Dimensionless Velocity Components Research Articles

Electrokinetic cells powered by osmotic gradients: an analytic survey of asymmetric wall potentials and hydrophobic surfaces

Nowadays, the fabrication of microelectromechanical systems has given rise to several studies whose main purpose is to obtain the greater benefit of micro-nano scales, putting special interest in the improvement of the design of such devices. One of several applications is harvesting energy due to electrokinetic phenomena, more specifically, streaming potential. Nonetheless, there is a lack of theoretical studies encompassing coupled asymmetries in both slip conditions and electric potentials (these being associated with the chemical and physical characteristics of the surfaces). By virtue of the previous explanation, ideal assumptions based on the symmetry of some variables must be reconsidered, especially when manufacturing symmetric flat surfaces on a tiny scale is quite difficult to achieve. This work presents a theoretical study in power generation, exploiting streaming potentials produced by an asymmetric membrane which in turn prompts a flux inside a microchannel made of two flat parallel surfaces. The driving force in this electrokinetic battery is the osmotic gradient on both sides of the membrane. The model uses the Debye–Hückel approximation together with the appropriate asymmetric boundary conditions for both slips and potentials on the surfaces. The main variables of interest, such as the dimensionless horizontal velocity component, the pressure field, and the average streaming potential, were estimated.

Optimization of cooling of three radiant heat source inside an inclined porous medium using particle swarm optimization

In this study, an optimization of the maximum cooling of three radiant heat sources inside a closed square porous environment is performed. Three radiant-heat sources are cooled by airflow in a porous medium with an inclination angle. It is applied in the cooling of electronic equipment inside laptop computers. The cooling phenomenon is a function of five independent variables, such as the length of heat source, radiation parameter, Darcy number, the angle of inclination of a porous medium, and Rayleigh number. Differential equations are solved using the finite-difference approach. And those are solved by the Gauss-Seidel approach. Simulation is a numerical solution of the vorticity–stream equations. Coding is done in MATLAB software. And it is obtained the maximum objective function using the algorithm of particle swarm optimization. Cooling simulations are performed by drawing flow lines, constant temperature lines, dimensionless velocity component profiles, local Nusselt numbers, and mean Nusselt numbers. The main goal is to find the highest cooling rate in different amounts of five independent variables. The flow is in the laminar flow regime, and inclination angles are between 0 to 360°. The present study is the first study on the numerical solution of the cooling of three radiant-heat sources with an inclination angle by the porous media-filled square environment. And it is developed from the cooling of hot radiation walls problems in an inclined enclosure with constant temperature local radiant heat sources. This investigation showed the flow lines and their direction are influenced by the inclination angle of the porous medium strongly, and the maximum heat transfer is achieved at an angle of inclination of zero degrees. This investigation showed at the Darcy number, 0.001, and the radiation parameter, 1. The maximum and minimum Nusselt number is obtained for the inclination angle 60 and 180°, respectively.

Investigation of the Flow Structures for Two Tandem Arrangement of Torpedo-Like Geometries

Experimental studies on autonomous underwater vehicles for a torpedo-like geometry are limited in the literature. In this study, flow structures of a streamlined torpedo-like geometry having an elliptical nose and tampered stern at a length to diameter aspect ratio of L/D=5 for a single and double tandem arrangement with various spacings have been investigated using Particle Image Velocimetry (PIV) method in a closed loop water channel. Reynolds number defined for length of the geometry (L=200 mm), free stream water velocity of 100 mm/s was taken as Re=20000, the spacing (G) between two identical torpedo-like geometries is changed from 0 to 120 mm. Instantaneous 1000 images and their time-averaged results are comparatively presented for all configurations of the torpedo-like geometry. It is demonstrated that the tandem arrangements depending on the dimensionless spacing ratios (G/L) between 0 to 0.6 are significantly different from the single torpedo-like geometry for the flow patterns of instantaneous and time-averaged velocity field, dimensionless streamwise velocity component and streamline topology. For the contacting case in which the following model nose is placed on the trailing-edge of the front model, wake region of the back geometry is similar to the single model wake but the all of time-averaged flow patterns elongated and symmetrical flow patterns are slightly deformed. When flow area is provided between two models for spacing ratios of 0.15≤G/L≤0.30, chaotic and rotational flow patterns occur due to the impinging separated flow patterns from the front geometry to the nose of the downstream one. As the gap distance increases to the largest value at G/L=0.6, the wake region of both the single and tandem arrangement becomes almost identical. More detailed information for the flow characteristics of the examined torpedo-like geometry can be determined by using computational fluid dynamics after validation with PIV results in the present study.

Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects

In recent years, significant progress has been made in modern micro- and nanotechnologies for micro/nano-electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro-organisms. Motivated by bio-nanofluid rotating disk oxygenators in medical engineering, in the current work, a mathematical model is developed for steady convective von-Karman swirling flow from an impermeable radially stretched disk rotating in a Darcy porous medium saturated with nanofluid doped with gyrotactic micro-organisms. Anisotropic slip at the wall and blowing effects due to concentration are incorporated. The nano-bio transport model is formulated using nonlinear partial differential equations, which are transformed to a set of similarity ordinary differential equations (SODEs) by appropriate transformations. The transformed boundary value problem is solved by a Chebyshev spectral collocation method (CSCM). Impacts of key parameters on dimensionless velocity components, concentration, temperature and motile microorganism density distributions are investigated and graphically visualized. Validation with previous studies is included. It is found that that the effects of suction provide a better enhancement of the heat, mass and microorganisms transfer in comparison to blowing. Moreover, physical quantities decrease with higher slip parameters irrespective of the existence of blowing. Temperature is suppressed with increasing thermal slip, while nanoparticle concentration is suppressed with increasing wall mass slip. Micro-organism density number increases with the greater microorganism slip. Radial skin friction is boosted with positive values of the power law stretching parameter, whereas it is decreased with negative values. The converse response is computed for circumferential skin friction, nanoparticle mass transfer rate and motile micro-organism density number gradient. Results from this study are relevant to novel bioreactors, membrane oxygenators, food processing and bio-chromatography.

Electrothermal transport of third-order fluids regulated by peristaltic pumping.

The study of heat and electroosmotic characteristics in the flow of a third-order fluid regulated by peristaltic pumping is examined by using governing equations, i.e., the continuity equation, momentum equation, energy equation, and concentration equation. The wavelength is considered long compared to its height and a low Reynolds number is assumed. The velocity slip condition is employed. Analytical solutions are performed through the perturbation technique. The expressions for the dimensionless velocity components, temperature, concentration, and heat transfer rate are obtained. Pumping features were computed numerically for discussion of results. Trapping and heat transfer coefficient distributions were also studied graphically. The findings of the present study can be applied to design biomicrofluidic devices like tumor-on-a-chip and organ-on-a-chip.

Non-Newtonian fluid flow around a Y-shaped fin embedded in a square cavity

This study investigates the free convection of Casson fluid inside a square cavity with intruded Y-shaped fin at the bottom surface. The Casson fluid is a non-Newtonian fluid and has an infinite viscosity at zero rates of shear. This is the first time that this fluid is used in the square cavity containing Y-shaped fin at the bottom surface. The Y-shaped fin helps in understanding the constructal theory and enhancing the heat transfer rate from the fin. The main objective of using this fin is to increase the convective heat transfer surface area. The sidewalls of the cavity are kept at cold temperature, the bottom surface at a hot temperature, and the top surface as adiabatic. The tips of the Y-shaped fin are considered as hot, cold, and adiabatic. The effects of the magnetic field and radiation are included in the momentum and energy equations. The influence of viscous heating is neglected. The buoyancy term is included in the momentum equation using Boussinesq approximation. The dimensionless governing equations are solved numerically using a Galerkin weighted residual technique of the finite element method. The effects of Rayleigh number (Ra = 104–106), radiation parameter (Rd = 0–103), Hartmann number (Ha = 0–103), and Casson parameter (γ = 0.1–1) on streamlines, isotherms, dimensionless velocity components, temperature, and local Nusselt numbers along the fin and the bottom heated wall are investigated and presented graphically. It is demonstrated that, in the presence of Y-shaped fin, all the pertinent parameters and dimensionless numbers help in enhancing the heat transfer rate along the bottom surface.

Tangent hyperbolic nanofluid with mixed convection flow: An application of improved Fourier and Fick's diffusion model

AbstractThis article presents a tangent hyperbolic fluid with the effect of the combination of forced and natural convection flow of nanoparticle past a bidirectional extending surface. Modified Fick's and Fourier's diffusion theories are incorporated into concentration and energy equations, respectively. Convective boundary conditions and second‐order slip flow are taken in the boundary condition. Nonlinear partial differential equations result after boundary layer approximations of the mathematical formulation of the flow problem. Nonlinear high order ordinary differential equations (ODEs) are formed by applying similarity transformation on the nonlinear partial differential equations. The transformed equations are solved with the bvp4c algorithm from Matlab. The numerical solution of ODEs was obtained and the effect of interesting parameters, dimensionless velocity component along x‐ and y‐axis, temperature, and concentration particle, Rex, Rey, , and , were presented through tables and graphs and discussed thoroughly. The results indicated that a decrease in velocity along with the y‐axis results from the increasing behavior of S, M, and n. Decrease in both temperature and concentration results in an increase of but their elongation is a result of increase in Bi. An increase in concentration results in decrease of N and S but a decrease in concentration results in the widening of Sc, Nb, and . Furthermore, enlargement of and results in increase of and modules and elongation of both and results in increase of and (Sc and Nb), respectively. A comparison with previously published literature was performed and a good agreement was found.

Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium

The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two parallel plates. The boundaries of the plates are maintained at distinct temperatures and concentrations while the fluid is being sucked and injected periodically through upper and lower plates. The buoyancy forces, thermophoresis and Brownian motion are also considered due to the temperature and concentration differences across the channel. The system of governing partial differential equations has been transferred into a system of ordinary differential equations (ODEs) by appropriate similarity relations, and a shooting method with the fourth-order Runge-Kutta scheme is used for the solutions. The results are analyzed in detail for dimensionless velocity components. The temperature, concentration distributions, the entropy generation number, and the Bejan number corresponding to various fluid and geometric parameters are shown graphically. The skin friction, heat and mass transfer rates are presented in the form of tables. It is noticed that the temperature profile of the fluid is enhanced with the Brownian motion, whereas the concentration profile of the fluid is decreased with the thermophoresis parameter, and the entropy and Bejan numbers exhibit the opposite trend for the suction and injection ratio.

MHD free convection flow of a viscous fluid in a rotating system with damped thermal transport, Hall current and slip effects

Unsteady hydromagnetic free convection flows of a rotating incompressible viscous fluid over an infinite moving plate with fractional thermal transport are studied in the presence of heat source, Hall current and slip velocity effects. The modern definition of the fractional integral Caputo-Fabrizio operator with non-singular kernel is used in the constitutive equation for the thermal flux and closed form solutions for the dimensionless temperature and velocity components are established by using the Laplace transform technique. For comparison, the solutions for the ordinary fluid as well as those corresponding to the no-slip condition on the boundary are also determined. The influence of fractional, magnetic, Hall and rotation parameters as well as that of heat generation/absorption coefficient on the fluid motion and the heat transfer is graphically underlined and discussed. It is found that the damping of the thermal transport has significant influence on the fluid temperature and motion. The Hall current mainly affects the secondary flow.

Simulation of gaseous pollutant dispersion around an isolated building using the k–ω SST (shear stress transport) turbulence model

ABSTRACTThe dispersion of gaseous pollutant around buildings is complex due to complex turbulence features such as flow detachment and zones of high shear. Computational fluid dynamics (CFD) models are one of the most promising tools to describe the pollutant distribution in the near field of buildings. Reynolds-averaged Navier-Stokes (RANS) models are the most commonly used CFD techniques to address turbulence transport of the pollutant. This research work studies the use of closure model for the gas dispersion around a building by fully resolving the viscous sublayer for the first time. The performance of standard model is also included for comparison, along with results of an extensively validated Gaussian dispersion model, the U.S. Environmental Protection Agency (EPA) AERMOD (American Meteorological Society/U.S. Environmental Protection Agency Regulatory Model). This study’s CFD models apply the standard and the turbulence models to obtain wind flow field. A passive concentration transport equation is then calculated based on the resolved flow field to simulate the distribution of pollutant concentrations. The resultant simulation of both wind flow and concentration fields are validated rigorously by extensive data using multiple validation metrics. The wind flow field can be acceptably modeled by the model. However, the model fails to simulate the gas dispersion. The model outperforms in both flow and dispersion simulations, with higher hit rates for dimensionless velocity components and higher “factor of 2” of observations (FAC2) for normalized concentration. All these validation metrics of model pass the quality assurance criteria recommended by The Association of German Engineers (Verein Deutscher Ingenieure, VDI) guideline. Furthermore, these metrics are better than or the same as those in the literature. Comparison between the performances of and AERMOD shows that the CFD simulation is superior to Gaussian-type model for pollutant dispersion in the near wake of obstacles. AERMOD can perform as a screening tool for near-field gas dispersion due to its expeditious calculation and the ability to handle complicated cases. The utilization of to simulate gaseous pollutant dispersion around an isolated building is appropriate and is expected to be suitable for complex urban environment.Implications: Multiple validation metrics of turbulence model in CFD quantitatively indicated that this turbulence model was appropriate for the simulation of gas dispersion around buildings. CFD is, therefore, an attractive alternative to wind tunnel for modeling gas dispersion in urban environment due to its excellent performance, and lower cost.

Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inflow

A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, Uo. Results show that boundary layers merge for Re < < 10 and Ro > > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high Uo. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.

Anisotropicq-Gaussian 3D velocity distributions in ΛCDM haloes

The velocity distribution function (VDF) of dark matter (DM) haloes in Λ cold dark matter (ΛCDM) dissipationless cosmological simulations, which must be non-separable in its radial and tangential components, is still poorly known. We present the first single-parameter, non-separable, anisotropic model for the VDF in ΛCDM haloes, built from an isotropic q-Gaussian (Tsallis) VDF of the isotropic set of dimensionless spherical velocity components (after subtraction of streaming motions), normalized by the respective velocity dispersions. We test our VDF on 90 cluster-mass haloes of a dissipationless cosmological simulation. Beyond the virial radius, rvir, our model VDF adequately reproduces that measured in the simulated haloes, but no q-Gaussian model can adequately represent the VDF within rvir, as the speed distribution function is then flatter-topped than any q-Gaussian can allow. Nevertheless, our VDF fits significantly better the simulations than the commonly used Maxwellian (Gaussian) distribution, at virtually all radii within 5 rvir. Within 0.4 (1) rvir, the non-Gaussianity index q is (roughly) linearly related to the slope of the density profile and also to the velocity anisotropy profile. We provide a parametrization of the modulation of q with radius for both the median fits and the fit of the stacked halo. At radii of a few per cent of rvir, corresponding to the solar position in the Milky Way, our best-fitting VDF, although fitting better the simulations than the Gaussian one, overproduces significantly the fraction of high-velocity objects, indicating that one should not blindly use these q-Gaussian fits to make predictions on the direct detection rate of DM particles.

Lattice BGK Study on Flow Pattern in Two-Dimensional Wall-Driven Semi-Circular Cavity

The flow pattern in a two-dimensional wall-driven semi-circular cavity is analyzed using the lattice Boltzmann method (LBM). The treatment of curved boundary with second-order accuracy is used. The streamline contours as well as dimensionless velocity component along the central line of a semi-circular cavity are obtained for different Reynolds numbers. The numerical results show that the LBM can capture the formation of primary, secondary and tertiary vortices exactly as the Reynolds number increases and has a great agreement with those of current literatures.

Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium

This paper describes the heat transfer analysis with thermal radiation on the two-dimensional magnetohydrodynamic (MHD) flow in a channel with porous walls. The upper-convected Maxwell (UCM) fluid fills the porous space between the channel walls. The corresponding boundary layer equations are transformed into ordinary differential equations by means of similarity transformations. The resulting problems are solved by employing homotopy analysis method (HAM). Convergence of the derived series solutions is ensured. The effects of embedded parameters on the dimensionless velocity components and temperature are examined through plots. The variation of local Nusselt number is also analyzed.

Three-dimensional saltating processes of multiple sediment particles

The purpose of this study was to investigate the interacting mechanism between the saltating particles near a channel bed. A three-dimensional real-time flow visualization technique was developed to measure the interparticle collision behaviors during the saltating process. Based on the experimental data, the distribution of the collision points was found to be symmetric. This confirms the assumption that the projections of the collision points onto the reasonable plane are uniformly distributed. A three-dimensional saltating model was also developed. This model produced satisfactory results. The model is able to simulate the continuous saltating trajectories of several particles. The simulated dimensionless saltating height, longitudinal and vertical saltation velocity components were found to increase as the dimensionless particle diameter and the dimensionless flow transport capacity parameter increase, while the simulated lateral saltation velocity component varies inversely with the dimensionless flow transport capacity parameter. A regression equation for the bed load transport rate was also obtained.

Extensive study on laminar free film condensation from vapor–gas mixture

The dimensionless velocity component method was successfully applied in a depth investigation of laminar free film condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the film condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the film condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for condensation was proposed, and evaluated for the film condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the film condensation from the vapor–gas mixture were achieved. The laminar free film condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the film condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the film condensation from the vapor–gas mixture.

Swirling Flow of a Viscoelastic Fluid in a Cylindrical Casing

The swirling flow of a viscoelastic fluid in a cylindrical casing is investigated experimentally, using aqueous solutions of 0.05–1.0wt.% polyacrylamide as the working fluid. The velocity measurements are made using laser Doppler anemometer. The aspect ratios H∕R (H: axial length of cylindrical casing; R: radius of rotating disk) investigated are 2.0, 1.0, and 0.3. The Reynolds numbers Re0 based on the zero shear viscosity and the disk-tip velocity are between 0.36 and 50. The velocity measurements are mainly conducted for the circumferential velocity component. The experimental velocity data are compared to the velocity profiles obtained by numerical simulations using Giesekus model and power-law model. It is revealed that at any aspect ratios tested the dimensionless circumferential velocity component Vθ′ decreases with increasing Weissenberg number We. Both the Giesekus and power-law models could predict the retardation of circumferential velocity fairly well at small We. The extent of the inverse flow region, where the fluid rotates in the direction opposite to the rotating disk, is clarified in detail.

Flow kinematics in a rotating axial diffuser

A study of the flow velocity field inside a rotating axial diffuser with a circular cross-section is presented in the paper. Measurements of the flow velocity components were performed by the LDA system and confirmed the existence of two types of the flow: a rotating region near the spinning wall and a non-rotating region near the longitudinal axis of the diffuser. Significant increase of all three-velocity components was observed in a thin layer at the rotating diffuser wall. Influence of the diffuser rotation and its geometry on the radial outflow was observed as well. In addition, a phenomenological model for prediction of the distribution of the velocity components in the diffuser near-wall region was developed. Exponential law was applied to the phenomenological model, which included the dimensionless velocity component as a function of two Reynolds numbers––axial and tangential. The developed model confirmed experimental results and showed substantial influence of axial and tangential Reynolds numbers on all velocity components in the vicinity of the diffuser wall.

Contents Volume 28

A new similarity transformation has been devised for extensive studies of accelerating non-Newtonian film flow. The partial differential equations governing the hydrodynamics of the flow of a power-law fluid down along an inclined plane surface are transformed into a set of two ordinary differential equations by means of the dimensionless velocity component approach. Although the analysis is applicable for any angle of inclination α(0⩽α<π/2), the resulting one-parameter problem involves only the power-law index n. Nevertheless, physically essential quantities, like the velocity components and the skin-friction coefficient, do depend on α and relevant relationships are deduced between the vertical and inclined cases. Accurate numerical similarity solutions are provided for n in the range from 0.1 to 2.0. The present method enables solutions to be obtained also for highly pseudo-plastic films, i.e. for n below 0.5. The mass flow rate entrained into the momentum boundary layer from the inviscid freestream is expressed in terms of a dimensionless mass flux parameter Φ, which depends on the dimensionless boundary layer thickness and the velocity components at the edge of the viscous boundary layer. Φ, which is thus an integral part of the similarity solution, turns out to decrease monotonically with n. This parameter is of particular relevance in the determination of the streamwise position at which the entire freestream has been entrained and viscous stresses prevail all the way to the free surface of the film. A short-cut method to facilitate rapid and yet accurate estimates of the mass flux parameter is developed to this end.

An extended study of the hydrodynamics of gravity-driven film flow of power-law fluids

A new similarity transformation has been devised for extensive studies of accelerating non-Newtonian film flow. The partial differential equations governing the hydrodynamics of the flow of a power-law fluid down along an inclined plane surface are transformed into a set of two ordinary differential equations by means of the dimensionless velocity component approach. Although the analysis is applicable for any angle of inclination α (0⩽α< π/2) , the resulting one-parameter problem involves only the power-law index n. Nevertheless, physically essential quantities, like the velocity components and the skin-friction coefficient, do depend on α and relevant relationships are deduced between the vertical and inclined cases. Accurate numerical similarity solutions are provided for n in the range from 0.1 to 2.0. The present method enables solutions to be obtained also for highly pseudo-plastic films, i.e. for n below 0.5. The mass flow rate entrained into the momentum boundary layer from the inviscid freestream is expressed in terms of a dimensionless mass flux parameter Φ, which depends on the dimensionless boundary layer thickness and the velocity components at the edge of the viscous boundary layer. Φ, which is thus an integral part of the similarity solution, turns out to decrease monotonically with n. This parameter is of particular relevance in the determination of the streamwise position at which the entire freestream has been entrained and viscous stresses prevail all the way to the free surface of the film. A short-cut method to facilitate rapid and yet accurate estimates of the mass flux parameter is developed to this end.