Parallel Flat Plates Research Articles

Modelling of Fluid Permeability at the Interface of the Metal-to-Metal Sealing Surface.

This paper presents a method for modelling the permeability of fluid at the interface formed between flat parallel plates and the sharp-edged ridges of a metal gasket. This work was divided into three stages. In the first stage, numerical calculations simulating the deformation (compression of the gasket) were performed. The calculations were carried out using thermomechanical static analysis with commercial software. The purpose of these calculations was to determine the contact area of the gasket ridges with the plates, the deformation of the gasket ridges, and the reaction force resulting from the degree of compression of the gasket. In the second part of this work, analytical calculations were performed to estimate the tightness level. The analytical model proposed in this paper was based on Darcy's equation, simulating fluid flow through a ring-shaped porous layer. The analytical model also took into account the shape of the roughness profile of the sealed surfaces. A mathematical Ausloos-Berman function based on fractal theory was used to represent it. In the last part of this work, experimental tests were carried out to determine the actual fluid permeability and thus verify the numerical and analytical calculations.

Influence of magnetohydrodynamics and chemical reactions on oscillatory free convective flow through a vertical channel in a rotating system with variable permeability

This study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity [Formula: see text]. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation.

Non-isothermal electroosmotic flow of a viscoelastic fluid through a porous medium in a microchannel

The influence of the temperature-dependent viscosity on the electroosmotic flow through a porous medium in a microchannel of parallel flat plates. At the end, an imposed electric field induces Joule heating and temperature gradients, modifying the viscosity of the fluid. The Phan-Thien–Tanner and Darcy–Forchheimer models describe the viscoelastic fluid through the porous media. Consequently, the electric double layer (EDL) overlaps at the center plane of the microchannel, causing an electrically charged porous matrix and modifying the zeta potential along the microchannel walls. Therefore, we define a zeta potential ratio of the porous matrix and that at the microchannel walls. Unlike similar investigations, the boundary condition for the zeta potential varies locally due to the temperature field, modifying the interaction among hydrodynamics, electrical, viscoelastic, thermal and porosity effects. A modified Péclet number is defined as a function of the porosity and thermal conductivity of the fluid and an effective charge density is determined based on the Poisson–Boltzmann equation, accounting for the pore size and the zeta potential ratio. The set of equations are solved numerically considering the lubrication approximation theory. We found that the influence of the temperature-dependent viscosity increases the shear stresses at the EDL region, particularly where the temperature rises to maximum values. Also, the overlapping of the EDL occurs mainly for low values of permeability. Finally, the pressure gradient involved in the Darcy law can be altered through the zeta potential ratio.

Two-dimensional model in a laminar flow slit photoreactor for the determination of surface kinetic constants considering the presence of diffusion limitations

Narrow slit reactors are widely used in laboratory testing of photocatalytic materials, as well as for the determination of kinetic coefficients in surface photocatalyzed reactions. In this work, the behavior of a continuous laminar flow slit reactor was described by a two-dimensional model, addressing the advection–diffusion problem in the fluid phase, coupled with a first-order chemical reaction on the reactor walls. The concentration profile of the reactant, in the transverse and longitudinal directions of the reactor, depends on two parameters that characterize the system; the Péclet number and the Damköhler number, in addition to the geometry of the reactor. Once a short distance from the reactor’s entrance has been surpassed, the relationship between the transversally averaged reactant concentration and the concentration existing on the catalytic surface becomes essentially constant, thus defining an (external) effectiveness factor. The simulations carried out for a wide range of values of the parameters characterizing the model showed that the effectiveness factor only depends on the Damköhler number, being independent of the value of the Péclet number and of the relationship between the reactor length and the distance separating the plates. An analytical expression for the effectiveness factor as a function of the Damköhler number was proposed, which allows to determine the value of the kinetic coefficient for the surface reaction (ks), even in the presence of important limitations to mass transfer. The methodology proposed was illustrated performing experiments of photocatalytic oxidation of toluene in air (with Péclet numbers ranging from 20 to 40), employing a paint formulated with carbon-doped TiO2 in a continuous laboratory photoreactor of flat parallel plates. The observed toluene conversions were in the range of 13 to 26 %, consequently, the calculated Damköhler number was Da = 0.0307 and the surface kinetic coefficient thus determined (for 50 % of relative humidity and 42.3 W/m2 of irradiance flux) was ks = 1.262 10-4 m/s. The significance of this work lies in the development of a comprehensive model that can be used to know the surface kinetics in photocatalytic reactions, applicable to scenarios where there are considerable mass transfer limitations or not.

Structure and dynamics of amphiphilic patchy cubes in a nanoslit under shear.

Patchy nanocubes are intriguing materials with simple shapes and space-filling and multidirectional bonding properties. Previous studies have revealed various mesoscopic structures such as colloidal crystals in the solid regime and rod-like or fractal-like aggregates in the liquid regime of the phase diagram. Recent studies have also shown that mesoscopic structural properties, such as an average cluster size M and orientational order, in amphiphilic nanocube suspensions are associated with macroscopic viscosity changes, mainly owing to differences in cluster shape among patch arrangements. Although many studies have been conducted on the self-assembled structures of nanocubes in bulk, little is known about their self-assembly in nanoscale spaces or structural changes under shear. In this study, we investigated mixtures of one- and two-patch amphiphilic nanocubes confined in two flat parallel plates at rest and under shear using molecular dynamics simulations coupled with multiparticle collision dynamics. We considered two different patch arrangements for the two-patch particles and two different slit widths H to determine the degree of confinement in constant volume fractions in the liquid regime of the phase diagram. We revealed two unique cluster morphologies that have not been previously observed under bulk conditions. At rest, the size of the rod-like aggregates increased with decreasing H, whereas that of the fractal-like aggregates remained constant. Under weak shear with strong confinement, the rod-like aggregates maintained a larger M than the fractal-like aggregates, which were more rigid and maintained a larger M than the rod-like aggregates under bulk conditions.

Heat transfer characteristics in Williamson fluid flow in a vertical channel with chemical reaction and entropy production

This research endeavor investigates the natural convection flow of Williamson fluid in the region between two vertical parallel flat plates via a porous medium. Impacts of viscous dissipation, joule heating, exponential space, and thermal-dependent heat sources (ESHS/THS) are invoked. Mass transfer is also studied in accounting for chemical reaction impact. The governing non-linear PDEs are reduced to ODEs in non-dimensional form under adequate transformation relations. The numerical technique, namely, Runge-Kutta fourth-order, is utilized to tackle the problem with the shooting method. Additionally, second-law analysis is presented in terms of entropy production. The effects of numerous regulating parameters occurred in the problem relevant to flow, heat and mass transport, and entropy production are discussed via graphical mode of representation. Moreover, the quantities of physical significance are computed, displayed in graphical form, and discussed. For verification of acquired results, a comparison is also made using HPM with prior research, which was found to be in excellent agreement. It is concluded that the fluid temperature field enhances with upsurging values of pertinent parameters. The influence of the convective surface parameter and order of reaction are found to make augmentation in mass diffusion. Further, the effect of joule heating is noticed to increase the rate of heat transfer, while the reverse scenario is observed with upsurging values of heat source parameters. The influence of viscous dissipation is seen to increase entropy production.

Proposal for a New Differential High-Sensitivity Refractometer for the Simultaneous Measurement of Two Refractive Indices and Their Differences.

The refractive index of a liquid serves as a fundamental parameter reflecting its composition, thereby enabling the determination of component concentrations in various fields such as chemical research, the food industry, and environmental monitoring. Traditional methods for refractive index (RI) measurement rely on light deflection angles at interfaces between the liquid and a material with a known refractive index. In this paper, the authors present a new differential refractometer for the highly sensitive measurement of RI differences between two liquid samples. Using a configuration with two cells equipped with flat parallel plates as measuring elements, the instrument facilitates accurate analysis. Namely, the sensor signals from both the solution and the solvent cuvette are generated simultaneously with one laser pulse, reducing the possible fluctuations in the laser radiation intensity. Our evaluation shows the high sensitivity of RI measurements <7×10-6), so this differential refractometer can be proposed not only as a high-sensitivity sensing tool that can be used for mobile detection of nanoparticles in solution samples but also to determine the level of environmental nano-pollution using water (including rain, snow) samples from various natural as well as industrial sources, thus helping to solve some important environmental problems.

Rarefied Flow Simulations of Heat Transfer Across Evacuated Cryogenic Tank Insulation Structures

The Direct Simulation Monte Carlo Method computations are performed to investigate the heat transfer across highly evacuated cryogenic tank insulation structures. These structures usually consist of one cold and one hot wall with a temperature difference up to 260 K surrounding a rarefied gas which originates from permeating or leaking propellant. To validate the flow solver PICLas for this application, heat transfer results across parallel flat plates with nonflowing gaseous hydrogen and methane are compared to empirical relations of rarefied gas heat transfer and reference computations, showing good agreement with a deviation of less than 11%. Because gas flow usually occurs during and after evacuation, the heat transfer and skin friction coefficient in a symmetrical hydrogen channel flow with a wall distance of 30 mm is compared with literature data, showing a good match with a Nusselt number deviation of less than 20%. Furthermore, honeycomb tank insulation structures are analyzed, which can be used for future cryogenic liquid rocket tanks. Here, rarefied flow simulations are performed for slitted honeycomb structures with and without throughflow of hydrogen gas at a Knudsen number of 1.5 and transitional flow conditions at a Knudsen number of 0.1. The heat transfer results at the honeycomb sandwich are 50 to 70% below empirical relations for heat transfer across flat plates. Throughflow does not affect the heat transfer across the honeycomb because the Peclet number is less than 0.01.

Vortex-plate interaction in wake-induced vibration: A study of single and parallel flat plates behind a cylinder

This numerical study investigates the wake-induced vibration of single or parallel flat plates mounted in the wake of a circular cylinder in laminar flow. The results highlight the critical role of flat plate positioning, as it influences their ability to act as control mechanisms or experience significant vibrations. For a single plate, mounting outside the critical position initiates large amplitude vibrations, gradually decreasing as the plate moves away from the horizontal axis. Additionally, vibrations with moderate amplitudes are observed at specific short horizontal positions due to variations in the near-wake structure. In the case of parallel plates constrained to vibrate independently, vibrations only occur when there is sufficient space for shear-layer interaction. Different vortex suppression and plate vibration mechanisms are identified by adjusting the vertical gap, where increasing the gap reduces the non-vibrating zone. The study also examines a range of reduced velocities, revealing that although the plate(s) follow the upstream cylinder's shedding frequency in all configurations, this frequency may be affected and altered in short gaps. Comparing single and parallel plates demonstrates their potential for designing energy harvesting systems. However, parallel plates offer a slight advantage due to using independent objects within a relatively identical area.

Simulation Analysis of Metallic Particles Movement in Typical Structure of Oil-immersed Power Transformer

The insulation performance of oil-immersed power transformers is closely involved with the movement of metal particle impurities, and the movement characteristics of metal particles are not only influenced by the electric field, but also by the oil flow. In this paper, a solid-liquid two-phase flow simulation model was constructed, and the effect of electric field on the motion of metal particles was considered. Firstly, the validity of the simulation model was verified by using the experimentally observed motion of metal particles in the horizontal oil channel between parallel flat plate electrodes, based on which the motion of metal particles in the typical oil channels of a 500kV power transformer was studied. It was found that when the metal particles passed through the oil flow inlet, the number of metal particles settling increased with the increase of particle size. All the metal particles with 1mm particle size sank in the oil flow inlet during the oil migration process, it was almost impossible to enter the low, medium and high voltage winding parts. Through the middle or upper end of the high voltage winding, the smaller particles (50μm, 150μm) would easily migrate with the oil flow and move faster; the larger particles (500μm) would move slower or be more easily deposited. This research holds significant practical implications in the engineering study of metal particle motion distribution within transformers.

COMBINED EFFECT OF LOCAL THERMAL NONEQUILIBRIUM AND GRAVITY MODULATION ON THERMAL INSTABILITY IN MICROPOLAR NANOFLUID SATURATED POROUS MEDIA

In the present paper an effect of gravity modulation in a horizontal parallel flat plate having micropolar nanofluid saturated by a porous medium is examined. Local thermal nonequilibrium (LTNE) has been observed for the problem, i.e., the fluid, particle, and solid matrix are at different temperatures. Onset of convection and heat and mass transfer for both the cases, i.e., linear stability and nonlinear stability, is analyzed. We conclude that rate of convection in the LTNE case is faster than in the LTE case. Effect of porosity is observed in the LTNE region, which is opposite to the effect observed in the LTE region. Increase in value of A, K&lt;sub&gt;1&lt;/sub&gt;, and &amp;delta; delay the rate of convection. Small value of frequency of gravity modulation forms a greater number of small periods which delay the rate of convection. On increasing the value, heat transfer increases. At higher frequency of modulation we obtain the case similar to unmodulated case.

A Study of the Factors Influencing Multipactor to Low-Pressure Gas Discharge

Multipactor and low-pressure gas discharges have a negative impact on the performance and security of microwave components in space. In this manuscript, a 2-dimensional parallel flat plate structural model was designed to simulate the breakdown of multipactor to low-pressure gas discharges. The breakdown levels in the pressure range of 0.1 to 100 torr were verified under the conditions of the Ag material, 4-mm gap, 2.6-GHz frequency, and air as the background gas. Random secondary electron emission and gas molecule collision processes are incorporated, and the effect of their transition section is studied using trajectory tracking and Monte Carlo methods. A comparison of the model to the available experimental data demonstrates the model’s accuracy. On this basis, the variation of gas adsorption in relation to the surface secondary electron yields was considered, and the effect of the gas adsorption issues on breakdown level was calculated by means of numerical simulations based on some assumptions. The calculation reveals that in a finite volume of space, smaller desorption volumes cause negligible pressure changes, but the secondary electron emission capacity of the material decreases, which, in turn, leads to a flat or rising breakdown level. On the contrary, the larger the desorption volume, the more the gas is collisionally ionized and the breakdown level decreases.

Numerical study of the thermophoretic velocity of ternary hybrid nanofluid in a microchannel bounded by the two parallel permeable flat plates

Numerical study of the thermophoretic velocity of ternary hybrid nanofluid in a microchannel bounded by the two parallel permeable flat plates

Effect of aspect ratio and inclined angle on the fluid flow and heat transfer past two parallel flat plates

The flow past two parallel flat plates is undoubtedly one of the most classic problems in fluid mechanics, as the aerodynamic and heat transfer performance can be significantly affected by the geometry of the flat plate. In this work, using the open-source package OpenFOAM, we first performed a numerical investigation on the fluid flow and heat transfer past two parallel flat plates with different aspect ratios (AR) and inclined angles (α). The representative vortex structures and instantaneous flow patterns were presented and analyzed. We then discussed the local force characteristics and heat transfer rate on the plate walls, as well as the velocity and temperature distributions near the wake. The global flow unsteadiness and heat transfer characteristics were obtained. The numerical results revealed that larger AR and α enhanced the flow unsteadiness and increased the fluid force. The global heat transfer performance increased with increasing α, but first decreased and then increased with increasing AR. The objective of this work was to further achieve a more effective flat plate application and to provide theoretical support for its improvement.

A non-iterative solution for frost growth on flat surfaces

An algebraic, first-principles solution for frost growth on horizontal flat surfaces is derived. To avoid dependence on the frost surface temperature, the proposed solution uses a generic, power-law frost density expression. This yields a new class of non-iterative, fully-algebraic solutions to the problem of frost growth and densification on flat surfaces that are based explicitly on time and heat transfer characteristics. Closure of the derived solution is reached via semi-empirical frost property expressions. With three frost density expressions selected from literature, the predictive accuracy of the proposed frost thickness solution for each density expression is compared to flat plate and parallel plate frost thickness databases. The proposed solution is shown to accurately predict frost thickness, with 73.2% and 81.5% of the predictions falling within ±20% proportional error bands for the flat and parallel plate geometries respectively. Moreover, the proposed solution is shown to be comparably accurate to other predictive methods. The proposed approach is particularly useful in applications that require a non-iterative implementation, or those interested in decreasing computational effort in frost predictions.

On fast peristaltic waves

An asymptotic analysis is conducted of the effect surface vibrations may play in mitigating the resistance present in the system consisting of a fluid contained between a pair of parallel flat plates in relative motion. Previous numerical computations of this situation, which has applications in both biological and technological contexts, have suggested that small vibrations that move at a fast phase speed can lead to substantial reductions in the resistance. The effect seems to be a somewhat intricate function of the wavelength of the vibration modes. Our analysis uncovers the properties of the various phenomena that are at work and describes the interplay between them. The techniques employed here lend themselves to the extension to other situations including problems in which propulsion effects in fluid systems can be induced by vibrations.

Effect of Flow Distributor Configuration on the Hydrodynamics in a Multipurpose Flow Electrochemical Reactor: Numerical Analysis and Experimental Characterization Employing Digital Image Treatment

Electrochemical reactors with a flat parallel plate electrode configuration and diverse flow channel designs have been extensively used in the study of different electrochemical processes at lab and bench scales, and they have been scaled up for some electrosynthesis and energy-storage processes at semipilot and industrial levels. Progress in the electrochemical process applications demands the use of different computer and experimental-assisted techniques to design novel electrochemical reactors. The objective of this work is to evaluate the hydrodynamic performance of different electrochemical reactor designs and quantify their effect on velocity magnitude through numerical and experimental studies using computational techniques like computational fluid dynamics (CFD) and digital image treatment. For local velocity magnitude measurements, a digital imaging treatment, based on the use of an optical flow algorithm, to try the validation of velocity profiles obtained by CFD is implemented. This experimental technique determined reliably that the problems associated with the use of the empty channel in the flow pattern are mainly associated with high velocities and recirculation zones, which are not detected by CFD simulations in the first instance. Also, the findings associated with the velocity behavior using this proposed technique agreed with those obtained by the traditional experimental flow characterization technique like residence time distribution, nevertheless, further work will be needed to refine the measurements and perform its comparison with other most employed velocimetry techniques.

Casimir effect associated with fractional laplacian and fractal dimensions

Casimir effect predicts that two parallel flat neutral plates are attracted to each other due to quantum fluctuations of the electromagnetic field. In this communication, we study Casimir effect based on two different approaches: the first one is correlated to fractional Laplacian by means of fractional derivatives operators whereas the second one is associated to fractal dimensions. It was observed that, in both approaches, the Casmir zero-point energy of the fields is affected by the fractional order parameter and the numerical value of the fractal dimensions. The first model requires the use of the Hurwitz zeta function and no regularization technique is strongly required. Nevertheless, the second model necessitates the use of the regularization technique augmented by the Lifshitz fixed point and Schwinger proper-time representation mainly when a particular eigenvalue problem is used. • 1-Casimir effect has been studied based on fractional Laplacian and fractal dimensions. • 2-Casmir zero-point energy is affected by the fractional order parameter and fractal dimensions. • 3-The fractional model requires the use of the Hurwitz zeta function without the need of the regularization technique. • 4-The fractal model requires the use of regularization technique and the Lifshitz fixed point approach.

Mixed electroosmotic/pressure-driven flow for a generalized Phan–Thien–Tanner fluid in a microchannel with nonlinear Navier slip at the wall

This work derives an approximate solution of the laminar viscoelastic fluid flow through a parallel flat plate microchannel, driven by electroosmotic and external pressure forces. In contrast to other works published in the past, in the present analysis, the fluid’s rheology obeys the generalized Phan–Thien–Tanner model that has been proposed recently, which uses the Mittag-Leffler function instead of linear or exponential functions of the trace for the stress tensor. The hydrodynamic analysis considers a non-linear Navier slip law at the wall that follows a power-law behavior on the shear stress. For the electric potential in the electric double layer, the Debye–Hückel approximation was used, and it is assumed that the wall’s zeta potentials are symmetric. The solution obtained in this work depends on several dimensionless parameters that allow controlling the flow: ɛWi2 characterizes the fluid’s viscoelasticity, the electrokinetic parameter κ̄, the dimensionless slip coefficient L̄, the slip-power exponent m, and the ratio between pressure and electroosmotic forces, G. Besides, the influence of two parameters of the Mittag-Leffler function, α and β, notably affects the flow’s characteristics. Our results evidence the important consequences of considering the generalized Phan–Thien–Tanner model and the slippage effect on the flow field compared to that described by the Phan–Thien–Tanner model.

Critical Velocity Experimental Assessment in Flat Plate Fuel Element for Nuclear Research Reactor

Aluminum-coated plates, containing a uranium silicide (U3Si2) meat dispersed in an aluminum matrix, are commonly used in the fuel elements of Material Testing Reactors (MTRs). These fuel elements are typically comprised of narrow channels formed by parallel flat plates, which allow coolant flow to remove the heat of fission reactions. It is important to mention that the thickness of the plates is much smaller than their width and height. The high flow rates needed to ensure efficient fuel-element cooling may cause fuel-plate mechanical failures due to instability induced by the flow in the channels. In the case of critical velocity, excessive permanent deflections of these plates can cause blockage of the flow channels and lead to overheating. An experimental facility that simulates a plate-like fuel element with three coolant channels was developed for this work. The test-section dimensions were based on the Fuel Element design of the Brazilian Multipurpose Reactor (RMB), project being coordinated by the National Commission of Nuclear Energy (CNEN). Experiments were performed to reach Miller's critical velocity condition. This critical condition was reached at 14.5 m/s leading to consequent plastic deformation of the fuel plates