marangoni convective fluid flow over a rotating disk with an inclined magnetic field and in the presence of a nonuniform heat source when the disk moves upward/downward with nonconstant velocity with the incorporation of the second law of thermodynamics. The Keller-box method is applied to the reduced system of equations to draw graphical illustrations. The study of these illustrations to examine the effects of involved pertinent parameters, like, magnetic field, Marangoni number, angle of inclination, vertical disk movement parameter, heat source, and disk rotation, on velocity and temperature profiles, reveals some interesting findings. From the analysis, it can be concluded that the skin friction coefficient increases with more angle of inclination and the Marangoni number with the reverse trend in case of vertical disk movement. Also, the Marangoni number and vertical disk motion diminish the Nusselt number with a positive effect in the case of more angle of inclination. The rate of entropy generation is enhanced with the temperature ratio parameter while it diminishes with the inclined magnetic field of any strength. The current study in its reduced form is in excellent agreement with earlier published work to ensure the validity of the used numerical scheme.     

Unsteady flow and heat transfer of a ferrofluid between two rotating,vertical moving and stretching disks

Unsteady flow and heat transfer of a magnetic fluid between two rotating disks is investigated. Both the disks are stretchable and the lower disk moves in the vertical direction. A new approach of similarity transformation is adopted to transform the equation of continuity, momentum, and the energy equation into ordinary nonlinear coupled differential equations. The numerical solution of the converted nonlinear differential equations is obtained using the finite element method. The effects of magnetization force, rotational viscosity, Prandtl number, and Eckert number on the velocity and temperature distributions are studied. The impact of stretching, movement, and rotation of the disk is also considered in this computational study. The skin friction coefficients and heat transfer rate on the lower disk for different physical parameters are calculated. Different types of motion of the disks and the magnetization force are crucial aspects in the stress distribution and heat transfer rate near the lower disk.     

Magnetohydrodynamics slip flow of a nanofluid through an oscillatory disk under porous medium supremacy

Unsteady, three‐dimensional, hydromagnetic, nanofluid flow via a circular disk in porous medium is considered. The fluid motion is subject to disk rotation and time‐based sinusoidal oscillations. The flow problem is normalized via similarity variables. Partial slip boundary conditions on velocity, concentration, and temperature are considered. A well‐established numerical technique (successive over relaxation method) is used for the time‐based flow problem. Results are discussed for both the time‐based and linearly rotating disk case. Graphical representations for one, two, and three dimensions are sketched. The results are also discussed through tabular forms.     

Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model

Nonlinear, steady‐state, viscous flow, and heat transfer between two stretchable rotating disks spinning at dissimilar velocities are studied with a non‐Fourier heat flux model. A nondeformable porous medium is intercalated between the disks and the Darcy model is used to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless parameters, that is, Prandtl number, upper disk stretching, lower disk stretching, permeability, non‐Fourier thermal relaxation, and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial, and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to rotating disk bioreactors in chemical engineering.     

Semianalytical solution of axisymmetric flows of Cu‐ and Ag‐water nanofluids between two rotating disks

Present study analyses the axisymmetric flows of copper‐ and silver‐water nanofluids between two rotating disks in the presence of Hartmann number, porous medium, and drag coefficient. Effect of thermal radiation enriches the study as well. In addition to that, the coupling parameter and the Eckert number appear because of the inclusion of viscous dissipation in energy equation. The well‐posed transformations are used to transform the governing equation into ordinary and semianalytical procedure, that is, Adomain Decomposition method is used to solved these coupled ODEs. The surface and contour plots for the velocity profiles of both Cu‐ and Ag‐water nanofluids for the effect of physical parameters such as solid volume fraction, drag coefficient, and Reynolds number are obtained and presented in graphs. Also, the behavior of other pertinent parameters characterizes the flow phenomena on the nanofluid velocity and temperature are presented through graphs. The numerical computation of skin friction and Nusselt number are obtained and presented through tables. For the validity, the present results show a good agreement with earlier studies. The major findings of this study are as follows: an increase in solid volume fraction, a resistive force like drag opposes the velocity of the nanofluid, whereas Eckert number enhances the fluid temperature significantly.     

MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk

The aim of this analysis is to examine the steady, laminar boundary layer flow of a micropolar nanofluid owing to a rotating disk in the presence of a magnetic field and thermal and solutal nonlinear convection and nonisothermal parameters. The governing joined partial differential equations are converted into nonlinear ordinary differential equations by means of available transformations. The equations are calculated using the method bvp4c from Matlab software. The convergence test has been maintained; for the number of spots greater than the appropriate mesh number of points, the precision is not influenced, but the set time is boosted. Moreover, various quantities of the main parameters on skin friction coefficients, wall couple stress coefficients, Nusselt number, Sherwood number, velocities, temperature, and concentration of nanofluid are analyzed by means of tables and graphs. The results indicate that the presence of the nonisothermal parameter boosts the radial skin friction, temperature, and Sherwood number but causes decaying concentration distributions, the azimuthal skin friction coefficient, and Nusselt number that indicate the diffusion of momentum occurs more around the surface of the rotating disk.     

Silver–ethylene glycol and copper–ethylene glycol based thermally radiative nanofluid characteristics between two rotating stretchable disks with modified Fourier heat flux

In the present analysis, our aim is to investigate the mass and heat transport of silver (Ag)–ethylene glycol (EG) and copper (Cu)–EG-based nanofluids between two rotating stretchable disks under the convective boundary conditions. We have also incorporated Cattaneo–Christov heat flux, thermal radiation, and chemical reaction in the fluid flow. The system of coupled partial differential equations is transformed into ordinary differential equations by using similarity transformations. The finite element method has been accomplished to find numerical solutions to transformed equations. The behavior of radial and tangential velocity, temperature fields, and concentration fields influenced by the various parameters are sketched through graphs. The local skin friction coefficient, Nusselt number, and Sherwood number are also calculated for the pertinent parameters and displayed the results through tables. It is perceived that velocity sketches of both nanoliquids degenerate with larger values of thermal relaxation parameters. Also, the values local Nusselt number of both Ag–EG, and Cu–EG based Cattaneo–Christov nanofluid intensifies with improving values of stretching parameter at the lower disk, whereas, it impedes at the upper disk.     

Statistical approach on 3D hydromagnetic flow of water-based nanofluid between two vertical porous plates moving in opposite directions

The nanofluid flow between two plates is a common topic of research. However, studies dealing with the flow between two vertical plates moving in different directions have not been largely accounted for. The main aim of this study is to analytically and statistically investigate the MHD flow of water-based nanofluid between two vertical porous plates moving in opposite directions using perturbation technique and multiple linear regression, respectively. The consequence of various parameters on concentration, temperature, and velocity are examined via graphs using MATLAB software. It is observed that the main flow velocity profile is greater when the magnetic field is applied on the upward moving plate as compared to the main flow velocity when the magnetic field is applied on the downward-moving plate. The physical quantities are scrutinized using statistical tools like probable error and multiple linear regression and an excellent agreement is noted. It is noted that the Nusselt number is highly positively correlated with the injection parameter and highly negatively correlated with nanoparticle volume fraction. Furthermore, the simultaneous effects of parameters on drag coefficients are studied with the aid of three-dimensional surface plots.     

Impact of activation energy and gyrotactic microorganisms on flow of Casson hybrid nanofluid over a rotating moving disk

Many models of various non-Newtonian fluid flows for different geometries are available for analyzing the mass and heat transfer. Nevertheless, for researchers, it is challenging to choose the most suitable model for a specific geometry. Here, we have adopted a modified Buongiorno model to explore the impact of activation energy on the Casson hybrid nanofluid flow over an upward/downward-moving rotating disk filled with the gyrotactic microorganisms. Moreover, the external magnetic field can establish the magnetic effect, which normalizes the features of heat, mass transfer, and fluid flow. Here, we used silver and copper as nanoparticles suspended in human blood as the carrier fluid. The modeled partial differential equations are converted to ordinary differential equations by opting suitable similarity variables. The numerical solutions of these reduced equations are attained by means of Runge–Kutta–Fehlberg fourth-fifth-order method by adopting a shooting scheme. An investigation of the attained outcomes reveals that the flow field is affected appreciably by the activation energy, bioconvection, and magnetic effect. Peclet and concentration difference numbers diminish the microorganism's profile. A rise in values of the Brownian motion parameter leads to an increase in the rate of heat transfer.     

Flow between two stretchable disks—An exact solution of the Navier–Stokes equations

In this work, an exact solution for the steady state Navier–Stokes equations in cylindrical coordinates is presented by similarity transformation technique. The solution involves the flow between two stretchable infinite disks with accelerated stretching velocity. The similarity equation was solved numerically and the effects of disk stretching parameter and stretching Reynolds number were studied. With the increase of the stretching Reynolds numbers, the fluid begins with a creeping type flow at R = 0 to a typical boundary layer type flow for large Reynolds numbers. The pressure parameter β changes from a positive number to a negative value with the increase of non-zero stretching parameter. The upper wall stretching parameter also greatly affects the velocity distribution between the two disks with a downward net flow for γ ≠ 1. The results are also useful as a benchmark problem for the validation of three-dimensional numerical computation code.     

Effect of SWCNTs and MWCNTs Maxwell MHD nanofluid flow between two stretchable rotating disks under convective boundary conditions

The aim of the current analysis is to investigate heat and mass transfer characteristics of single and multi‐walled water‐based carbon nanotubes Maxwell nanofluid flow between continuously rotating stretchable disks under the sway of chemical reaction and radiation. Boundary conditions of the convective type of temperature are employed at both lower and upper rotating disks in the preparation. Similarity variables are employed to transform the governing partial differential equations into the nonlinear ordinary differential equations. The computational finite element method is applied to solve this nonlinear system of equations along with boundary conditions. The sway of different admissible parameters on the profiles of concentration, temperature, and velocity are inspected and revealed through graphs. Furthermore, the numerical solutions for rates of temperature, concentration, and rates of velocity are depicted in tabular form. It is revealed that temperature sketches deteriorate with augmented values of Deborah number at both upper and lower disks of single‐walled carbon nanotubes and multi‐walled carbon nanotubes with water‐based Maxwell nanofluids.     

Numerical Modeling of Fluid Flow and Thermal Behavior of Different Nanofluids on a Rotating Disk

The thermal and velocity profiles of various nanofluid systems on a rotating disk are simulated. Finite difference method, the orthogonal collocation method, and the differential quadrature method (DQM) of numerical approaches are used to solve the governing equations and are compared to determine the faster and more accurate solution procedure. Five nanoparticles Al, Al₂O₃, Cu, CuO, and TiO₂ solved in three base fluids water, ethylene glycol, and engine oil are considered to be used on the disk at different volume fractions. A new general algorithm is presented for solving equations of a rotating‐disk problem quickly and accurately and it is found that the DQM method is the best approach for this numerical simulation. Heat transfer performance of a rotating disk would be much better enhanced with water based Al nanofluid. A wide range of results for different base–fluid combinations with nanoparticles is presented with untransformed 3D results and effects of the variation of different parameters provides comprehensive insight and prevents inaccurate deductions.     

An Exact Solution for Heat Transfer of a Jet Co-Axially Impinging on a Rotating Disk and Its Comparisons with Stagnation Point Experiments

IntroductionJet impingement is a widely used high-efficiencytechnique fOr cooling rotating disks, which are end-wallsurfaces of gas turbine rotors, comPuter disk drives etc.Fluid f'low, heat trallsfer and geometric arrangement inthe case of a single round jet impinging co-axially in anorthogonal mode on a rotatng disk are characterized byFig. l.Many peculiarihes of fluid fIow and heat transfer ofreal impinging jets under comPlicated conditions(different system geometry, impinging flow proper…     

On the effectiveness of viscous dissipation and Joule heating on steady MHD flow and heat transfer of a Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents

The combined effects of viscous dissipation and Joule heating on steady magnetohydrodynamics (MHD) flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents is studied. An external uniform magnetic field is applied in the z-direction and the fluid is subjected to uniform suction. Numerical solutions are obtained for the governing momentum and energy equations. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.     

Electromagnetohydrodynamic boundary layer flow in hybrid nanofluid with thermal radiation effect: Numerical simulation

Hybrid nanofluid boundary layer flow past a stretching surface with zero mass flux boundary condition is explored in this article. The main aim of this article is to analyze the electromagnetohydrodynamic role in a hybrid nanofluid containing silver and molybdenum disulfide nanoparticles. The self-similar solution is embedded to reduce the governing partial differential equation into algebraic equations and a shooting algorithm is applied to obtain the solution of the resultant boundary value problem. Variation in momentum, energy, and nanoparticle concentration is explained through graphical profiles. Nusselt number and drag force coefficients are computed for various flow parameters and their impact on the nanofluid and hybrid nanofluid is computed and presented and explained in a comparative fashion. It is observed that the velocity profile shows the opposite nature with respect to the electric field and magnetic field. For electric field parameter velocity accelerates whereas for magnetic parameter velocity diminishes. Nusselt number increases with electric field parameter and nanoparticle volume fraction.     

Zinc oxide–silver/water hybrid nanofluid flow toward an off-centered rotating disk using temperature-dependent experimental-based thermal conductivity

Herein, the off-centered stagnation flow and heat transfer of zinc oxide–silver/water hybrid nanofluid over a rotating disk according to the mass-based algorithm is studied. It is assumed that the nanoparticles have a spherical shape. Also, the velocity slip between the base fluid and nanoparticles is negligible. The Prandtl number is kept constant at 6.2. In addition, it has been used an experimental relation for effective thermal conductivity which is a function of volume fraction and temperature. The governing partial differential equations are converted to dimensionless ordinary differential equation (ODE)s by the similarity transformation method. The simplified ODEs are solved numerically by the bvp4c function from MATLAB which is an efficient and reliable code according to the three-stage Lobatto IIIa formula. The influence of rotational parameters and both nanoparticles masses on the profiles and quantities of engineering interest are presented and discussed in detail. It is shown that the flow becomes complicated when there is a distance between the flow axis and the disk axis. Under determined conditions for a hybrid nanofluid with 30-g mass for both nanoparticles and 100-g mass for pure water, adding 30 g of the second nanoparticle's mass into the base fluid leads to enhance all hydrodynamic quantities of engineering interest by about 4.3%, while dispersing 30 g of the first nanoparticle's mass inside water results in decreasing the similarity temperature gradient at the surface about 3.6%. Also, when the disk rotates faster, the maximum radial velocity near the disk, s′(0) and f″(0) increases.     

Thermo-electrokinetic rotating non-Newtonian hybrid nanofluid flow from an accelerating vertical surface

This paper explores the combined effects of Coriolis force and electric force on the rotating boundary layer flow and heat transfer in a viscoplastic hybrid nanofluid from a vertical exponentially accelerated plate. The hybrid nanofluid comprises two different types of metallic nanoparticles, namely silver (Ag) and magnesium oxide (MgO) suspended in an aqueous base fluid. The Casson model is deployed for non-Newtonian effects. An empirical model is implemented to determine the thermal conductivity of the hybrid nanofluid. Rosseland's radiative diffusion flux model is also utilized. An axial electrical field is considered and the Poisson–Boltzmann equation is linearized via the Debye–Hückel approach. The resulting coupled differential equations subject to prescribed boundary conditions are solved with Laplace transforms. Numerical evaluation of solutions is achieved via MATLAB symbolic software. A parametric study of the impact of key parameters on axial velocity, transverse velocity, nanoparticle temperature and Nusselt number is conducted for both the hybrid (Ag–MgO)–water nanofluid and also unitary (Ag)–water nanofluid. With increasing volume fraction of silver nanoparticles, there is a reduction in both axial velocity and temperatures, whereas there is a distinct elevation in transverse velocity for both unitary and hybrid nanofluids. Elevation in the heat absorption parameter strongly decreases axial velocity, whereas it enhances transverse velocity. Increasing the radiation parameter strongly boosts temperatures. Increasing the heat absorption parameter significantly accelerates the transverse flow. Negative values of Helmholtz–Smoluchowski velocity decelerate the axial flow whereas positive values accelerate it; the opposite behavior is observed for transverse velocity. Increasing Taylor number significantly damps both the axial (primary) and transversal (secondary) flow. Increasing thermal Grashof number strongly enhances the axial flow but damps the transverse flow. The unitary nanofluid achieves higher Nusselt numbers than the hybrid nanofluid but these are decreased with greater radiative effect (due to greater heat transport away from the plate surface), Prandtl number and heat absorption. Nusselt number is significantly reduced with greater time progression and values are consistently higher for the unitary nanofluid compared with hybrid nanofluid. The computations provide insight into more complex electrokinetic rheological nanoscale flows of relevance to biomedical rotary electro-osmotic separation devices.     

Influences of the Exhaust Flow on the Boundary Layer Flow on the Wafer Surface in Spin Coating System

Recently, development of high technology has been required for the formation of thin uniform film in manufacturing processes of semiconductor as the semiconductor become more sophisticated. Spin coating is usually used for spreading photoresist on a wafer surface. However, since rotating speed of the disk is very high in spin coating, the dropped resist scatters outward and reattaches to the film surface. So, the scattered resist is removed by the exhaust flow generated at the gap between the wafer edge and the catch cup. It is seriously concerned that the stripes called Ekman spiral vortices appears on the disk in the case of high rotating speed and the film thickness increases near the wafer edge in the case of low rotating speed, because it prevent the formation of uniform film. The purpose of this study is to make clear the generation mechanism of Ekman spiral vortices and the influence of exhaust flow on it Moreover the influence of the catch cup geometry on the wafer surface boundary layer flow is investigated.     

Scattering characteristics of liquid droplets spun off from rotating disk edge

Scattering characteristics of liquid droplets spun off from a rotating disk edge are experimentally investigated. In the present research, aluminum disks are utilized and ethanol is employed for liquid. Scattering phenomena of the droplets are captured by the high-speed digital camera. Frequency distribution of the droplet diameter is evaluated from these images and distributions of horizontal flying velocity and angle of the droplets were measured by PTV. Liquid filaments are stretched outward from the stagnant liquid layer by centrifugal force and skew complicatedly by aerodynamic force. Some peaks appear in the distribution of the scattered droplet diameter and they are origi- nated from large terminal droplets and small droplets generated from filamentwise breakup. Most of the scattered droplets fly slightly inside in the tangential direction of the disk edge. The droplets spun off from the thin disk scatter widely compared with that from the thick one.