scholarly journals Application of Schwarz–Christoffel mapping to the analysis of conduction through a slot

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150292 ◽  
Author(s):  
Ehud Yariv ◽  
John D. Sherwood
Keyword(s):  
Current Density ◽  
Plate Thickness ◽  
Slow Decay ◽  
Slot Length ◽  
Conducting Plate ◽  
Implicit Equations ◽  
Generic Problem ◽  
Two Parameters ◽  
Christoffel Transformation ◽  
Excess Resistance

We consider the generic problem of steady conduction through a slot traversing a non-conducting plate that separates two semi-infinite conducting regions. The current-density field is conservative; the dimensionless problem governing its potential depends upon a single geometric parameter, h , the ratio of the slot length (i.e. the plate thickness) to its width. We construct a Schwarz–Christoffel transformation to handle this two-dimensional transport problem. The transformation is expressed in terms of two parameters which are related to h through two implicit equations; in the limit h →0, it becomes explicit. Because of the slow decay of the current density at large distances from the slot, the integral representing the slot resistance diverges. The excess resistance of a finite-length slot relative to that of a zero-length slot is, however, finite. This excess resistance depends only upon the asymptotic behaviour of the potential far from the slot; it may therefore be directly obtained as a function of the two transformation parameters. Asymptotic approximations are found for the excess resistance at small and large h , respectively, scaling as h ln ⁡ h and h . The single-slot solution is used to analyse conduction through a periodic array of widely spaced slots.

Phosphate removal from source separated urine by electrocoagulation using iron plate electrodes

2009 ◽  
Vol 60 (11) ◽  
pp. 2929-2938 ◽  
Author(s):  
Xiang-yong Zheng ◽  
Hai-Nan Kong ◽  
De-yi Wu ◽  
Chong Wang ◽  
Yan Li ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Current Density ◽  
High Current Density ◽  
Tap Water ◽  
Complete Removal ◽  
Phosphate Removal ◽  
Electrolysis Time ◽  
Two Parameters ◽  
Hydrolysis Of ◽  
P Removal

The aim of this study was to investigate the effects of current density, gap between electrodes, urine dosage, dilution and hydrolysis on phosphate removal from human urine by electrocoagulation technique using iron as electrodes. It was shown that, although a high current density and a long electrolysis time favored the removal of phosphate, an appropriate value for these two parameters can be obtained by taking into account the consumption of energy and iron in addition to P removal. In this study, current density 40 mA/cm2 and electrolysis time 20 min were shown to be optimal for 1.0 L pure urine to achieve nearly a complete removal (98%) efficiency of phosphate under the conditions of electrode area 160 cm2, the stirring speed 150 rpm, and the gap between electrodes 5 mm. Increase of gap between electrodes had little effect on phosphate removal, although it increased the energy consumption dramatically. The use of a high urine dosage reduced the efficiency of phosphate removal but increased the amount of removed phosphate. When pure urine was diluted with tap water, use of a higher tap water proportion for dilution expedited the electrolysis to achieve a nearly complete removal of phosphate in solution, but dilution caused the increase in energy consumption. It was also revealed that the hydrolysis of urine prior to electrocoagulation treatment impeded phosphate removal.

Numerical Study on Geometric Parameter effects of Power Generation Performances for Segmented Thermoelectric Generator

2018 ◽  
Vol 26 (01) ◽  
pp. 1850004 ◽  
Author(s):  
Mahesh Suresh Patil ◽  
Jae-Hyeong Seo ◽  
Moo-Yeon Lee
Keyword(s):  
Power Generation ◽  
Waste Heat Recovery ◽  
Thermoelectric Generator ◽  
Waste Heat ◽  
Numerical Study ◽  
Plate Thickness ◽  
Area Ratio ◽  
Physical Parameters ◽  
Thermoelectric Element ◽  
Conducting Plate

Thermoelectric generator (TEG) is a promising option in waste heat recovery with various advantages including nonmoving components, very low operating noise and overall high stability. However, low power generation efficiency of TEGs is still concerned for application in wider fields. The objective of the present study is to investigate the parameters affecting the performance and efficiency of segmented TEG. The physical parameters including length ratio, length-to-area ratio and thickness of conducting plate were considered. In addition, the effect of varying hot side temperature was analyzed. Performance of segmented TEG was compared based on the power generation and conversion efficiency. The results of the investigation showed that increasing Bi2Te3 length in the segmented TEG made up of Bi2Te3 and SiGe increased the maximum power generation and efficiency. As length-to-area ratio increased, the power generation decreased, however, efficiency increased slightly. In addition, as the hot side temperature increased from 150[Formula: see text]C to 650[Formula: see text]C, the power generation and efficiency both increased. Power generation and efficiency of segmented TEG increased when the conducting plate thickness was increased. The power generation and efficiency were 39.2% and 51.9% higher for TEG with asymmetrical element than TEG with symmetrical element showing that asymmetrical element would be better option for same thermoelectric element volume.

INTERNAL STRESS OF CHROME COATINGS ELECTRODEPOSITED FROM SOLUTIONS OF CHROMIUM (III) SALTS

2019 ◽  
Vol 62 (12) ◽  
pp. 33-38 ◽  
Author(s):  
Evgeniy G. Vinokurov
Keyword(s):  
Experimental Data ◽  
Tensile Stress ◽  
Internal Stress ◽  
Compressive Stress ◽  
Current Density ◽  
Plate Thickness ◽  
Similar Data ◽  
Thin Coatings ◽  
The Difference

Experimental data on internal stress in chromium coatings electrodeposited from Cr(III)-solutions have been obtained. Tensile stress 250-300 MPa is observed in thin coatings with thickness was below 1-3 μm. The internal stress is practically independent on current density and pH of the solution. A reduction in the plate thickness corresponding to σ=0 is observed, when pH has changed from 1.2 to 1.6 and current density from 30 to 35 A/dm2 at higher values of pH and current density compressive stress is observed and increases the difference in the stress values at greater thicknesses of the coatings: ((– 10) - (– 50) MPa). These results have been compared with similar data for the coatings deposited from Cr(VI) solutions including the effects of the non-metal inclusions in the coatings (for Cr(III)-bath H – 10.5 - 13 at. % (26 - 32 ml H2 / g Cr), O – 0.06-0.6 at. %, С – 0.04-7.8 at. %; for Cr(VI)-bath H – 1.8 at. %, O – 1.2 at. %, С – 0 at. %)). Compressive stress, related with the inclusions (including carbides) is the major cause, limiting the possibility to improve the characteristics of chromium coatings and to deposit coatings of the quality comparable to that of chrome plated from Cr(VI) baths.

Electrochemical reactions at PbO2 electrodes. Part I. The passivation of β-PbO2 in perchloric acid

1967 ◽  
Vol 45 (18) ◽  
pp. 2039-2044 ◽  
Author(s):  
N. A. Hampson ◽  
P. C. Jones ◽  
R. F. Phillips
Keyword(s):  
Diffusion Equation ◽  
Current Density ◽  
Perchloric Acid ◽  
Electrochemical Reactions ◽  
Perchlorate Ion ◽  
Two Parameters ◽  
Pbo2 Electrodes

The cathodic passivation of β-PbO2 electrodes in electrolytes based on perchlorate ion has been studied as a function of current density and electrolyte composition.Before passivation the electrode remains free of films based on Pb(II).Passivation results are correlated in the form of a modified diffusion equation incorporating two parameters kp and i1. [Formula: see text]

scholarly journals Parameters of liquid cooling thermal management system effect on the Li-ion battery temperature distribution

2021 ◽  
pp. 223-223
Author(s):  
Yuzhang Ding ◽  
Minxiang Wei ◽  
Rui Liu
Keyword(s):  
Rectangular Channel ◽  
Plate Thickness ◽  
Heat Conducting ◽  
Generation Model ◽  
Li Ion Battery ◽  
Liquid Cooling ◽  
Channel Entrance ◽  
Conducting Plate ◽  
Channel Aspect Ratio ◽  
Li Ion

In order to investigated the influence on the liquid cooling system cooling effect by changing the structural parameters, single Li-ion battery heat generation model is conducted, and used in following simulation. Subsequently, sixteen models are designed by orthogonal array, and the results are obtained by extremum difference analysis, which can quantify the influence degree, identify major and minor factors, and find the relatively optimum combination. Finally, different channel entrance layout is adopted to investigated. With a series of work, the effective of single battery heat generation model is proved by the discharge experiment. The coolant velocity has most evident influence on the Li-ion battery temperature rise, rectangular channel aspect ratio is second one, and the heat conducting plate thickness has the smallest influence. Similarly, for Li-ion battery temperature difference, the effect of heat conducting plate thickness and rectangular channel aspect ratio as the same, both are secondary factor, and coolant velocity is main factor. With different channel entrance layout, both the maximum temperatures denote a same upward trend, and better balance temperature distribution is obtained by adopt Case C system which with alternating arrange channel entrance layout.

On longitudinal motion in a magnetic field

1960 ◽  
Vol 9 (3) ◽  
pp. 455-464 ◽  
Author(s):  
H. P. Greenspan
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Exact Solution ◽  
Density Distribution ◽  
Current Density ◽  
Current Density Distribution ◽  
Longitudinal Motion ◽  
Conducting Plate ◽  
Electric And Magnetic Fields ◽  
Oblique Magnetic Field

An exact solution is presented of the equations and boundary conditions governing the steady longitudinal motion of a semi-infinite non-conducting plate in an oblique magnetic field. The discussion covers the distortion of the boundary layer, the structure of the induced electric and magnetic fields, the current-density distribution, and the behaviour of the fields near the edge of the plate.

Fitting a Three Dimensional PEM Fuel Cell Model to Measurements by Tuning the Porosity and Conductivity of the Catalyst Layer

2004 ◽  
Author(s):  
Mads Bang ◽  
Madeleine Odgaard ◽  
Thomas Joseph Condra ◽  
So̸ren Knudsen Kær
Keyword(s):  
Fuel Cell ◽  
Current Density ◽  
Cell Model ◽  
Three Dimensional ◽  
Catalyst Layer ◽  
Pem Fuel Cell ◽  
Gas Diffusion ◽  
Computational Domain ◽  
Proposed Model ◽  
Two Parameters

A three-dimensional, computational fluid dynamics (CFD) model of a PEM fuel cell is presented. The model consists of straight channels, porous gas diffusion layers, porous catalyst layers and a membrane. In this computational domain, most of the transport phenomena which govern the performance of the PEM fuel cell are dealt with in detail. The model solves the convective and diffusive transport of the gaseous phase in the fuel cell and allows prediction of the concentration of the species present. A special feature of the model is a method that allows detailed modelling and prediction of electrode kinetics. The transport of electrons in the gas diffusion layer and catalyst layer is accounted for, as well as the transport of protons in the membrane and catalyst layer. This provides the possibility of predicting the three-dimensional distribution of the activation overpotential in the catalyst layer. The current density dependency on the gas concentration and activation overpotential can thereby be addressed. The proposed model makes it possible to predict the effect of geometrical and material properties on the fuel cell’s performance. It is shown how the ionic conductivity and porosity of the catalyst layer affects the distribution of current density and further how this affects the polarization curve. The porosity and conductivity of the catalyst layer are some of the most difficult parameters to measure, estimate and especially control. Yet the proposed model shows how these two parameters can have significant influence on the performance of the fuel cell. The two parameters are shown to be key elements in adjusting the three-dimensional model to fit measured polarization curves. Results from the proposed model are compared to single cell measurements on a test MEA from IRD Fuel Cells.

A 3-D analytic eddy current model for a finite width conductive plate

2013 ◽  
Vol 33 (1/2) ◽  
pp. 688-706 ◽  
Author(s):  
Subhra Paul ◽  
Jonathan Z. Bird
Keyword(s):  
Eddy Current ◽  
Finite Thickness ◽  
Translational Motion ◽  
Plate Thickness ◽  
Computational Time ◽  
Finite Width ◽  
Magnetic Vector Potential ◽  
Content Type ◽  
Conductive Plate ◽  
Conducting Plate

Purpose – A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thickness of the plate is thin but not negligible. The paper aims to discuss these issues. Design/methodology/approach – The conducting and non-conducting regions are formulated in terms of decoupled magnetic vector potential components. In order to accurately compute the eddy current fields and forces the source field only needs to be applied on the surface of the conducting plate. The primary focus is on reducing the eddy current computational time. Findings – The accuracy of the presented approach is verified by utilizing a magnetic rotor that has both a rotational and translational motion. The proposed method is computationally efficient and its accuracy is validated using the finite element method. Research limitations/implications – The conducting plate thickness is assumed to be thin (but not negligible), and this enables the field interaction through the edge of the plate to be neglected. The lateral force is not calculated in the proposed approach. Practical implications – The calculation procedure presented is computationally fast and therefore this can enable the 3-D eddy current forces to be computed in near real-time. Originality/value – This paper presents a fully 3-D analytic based eddy current formlation for computing the eddy current fields and forces in a conducting plate of finite thickness and finite width. The modeling approach is shown to be computationally accurate and relatively fast.

Interaction of induced currents with cracks in thin plates

1988 ◽  
Vol 418 (1854) ◽  
pp. 229-246 ◽  
Keyword(s):  
Current Density ◽  
Eddy Currents ◽  
Plate Theory ◽  
Plate Thickness ◽  
Infinite Plate ◽  
Skin Depth ◽  
Simple Expression ◽  
Thin Plates ◽  
Faraday’S Law ◽  
Induced Currents

The induction of eddy currents in a conducting, non-magnetic plate containing a through-the-thickness crack is considered in the limit where the plate thickness ( h ) is small compared with the electromagnetic skin depth ( δ ). The plate is represented by a current sheet and the crack by a distribution of generalized current vortices. The current density for these vortices must differ from that of conventional hydrodynamic vortices so as to be consistent with Faraday’s law for self-induction. The vortex density, and hence the induced current in the cracked plate, can be obtained by solving a one-dimensional singular integral equation involving the current density for the uncracked plate which is assumed to be known. The case where the induced currents are produced by a probe coil, as in eddy-current non destructive inspection, is investigated in detail and a simple expression is derived for ∆ Z , the change in coil impedance due to the crack. The formalism is applied to the specific problem of an infinite plate containing a straight crack. Analytical results are presented for the limiting cases of long and short cracks, and a numerical method based on Gauss-Chebyshev quadrature is used for intermediate crack length. These theoretical results are compared with experimental measurements of ∆ Z and the thin-plate theory is found to be in excellent agreement with experiment (to within 5% or better) for values of h / δ up to 0.4.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

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