On the role of the microporous layer in PEMFC operation

Size: px
Start display at page:

Download "On the role of the microporous layer in PEMFC operation"

Transcription

1 The final publicatin is available at Elsevier via This manuscript versin is made available under the CC-BY-NC-ND 4.0 license On the rle f the micrprus layer in PEMFC peratin Jeff T. Gstick, Maris A. Iannidis*, Michael W. Fler and Mark D. Pritzker Department f Chemical Engineering, University f Waterl, Waterl, ON N2L 5N5 *Crrespnding Authr: miannid@uaterl.ca

2 Abstract The cnditin f liquid ater breakthrugh at the cathde f plymer electrlyte fuel cells (PEMFC) is studied experimentally and data n crrespnding ater saturatin and capillary pressure are prvided fr gas diffusin layers (GDL) ith and ithut a micrprus layer (MPL). The data demnstrate that the GDL saturatin at ater breakthrugh is drastically reduced frm ca. 25% t ca. 5% in the presence f MPL. This bservatin is cnsistent ith cnsideratins f invasin perclatin in finite-size lattices and suggests an explanatin fr the rle f MPL in imprving PEMFC perfrmance at high current densities. Keyrds: plymer electrlyte membrane fuel cell, gas diffusin layer, micrprus layer, ater management, capillary pressure, perclatin

3 1. Intrductin The accumulatin f excessive prduct ater in plymer electrlyte membrane fuel cells (PEMFC) is a factr limiting perfrmance at high current densities. Liquid ater generated by the cathde reactin perclates thrugh the prus gas diffusin layer (GDL) tards the gas channel. Ntably, the capillary number and viscsity rati prevailing during displacement f the gaseus phase by ater are such that a highly ramified, finger-like pattern characteristic f invasin perclatin is established [1,2]. Cnsequently, ater saturatin in the GDL and resistance t gaseus reactant transprt bth increase until ater first breaks thrugh at the GDL-channel interface. The liquid saturatin and capillary pressure assciated ith ater breakthrugh in GDL materials are clearly imprtant fr understanding resistance t gaseus reactant transprt due t ater accumulatin. Effrts t imprve PEMFC ater management have fcused n (1) impregnating the GDL pres ith a hydrphbic plymer and (2) adding a micr-prus layer (MPL) n ne face f the GDL. A recent systematic experimental study f these treatments by Ramasamy et al. [3] has clearly demnstrated imprved mass transfer hen these treatments are applied, bth in terms f increased limiting current as ell as reduced mass transfer resistance measured via AC impedance. The MPL treatment has been shn t be particularly beneficial althugh the actual functin f this layer is still under debate. The MPL presumably creates better electrical and thermal cntact beteen the catalyst layer and the GDL by prviding a smther, mre cntinuus interface, but the benefits f the MPL are mst nticeable at higher current cnditins indicating that it smeh imprves mass transfer. Since the MPL actually adds a diffusive resistance t mass transfer, it is generally thught that the MPL smeh alters the liquid ater distributin in the cell t a mre favrable arrangement fr

4 gas phase transprt [4,5]. The MPL questin has been recently addressed ith full-cell mdels [6,7], hich predict that the MPL acts as a capillary barrier t ater entering the cathde GDL and frces ater t permeate frm the cathde t the ande. Experimental attempts t cnfirm this mechanism have been incnclusive r cntradictry. Using a transparent fl field t mnitr ater in the ande, Spernjak et al. [8] fund that ater appears in the ande channels nly hen an MPL is used n the cathde side, hich they ffer as prf fr the functin f MPL as a capillary barrier. Similar experiments by Ge and Wang [9], hever, have attributed the appearance f ater in the ande t cndensatin since ater drplets nly appeared n channel alls and ere never bserved emerging frm the GDL. Atiyeh et al. [10] cnducted quantitative ater balance experiments and fund n discernible increase in ater cllected frm the ande hen an MPL is present n the cathde fr any given set f perating cnditins. In this rk ex-situ measurements are presented f the ater saturatin and assciated capillary pressure precisely at the pint f ater breakthrugh in GDL samples ith and ithut MPL. It is demnstrated that the ater saturatin at breakthrugh is dminated by finite-size effects ing t the very small thickness f the GDL. Namely, hen the entire inlet face f the GDL is expsed t ater (i.e. n MPL), a significant fractin f the pre vlume is invaded by nn-perclating clusters f pres filled ith ater and S at breakthrugh in the sample tested. When access f ater t the inlet face f the GDL is restricted t a very small area, the number f nn-perclating clusters f ater-filled pres present at breakthrugh [2] is drastically reduced and S In the presence f MPL, S at breakthrugh, suggesting that the MPL restricts the number f pints f entry f ater int the GDL.

5 2. Experimental The simultaneus measurement f capillary pressure and ater saturatin at breakthrugh as achieved ith a simple mdificatin f a technique detailed elsehere [11]. In rder t determine the pint n the capillary pressure curve here breakthrugh ccurred, a small circular piece (1 cm diameter) f dry hydrphilic membrane as inserted abve the GDL sample and bel the hydrphbic capillary barrier. The test prceeded as nrmal, ith each capillary pressure change resulting in a saturatin change up t the pint f ater breakthrugh. The breakthrugh pint can be easily detected since the saturatin changes drastically and rapidly due t icking f ater int the dry hydrphilic membrane placed abve the sample. Figure 1(left) shs the ater uptake respnse btained frm this test. The pint f ater breakthrugh is clearly visible as a sudden change in GDL ater uptake, alling the saturatin and capillary pressure just befre breakthrugh can be easily determined. Figure 1(right) shs that the capillary pressure curve up t the pint f breakthrugh btained ith the mdified methd is essentially the same as the capillary pressure curve btained fr the same material ith the unmdified methd [11]. Slight differences in the t curves are due t the fact that they ere btained frm different samples. T independently verify the breakthrugh pints fund using the mdified capillary pressure device, a secnd test as perfrmed similar t that f Benziger et al. [12]. A piece f GDL as affixed t the end f a tube and the head f ater abve the sample as increased in 5 cm increments, aiting 5 minutes at each pint, until breakthrugh as bserved. This simple test des nt prvide saturatin at breakthrugh, but cnfirms that the mdified capillary pressure device bserves the crrect breakthrugh pressure.

6 Tests ere perfrmed n SGL10BA and SGL10BB gas diffusin layers. These materials had the same GDL substrate and hydrphbic plymer cntent (5 t%). The SGL10BB sample had an m thick MPL applied n ne side [13]. In tests ith the SGL10BB sample, the MPL as placed facing the ater inlet as ell as aay frm it. These tests are referred t as SGL10BB-I and SGL10BB-O, respectively. Tests ere als cnducted n an SGL10BA sample here the inlet face f the sample is cvered ith an impermeable PTFE mask having a 600- m hle punctured in the center fr ater fl (dented SGL10BA-P). Tests n SGL10BA ith the full face expsed t liquid ater are dented as SGL10BA-F.

7 3. Results and Discussin The main findings f this study are summarized in Figure 2. Regarding the plain GDL substrate material (SGL10BA), it is evident that the Pc S relatinship fr ater injectin is significantly affected by finite-size effects. Since GDL materials are very much thinner (ca pres acrss) than they are ide [14], a significant fractin f the sample pre vlume is invaded by nn-perclating clusters befre breakthrugh if the entire inlet face f the sample is expsed t ater (SGL10BA-F). In this case, ater breakthrugh ccurs at P 2500 Pa and a high saturatin ( S ). By cmparisn P 3800 Pa and c S 0.05 hen nly a very small fractin f the GDL inlet face is expsed t ater (SGL 10BA-P). This situatin is illustrated in the left and middle panels f Figure 3. c The Pc S relatinship fr ater injectin int SGL10BB is different depending n hether the MPL is fund n the inlet face (SGL10BB-I) r the utlet face (SGL10BB-O) f the sample. In the frmer case, the data are displaced tards higher capillary pressures, as expected since ater invasin int the GDL is cntrlled by the smaller pre sizes f the intervening MPL. In the latter case, the Pc S relatinship in the l capillary pressure range is essentially the same as in test SGL10BA-F, hich is expected since ater is first invading the substrate material in bth cases. In either case (SGL10BB-I r SGL10BB-O), the maximum ater saturatin achieved is abut 75%, demnstrating that the MPL is nt significantly filled ith ater at the maximum capillary pressure established. When the MPL is n the utlet face, ater breakthrugh in SGL10BB ccurs at P 6700 Pa and S Such high ater saturatin is easily understd since the GDL is filled substantially by ater c at the capillary pressure necessary fr ater t invade the smaller MPL pres. Water

8 breakthrugh in sample SGL10BB hen the MPL is n the inlet face ccurs at a similarly high capillary pressure ( P 6000 Pa), but in this case S c The fact that very similar breakthrugh saturatin is bserved in tests SGL 10BA-P and SGL10BB-I supprts the cnclusin that the MPL limits ater access t the GDL face. Water breaks thrugh the MPL at a fe islated lcatins at the MPL-GDL interface, in the same ay ater drplets emerge frm the GDL at the GDL-gas channel interface [2,15,16], regardless f hether r nt the MPL is cracked. Subsequent ater perclatin thrugh the GDL starts frm these lcatins, as ppsed t the entire face f the GDL, as depicted in Figure 3(right). This renders mst pres n the GDL face inaccessible t ater, dramatically reducing GDL saturatin at breakthrugh by reducing the number f dead end clusters (a finite-size effect). In this manner, reduced gas diffusivity is cnfined t a smaller part f the transprt dmain (the MPL), resulting in imprved perfrmance at high current densities. The breakthrugh pressures bserved in tests SGL10BA-P and SGL10BB-I shuld nt be expected t be the same due t the mre hydrphbic nature and smaller pres f the MPL cmpared t the hle punctured in the PTFE mask. Furthermre, breakthrugh pressures f the rder f 6000 Pa, bserved in tests SGL10BB-Iand SGL10BB-O are ler than expected frm the pre sizes f the MPL (<1 m). Rather, a breakthrugh pressure in this range indicates that cracks and defects in the MPL are the main pathays fr ater invasin. Interestingly, fl thrugh the MPL via cracks uld be beneficial since it eliminates the frmatin f dead-end clusters in the MPL that are characteristic f perclatin prcesses and cntribute significantly t ater saturatin at breakthrugh hen finite-size effects are imprtant. In fact, it might be advantageus t design the MPL ith strategically placed hles.

9 4. Cnclusins An explanatin fr the efficacy f the MPL in fuel cell peratin is prpsed based n finitesize effects related t invasin perclatin in thin GDLs. Water perclatin thrugh the MPL results in limited access f ater t the GDL inlet face. Cnsequently, far feer dead-end ater clusters cme int being at breakthrugh and therefre much ler ater saturatin is reached. Experimental evidence is prvided by a mdified versin f a recently reprted capillary pressure measurement technique [11] that alls bth the pressure and saturatin at breakthrugh t be simultaneusly identified. The saturatin at breakthrugh drps frm 27% t less than 3% hen an MPL intervenes beteen the GDL and the ater surce. A similar result is btained hen an therise impermeable mask ith a small puncture is placed beteen the ater and the GDL. These findings suggest that the effectiveness f the MPL might be further imprved by designing them ith large hles fr ater passage int the GDL, hile leaving the micr-prsity dry fr gas transprt.

10 5. References [1] R.Lenrmand, C.Zarcne, A.Sarr, Jurnal f Fluid Mechanics 135 (1983) 337. [2] P.K.Sinha, C.Y.Wang, Electrchim Acta 52 (2007) [3] R.P.Ramasamy, E.C.Kumbur, M.M.Mench, W.Liu, D.Mre, M.Murthy, Int J Hydrgen Energy 33 (2008) [4] U.Pasagullari, C.Y.Wang, J Electrchem Sc 151 (2004) A399. [5] J.H.Nam, M.Kaviany, Int J Heat Mass Trans 46 (2003) [6] A.Z.Weber, J.Neman, J Electrchem Sc 152 (2005) A677. [7] U.Pasagullari, C.Y.Wang, K.S.Chen, J Electrchem Sc 152 (2005) A1574. [8] D.Spernjak, A.K.Prasad, S.G.Advani, J Per Surces 170 (2007) 334. [9] S.Ge, C.Y.Wang, J Electrchem Sc 154 (2007) B998. [10] H.K.Atiyeh, K.Karan, B.Peppley, A.Phenix, E.Hallip, J.Pharah, J Per Surces 170 (2007) 111. [11] J.T.Gstick, M.A.Iannidis, M.W.Fler, M.D.Pritzker, Electrchem Cmm 10 (2008) [12] J.Benziger, J.Nehlsen, D.Blackell, T.Brennan, J.Itescu, J Membrane Sci 261 (2005) 98. [13] J.T.Gstick, M.W.Fler, M.A.Iannidis, M.D.Pritzker, Y.M.Vlfkvich, A.Sakars, J Per Surces 156 (2006) 375. [14] J.T.Gstick, M.A.Iannidis, M.W.Fler, M.D.Pritzker, J Per Surces 173 (2007) 277. [15] S.Litster, D.Sintn, N.Djilali, J Per Surces 154 (2006) 95. [16] X.G.Yang, F.Y.Zhang, A.L.Lubay, C.Y.Wang, Electrchem and Slid-State Let 7 (2004) A408.

11 6. Figure Captins Figure 1: Experimental results frm ater breakthrugh test. Left: Pressure and saturatin time traces fr SGL10BA shing the breakthrugh pint. Right: Cmparisn f capillary pressure curves btained using riginal and mdified methd up t the breakthrugh pint.

12 Figure 2: Capillary pressure curves fr SGL10BA and SGL10BB ith breakthrugh pints verlaid as filled markers ith crrespnding shapes. F: Full face expsed t ater, P: Punctured mask beteen ater and GDL, I: MPL facing ater inlet, O: MPL facing aay frm ater inlet.

13 Figure 3: Prpsed cnfiguratin f ater in the GDL ith different injectin cnditins. Left: Full face injectin leads t several dead-end clusters and a single breakthrugh cluster. Middle: Pint surce injectin leads t a single breakthrugh cluster. Right: Perclatin thrugh the MPL creates cnditins similar t pint-like injectin int the GDL. Grey shs ater and dashed line marks regins that uld be filled if they ere accessible.

The calculation method of small-scale water injection multiple in water drive reservoirs

The calculation method of small-scale water injection multiple in water drive reservoirs Available nline.jcpr.cm Jurnal f Chemical and Pharmaceutical Research, 04, 6(5):04-09 Research Article ISSN : 0975-7384 CODEN(USA) : JCPRC5 The calculatin methd f small-scale ater injectin multiple in

More information

Study Group Report: Plate-fin Heat Exchangers: AEA Technology

Study Group Report: Plate-fin Heat Exchangers: AEA Technology Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery

More information

EE247B/ME218: Introduction to MEMS Design Lecture 7m1: Lithography, Etching, & Doping CTN 2/6/18

EE247B/ME218: Introduction to MEMS Design Lecture 7m1: Lithography, Etching, & Doping CTN 2/6/18 EE247B/ME218 Intrductin t MEMS Design Lecture 7m1 Lithgraphy, Etching, & Dping Dping f Semicnductrs Semicnductr Dping Semicnductrs are nt intrinsically cnductive T make them cnductive, replace silicn atms

More information

Supporting information

Supporting information Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin

More information

Feasibility Testing Report Muscle Optimization Stage I

Feasibility Testing Report Muscle Optimization Stage I Feasibility Testing Reprt Muscle Optimizatin Stage I Team: P15001: Active Ankle Ft Orthtic Engineer: Nah Schadt Mechanical Engineer Engineer: Tyler Leichtenberger Mechanical Engineer Test Date: 10/14/2014

More information

A mathematical model for complete stress-strain curve prediction of permeable concrete

A mathematical model for complete stress-strain curve prediction of permeable concrete A mathematical mdel fr cmplete stress-strain curve predictin f permeable cncrete M. K. Hussin Y. Zhuge F. Bullen W. P. Lkuge Faculty f Engineering and Surveying, University f Suthern Queensland, Twmba,

More information

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment Science 10: The Great Geyser Experiment A cntrlled experiment Yu will prduce a GEYSER by drpping Ments int a bttle f diet pp Sme questins t think abut are: What are yu ging t test? What are yu ging t measure?

More information

Session #22: Homework Solutions

Session #22: Homework Solutions Sessin #22: Hmewrk Slutins Prblem #1 (a) In the cntext f amrphus inrganic cmpunds, name tw netwrk frmers, tw netwrk mdifiers, and ne intermediate. (b) Sketch the variatin f mlar vlume with temperature

More information

Lecture 02 CSE 40547/60547 Computing at the Nanoscale

Lecture 02 CSE 40547/60547 Computing at the Nanoscale PN Junctin Ntes: Lecture 02 CSE 40547/60547 Cmputing at the Nanscale Letʼs start with a (very) shrt review f semi-cnducting materials: - N-type material: Obtained by adding impurity with 5 valence elements

More information

Module 4: General Formulation of Electric Circuit Theory

Module 4: General Formulation of Electric Circuit Theory Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated

More information

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank CAUSAL INFERENCE Technical Track Sessin I Phillippe Leite The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Phillippe Leite fr the purpse f this wrkshp Plicy questins are causal

More information

Thermodynamics Partial Outline of Topics

Thermodynamics Partial Outline of Topics Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

More information

General Chemistry II, Unit II: Study Guide (part 1)

General Chemistry II, Unit II: Study Guide (part 1) General Chemistry II, Unit II: Study Guide (part 1) CDS Chapter 21: Reactin Equilibrium in the Gas Phase General Chemistry II Unit II Part 1 1 Intrductin Sme chemical reactins have a significant amunt

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

ChE 471: LECTURE 4 Fall 2003

ChE 471: LECTURE 4 Fall 2003 ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.

More information

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science Weathering Title: Chemical and Mechanical Weathering Grade Level: 9-12 Subject/Cntent: Earth and Space Science Summary f Lessn: Students will test hw chemical and mechanical weathering can affect a rck

More information

Math Foundations 20 Work Plan

Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

More information

Dead-beat controller design

Dead-beat controller design J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable

More information

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra Chem 115 POGIL Wrksheet - Week 8 Thermchemistry (Cntinued), Electrmagnetic Radiatin, and Line Spectra Why? As we saw last week, enthalpy and internal energy are state functins, which means that the sum

More information

3. Mass Transfer with Chemical Reaction

3. Mass Transfer with Chemical Reaction 8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,

More information

Lab 1 The Scientific Method

Lab 1 The Scientific Method INTRODUCTION The fllwing labratry exercise is designed t give yu, the student, an pprtunity t explre unknwn systems, r universes, and hypthesize pssible rules which may gvern the behavir within them. Scientific

More information

Question 2-1. Solution 2-1 CHAPTER 2 HYDROSTATICS

Question 2-1. Solution 2-1 CHAPTER 2 HYDROSTATICS CHAPTER HYDROSTATICS. INTRODUCTION Hydraulic engineers have any engineering applicatins in hich they have t cpute the frce being exerted n suberged surfaces. The hydrstatic frce n any suberged plane surface

More information

Part One: Heat Changes and Thermochemistry. This aspect of Thermodynamics was dealt with in Chapter 6. (Review)

Part One: Heat Changes and Thermochemistry. This aspect of Thermodynamics was dealt with in Chapter 6. (Review) CHAPTER 18: THERMODYNAMICS AND EQUILIBRIUM Part One: Heat Changes and Thermchemistry This aspect f Thermdynamics was dealt with in Chapter 6. (Review) A. Statement f First Law. (Sectin 18.1) 1. U ttal

More information

AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date

AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares

More information

A Study to Determine Reservoir Parameters and Remaining Oil Saturation by using Inter-well Tracer Test

A Study to Determine Reservoir Parameters and Remaining Oil Saturation by using Inter-well Tracer Test A Study t Determine Reservir Parameters and Remaining Oil Saturatin by using Inter-ell Tracer Test Erlng YANG, Tingting GU * Key Labratry n Enhanced Oil and Gas Recvery f the Ministry f Educatin, Nrtheast

More information

Biocomputers. [edit]scientific Background

Biocomputers. [edit]scientific Background Bicmputers Frm Wikipedia, the free encyclpedia Bicmputers use systems f bilgically derived mlecules, such as DNA and prteins, t perfrm cmputatinal calculatins invlving string, retrieving, and prcessing

More information

ALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?

ALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change? Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S

More information

Chapter 4. Unsteady State Conduction

Chapter 4. Unsteady State Conduction Chapter 4 Unsteady State Cnductin Chapter 5 Steady State Cnductin Chee 318 1 4-1 Intrductin ransient Cnductin Many heat transfer prblems are time dependent Changes in perating cnditins in a system cause

More information

THE MODIFIED ELECTRODES FOR THE APPLICATION OF POLAR MOLECULE DOMINATED ELECTRORHEOLOGICAL (PM-ER) FLUIDS

THE MODIFIED ELECTRODES FOR THE APPLICATION OF POLAR MOLECULE DOMINATED ELECTRORHEOLOGICAL (PM-ER) FLUIDS Internatinal Jurnal f Mdern Physics B ^fcfik \«i J e Vl. 21, Ns. 28 & 29 (2007) 4940-4944 WS Wrld Scientific x ' «www.wrldscientific.cm Wrld Scientific Publishing Cmpany THE MODIFIED ELECTRODES FOR THE

More information

CONSTRUCTING STATECHART DIAGRAMS

CONSTRUCTING STATECHART DIAGRAMS CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6

More information

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.

More information

A Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture

A Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu

More information

Dynamic network modeling of two-phase drainage in porous media

Dynamic network modeling of two-phase drainage in porous media PHYSICAL REVIEW E 71, 016308 2005 Dynamic netwrk mdeling f tw-phase drainage in prus media Mhammed S. Al-Gharbi and Martin J. Blunt Department f Earth Science and Engineering, Imperial Cllege, Lndn SW7

More information

Heat Effects of Chemical Reactions

Heat Effects of Chemical Reactions eat Effects f hemical Reactins Enthalpy change fr reactins invlving cmpunds Enthalpy f frmatin f a cmpund at standard cnditins is btained frm the literature as standard enthalpy f frmatin Δ (O (g = -9690

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

Determining the Accuracy of Modal Parameter Estimation Methods

Determining the Accuracy of Modal Parameter Estimation Methods Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system

More information

Numerical Simulation of the Thermal Resposne Test Within the Comsol Multiphysics Environment

Numerical Simulation of the Thermal Resposne Test Within the Comsol Multiphysics Environment Presented at the COMSOL Cnference 2008 Hannver University f Parma Department f Industrial Engineering Numerical Simulatin f the Thermal Respsne Test Within the Cmsl Multiphysics Envirnment Authr : C. Crradi,

More information

Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion

Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals f Diffusin Diffusin: Transprt in a slid, liquid, r gas driven by a cncentratin gradient (r, in the case f mass transprt, a chemical ptential

More information

NEW COREFLOOD INTERPRETATION METHOD BASED ON DIRECT PROCESSING OF IN-SITU SATURATION DATA

NEW COREFLOOD INTERPRETATION METHOD BASED ON DIRECT PROCESSING OF IN-SITU SATURATION DATA NEW COREFLOOD INTERPRETATION METHOD BASED ON DIRECT PROCESSING OF IN-SITU SATURATION DATA Matthe Gdfield, Stephen G Gdyear and Peter H Tnsley AEA Technlgy plc Winfrith, Drchester, Drset, DT2 8ZE, United

More information

NGSS High School Physics Domain Model

NGSS High School Physics Domain Model NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship

More information

Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Key Wrds: Autregressive, Mving Average, Runs Tests, Shewhart Cntrl Chart

Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Key Wrds: Autregressive, Mving Average, Runs Tests, Shewhart Cntrl Chart Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Sandy D. Balkin Dennis K. J. Lin y Pennsylvania State University, University Park, PA 16802 Sandy Balkin is a graduate student

More information

Lecture 13: Electrochemical Equilibria

Lecture 13: Electrochemical Equilibria 3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: 10.21.05 Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins

More information

[Abdurahman, 2(11): November, 2013] ISSN: Impact Factor: 1.852

[Abdurahman, 2(11): November, 2013] ISSN: Impact Factor: 1.852 IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Elucidate the Separatin Mechanisms f Cntinuus Micrave Radiatin Systems (CMWRS) Using Crude Oil Emulsins N.H.Abdurahman*1, N.H.Azharib2,

More information

EXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE

EXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

On Boussinesq's problem

On Boussinesq's problem Internatinal Jurnal f Engineering Science 39 (2001) 317±322 www.elsevier.cm/lcate/ijengsci On Bussinesq's prblem A.P.S. Selvadurai * Department f Civil Engineering and Applied Mechanics, McGill University,

More information

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal

More information

Guaranteeing Reliability with Vibration Simulation and Testing. Dr. Nathan Blattau

Guaranteeing Reliability with Vibration Simulation and Testing. Dr. Nathan Blattau Guaranteeing Reliability with Vibratin Simulatin and Testing Dr. Nathan Blattau . Nathan Blattau, Ph.D. - Senir Vice President Has been invlved in the packaging and reliability f electrnic equipment fr

More information

Bayesian nonparametric modeling approaches for quantile regression

Bayesian nonparametric modeling approaches for quantile regression Bayesian nnparametric mdeling appraches fr quantile regressin Athanasis Kttas Department f Applied Mathematics and Statistics University f Califrnia, Santa Cruz Department f Statistics Athens University

More information

Latz, p. Technjscpe. De lit. Observations made on board of. Dutch ships. June 1967

Latz, p. Technjscpe. De lit. Observations made on board of. Dutch ships. June 1967 Lat, p. Technjscpe De lit. Observatins made n bard f Dutch ships. June 1967 NETHERLANDS SHIP MODEL BASIN WAGENIN GEN Reprt N. 67-090-WO PAGE OBSERVATIONS MADE ON BOARD OF DUTCH SHIPS by Ir. R. Wahab. NETHERLANDS

More information

NAME TEMPERATURE AND HUMIDITY. I. Introduction

NAME TEMPERATURE AND HUMIDITY. I. Introduction NAME TEMPERATURE AND HUMIDITY I. Intrductin Temperature is the single mst imprtant factr in determining atmspheric cnditins because it greatly influences: 1. The amunt f water vapr in the air 2. The pssibility

More information

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS Christpher Cstell, Andrew Slw, Michael Neubert, and Stephen Plasky Intrductin The central questin in the ecnmic analysis f climate change plicy cncerns

More information

Modeling moisture absorption process of wood-based composites under over-saturated moisture conditions using two-part equations

Modeling moisture absorption process of wood-based composites under over-saturated moisture conditions using two-part equations Wd Sci Technl (2009) 43:143 152 DOI 10.1007/s00226-008-0201-x ORIGINAL Mdeling misture absrptin prcess f wd-based cmpsites under ver-saturated misture cnditins using tw-part equatins Sheldn Q. Shi Æ Dngfeng

More information

22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion

22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion .54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References -- J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (Addisn-Wesley, Reading, 966) T study neutrn diffusin

More information

3D FE Modeling Simulation of Cold Rotary Forging with Double Symmetry Rolls X. H. Han 1, a, L. Hua 1, b, Y. M. Zhao 1, c

3D FE Modeling Simulation of Cold Rotary Forging with Double Symmetry Rolls X. H. Han 1, a, L. Hua 1, b, Y. M. Zhao 1, c Materials Science Frum Online: 2009-08-31 ISSN: 1662-9752, Vls. 628-629, pp 623-628 di:10.4028/www.scientific.net/msf.628-629.623 2009 Trans Tech Publicatins, Switzerland 3D FE Mdeling Simulatin f Cld

More information

GEOL 2920C The Sedimentary Rock Cycle of Mars & Earth Eberswalde fan deposits: deltaic or alluvial? Deltas at Aeolis Dorsa(?

GEOL 2920C The Sedimentary Rock Cycle of Mars & Earth Eberswalde fan deposits: deltaic or alluvial? Deltas at Aeolis Dorsa(? GEOL 2920C The Sedimentary Rck Cycle f Mars & Earth Week 12 Basin Scale Prcesses n Mars I (April 16, 2018) Discussin Pints, Key Equatins, Key Figures (prepared by Jesse Tarnas) Eberswalde fan depsits:

More information

Interference is when two (or more) sets of waves meet and combine to produce a new pattern.

Interference is when two (or more) sets of waves meet and combine to produce a new pattern. Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme

More information

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter). Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)

More information

General Chemistry II, Unit I: Study Guide (part I)

General Chemistry II, Unit I: Study Guide (part I) 1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the

More information

THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC TESTS OF ELECTRONIC ASSEMBLIES

THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC TESTS OF ELECTRONIC ASSEMBLIES PREFERRED RELIABILITY PAGE 1 OF 5 PRACTICES PRACTICE NO. PT-TE-1409 THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC Practice: Perfrm all thermal envirnmental tests n electrnic spaceflight hardware in a flight-like

More information

Temperature Regime of Boreholes: Cementing of Production Liners

Temperature Regime of Boreholes: Cementing of Production Liners PROCEEINGS, Thirty-Ninth Wrkshp n Gethermal Reservir Engineering Stanfrd University, Stanfrd, Califrnia, February 4-6, 014 SGP-TR-0 Temperature Regime f Brehles: Cementing f Prductin Liners Izzy M. Kutasv

More information

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system

More information

2. Precipitation Chemistry Data

2. Precipitation Chemistry Data STIMATING TH ATMSPHRIC INT A WATRSH INPUT F PLLUTANTS PRRY J. SAMSN epartment f Atmspheric and ceanic Science, University f Michigan, Ann Arbr, All 4819-2143, U.S.A. (Received June 2, 1986; revised March

More information

Heat Management Methodology for Successful UV Processing on Heat Sensitive Substrates

Heat Management Methodology for Successful UV Processing on Heat Sensitive Substrates Heat Management Methdlgy fr Successful UV Prcessing n Heat Sensitive Substrates Juliet Midlik Prime UV Systems Abstract: Nw in 2005, UV systems pssess heat management cntrls that fine tune the exthermic

More information

A Study of Water and Carbonated Water Injection with Constant Pressure. Boundaries. Huan Yang

A Study of Water and Carbonated Water Injection with Constant Pressure. Boundaries. Huan Yang A Study f Water and Carbnated Water Injectin ith Cnstant Pressure Bundaries by Huan Yang A Thesis submitted t the Schl f Graduate Studies in partial fulfillment f the requirements fr the degree f Master

More information

Use a lens holder fabricated from SiC. SiC has a larger CTE than C-C, i.e. it is better matched to the SFL6.

Use a lens holder fabricated from SiC. SiC has a larger CTE than C-C, i.e. it is better matched to the SFL6. Frm: Steve Sctt, Jinsek K, Syun ichi Shiraiwa T: MSE enthusiasts Re: MSE mem 101b: allwable thickness f Vitn sheet Nvember 25, 2008 Update frm MSE Mem 101b Let s assume: Vitn thickness = 1 mm Vitn mdulus

More information

Rheology of carbon fibre reinforced cement-based mortar Banfill, Phillip Frank Gower; Starrs, Gerard; McCarter, William John

Rheology of carbon fibre reinforced cement-based mortar Banfill, Phillip Frank Gower; Starrs, Gerard; McCarter, William John Herit-Watt University Herit-Watt University Research Gateway Rhelgy f carbn fibre reinfrced cement-based mrtar Banfill, Phillip Frank Gwer; Starrs, Gerard; McCarter, William Jhn Published in: The Vth Internatinal

More information

800 Adenine Guanine. Gate Voltage (V)

800 Adenine Guanine. Gate Voltage (V) I. SUPPLEMENTARY FIGURES Surce-Drain Current (µa) 14 Thymine cverage (M.L.) 135 13 125 12 6 5 4 3.26.48.71.85 2.8-4 -2 2 4 7 Cytsine cverage (M.L.).6.2.5 1.1 3 6 8 Adenine cverage (M.L.).4.8 6 4 2 55 Guanine

More information

5.4 Measurement Sampling Rates for Daily Maximum and Minimum Temperatures

5.4 Measurement Sampling Rates for Daily Maximum and Minimum Temperatures 5.4 Measurement Sampling Rates fr Daily Maximum and Minimum Temperatures 1 1 2 X. Lin, K. G. Hubbard, and C. B. Baker University f Nebraska, Lincln, Nebraska 2 Natinal Climatic Data Center 1 1. INTRODUCTION

More information

Analysis of the Effect of Die Angle Variation on the Behavior of Temperature Profile in Extrusion Process by using ANSYS Poly Flow Software

Analysis of the Effect of Die Angle Variation on the Behavior of Temperature Profile in Extrusion Process by using ANSYS Poly Flow Software .ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 Vlume-7, Issue-3, May-June 2017 Internatinal Jurnal f Engineering and Management Research Page Number: 494-500 Analysis f the Effect f Die Angle

More information

11. DUAL NATURE OF RADIATION AND MATTER

11. DUAL NATURE OF RADIATION AND MATTER 11. DUAL NATURE OF RADIATION AND MATTER Very shrt answer and shrt answer questins 1. Define wrk functin f a metal? The minimum energy required fr an electrn t escape frm the metal surface is called the

More information

Better definition of the objective, novelty and relevance of this study improving the structure, content and length of the publication accordingly:

Better definition of the objective, novelty and relevance of this study improving the structure, content and length of the publication accordingly: Answers t REVIEW2 Interactive cmment n An imprved perspective in the representatin f sil misture: ptential added value f SMOS disaggregated 1km reslutin prduct by Samir Khdayar et al. Answers t Reviewer

More information

Checking the resolved resonance region in EXFOR database

Checking the resolved resonance region in EXFOR database Checking the reslved resnance regin in EXFOR database Gttfried Bertn Sciété de Calcul Mathématique (SCM) Oscar Cabells OECD/NEA Data Bank JEFF Meetings - Sessin JEFF Experiments Nvember 0-4, 017 Bulgne-Billancurt,

More information

Aerodynamic Separability in Tip Speed Ratio and Separability in Wind Speed- a Comparison

Aerodynamic Separability in Tip Speed Ratio and Separability in Wind Speed- a Comparison Jurnal f Physics: Cnference Series OPEN ACCESS Aerdynamic Separability in Tip Speed Rati and Separability in Wind Speed- a Cmparisn T cite this article: M L Gala Sants et al 14 J. Phys.: Cnf. Ser. 555

More information

A Polarimetric Survey of Radio Frequency Interference in C- and X-Bands in the Continental United States using WindSat Radiometry

A Polarimetric Survey of Radio Frequency Interference in C- and X-Bands in the Continental United States using WindSat Radiometry A Plarimetric Survey f Radi Frequency Interference in C- and X-Bands in the Cntinental United States using WindSat Radimetry Steven W. Ellingsn Octber, Cntents Intrductin WindSat Methdlgy Analysis f RFI

More information

A Study on Pullout Strength of Cast-in-place Anchor bolt in Concrete under High Temperature

A Study on Pullout Strength of Cast-in-place Anchor bolt in Concrete under High Temperature Transactins f the 7 th Internatinal Cnference n Structural Mechanics in Reactr Technlgy (SMiRT 7) Prague, Czech Republic, August 7 22, 23 Paper #H-2 A Study n Pullut Strength f Cast-in-place Anchr blt

More information

Chapter 39. A GUIDE TO THE DESIGN OP AIR BUBBLERS FOR MELTING ICE Simon Ince Hydraulics Section, National Research Council Ottawa, Canada

Chapter 39. A GUIDE TO THE DESIGN OP AIR BUBBLERS FOR MELTING ICE Simon Ince Hydraulics Section, National Research Council Ottawa, Canada Chapter 39 A GUIDE T THE DESIGN P AIR BUBBLERS FR MELTING ICE Simn Ince Hydraulics Sectin, Natinal Research Cuncil ttawa, Canada INTRDUCTIN The use f air bubblers fr maintaining ice-free areas in lakes

More information

Chapters 29 and 35 Thermochemistry and Chemical Thermodynamics

Chapters 29 and 35 Thermochemistry and Chemical Thermodynamics Chapters 9 and 35 Thermchemistry and Chemical Thermdynamics 1 Cpyright (c) 011 by Michael A. Janusa, PhD. All rights reserved. Thermchemistry Thermchemistry is the study f the energy effects that accmpany

More information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce

More information

Rangely RE 4 Curriculum Development 5 th Grade Mathematics

Rangely RE 4 Curriculum Development 5 th Grade Mathematics Unit Title Dctr We Still Need t Operate... Length f Unit 12 weeks Fcusing Lens(es) Inquiry Questins (Engaging Debatable): Structure Systems Standards and Grade Level Expectatins Addressed in this Unit

More information

DEFENSE OCCUPATIONAL AND ENVIRONMENTAL HEALTH READINESS SYSTEM (DOEHRS) ENVIRONMENTAL HEALTH SAMPLING ELECTRONIC DATA DELIVERABLE (EDD) GUIDE

DEFENSE OCCUPATIONAL AND ENVIRONMENTAL HEALTH READINESS SYSTEM (DOEHRS) ENVIRONMENTAL HEALTH SAMPLING ELECTRONIC DATA DELIVERABLE (EDD) GUIDE DEFENSE OCCUPATIOL AND ENVIRONMENTAL HEALTH READINESS SYSTEM (DOEHRS) ENVIRONMENTAL HEALTH SAMPLING ELECTRONIC DATA DELIVERABLE (EDD) GUIDE 20 JUNE 2017 V1.0 i TABLE OF CONTENTS 1 INTRODUCTION... 1 2 CONCEPT

More information

I.S. 239 Mark Twain. Grade 7 Mathematics Spring Performance Task: Proportional Relationships

I.S. 239 Mark Twain. Grade 7 Mathematics Spring Performance Task: Proportional Relationships I.S. 239 Mark Twain 7 ID Name: Date: Grade 7 Mathematics Spring Perfrmance Task: Prprtinal Relatinships Directins: Cmplete all parts f each sheet fr each given task. Be sure t read thrugh the rubrics s

More information

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical).

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical). Principles f Organic Chemistry lecture 5, page LCAO APPROIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (catin, anin r radical).. Draw mlecule and set up determinant. 2 3 0 3 C C 2 = 0 C 2 3 0 = -

More information

Surface and Contact Stress

Surface and Contact Stress Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated

More information

Diffusion- Migration-Reaction-Limited Aggregation of Point Defects: A Model for the Stability of Oxide-layers on Metals and Its Breakdown.

Diffusion- Migration-Reaction-Limited Aggregation of Point Defects: A Model for the Stability of Oxide-layers on Metals and Its Breakdown. Diffusin- Migratin-Reactin-Limited Aggregatin f Pint Defects: A Mdel fr the Stability f Oxide-layers n Metals and Its Breakdwn. K. Ragavendran a, Bsc Emmanuel b Institute f Mathematical Sciences, Chennai

More information

SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical model for microarray data analysis

SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical model for microarray data analysis SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical mdel fr micrarray data analysis David Rssell Department f Bistatistics M.D. Andersn Cancer Center, Hustn, TX 77030, USA rsselldavid@gmail.cm

More information

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)

More information

On Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION

On Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION Malaysian Jurnal f Mathematical Sciences 4(): 7-4 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate

More information

PAP Biology Unit 4 Cellular Structure and Function

PAP Biology Unit 4 Cellular Structure and Function PAP Bilgy Unit 4 Cellular Structure and Functin Unit Outline LT 1 I can label the parts f a micrscpe and describe hw t use ne crrectly in lab. I can lcate and describe the functin f the different cmpnents

More information

Matter Content from State Frameworks and Other State Documents

Matter Content from State Frameworks and Other State Documents Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with

More information

Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects

Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential

More information

Pipetting 101 Developed by BSU CityLab

Pipetting 101 Developed by BSU CityLab Discver the Micrbes Within: The Wlbachia Prject Pipetting 101 Develped by BSU CityLab Clr Cmparisns Pipetting Exercise #1 STUDENT OBJECTIVES Students will be able t: Chse the crrect size micrpipette fr

More information

Making and Experimenting with Voltaic Cells. I. Basic Concepts and Definitions (some ideas discussed in class are omitted here)

Making and Experimenting with Voltaic Cells. I. Basic Concepts and Definitions (some ideas discussed in class are omitted here) Making xperimenting with Vltaic Cells I. Basic Cncepts Definitins (sme ideas discussed in class are mitted here) A. Directin f electrn flw psitiveness f electrdes. If ne electrde is mre psitive than anther,

More information

Product authorisation in case of in situ generation

Product authorisation in case of in situ generation Prduct authrisatin in case f in situ generatin Intrductin At the 74 th CA meeting (27-29 September 2017), Aqua Eurpa and ECA Cnsrtium presented their cncerns and prpsals n the management f the prduct authrisatin

More information

Eric Klein and Ning Sa

Eric Klein and Ning Sa Week 12. Statistical Appraches t Netwrks: p1 and p* Wasserman and Faust Chapter 15: Statistical Analysis f Single Relatinal Netwrks There are fur tasks in psitinal analysis: 1) Define Equivalence 2) Measure

More information

ON THE EFFECTIVENESS OF POROSITY ON UNSTEADY COUETTE FLOW AND HEAT TRANSFER BETWEEN PARALLEL POROUS PLATES WITH EXPONENTIAL DECAYING PRESSURE GRADIENT

ON THE EFFECTIVENESS OF POROSITY ON UNSTEADY COUETTE FLOW AND HEAT TRANSFER BETWEEN PARALLEL POROUS PLATES WITH EXPONENTIAL DECAYING PRESSURE GRADIENT 17 Kragujevac J. Sci. 8 (006) 17-4. ON THE EFFECTIVENESS OF POROSITY ON UNSTEADY COUETTE FLOW AND HEAT TRANSFER BETWEEN PARALLEL POROUS PLATES WITH EXPONENTIAL DECAYING PRESSURE GRADIENT Hazem Ali Attia

More information

Homework 1 AERE355 Fall 2017 Due 9/1(F) NOTE: If your solution does not adhere to the format described in the syllabus, it will be grade as zero.

Homework 1 AERE355 Fall 2017 Due 9/1(F) NOTE: If your solution does not adhere to the format described in the syllabus, it will be grade as zero. 1 Hmerk 1 AERE355 Fall 217 Due 9/1(F) Name NOE: If yur slutin des nt adhere t the frmat described in the syllabus, it ill be grade as zer. Prblem 1(25pts) In the altitude regin h 1km, e have the flling

More information

Examiner: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data

Examiner: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data Benha University Cllege f Engineering at Banha Department f Mechanical Eng. First Year Mechanical Subject : Fluid Mechanics M111 Date:4/5/016 Questins Fr Final Crrective Examinatin Examiner: Dr. Mhamed

More information