HEAT AND MASS TRANSFER TO PARTICLES IN FLUIDIZED BED
|
|
- Sophie Reeves
- 5 years ago
- Views:
Transcription
1 IEA Technicl Meeting, Skive, Denmrk, October 2017 HEAT AND MASS TRANSFER TO PARTICLES IN FLUIDIZED BED Bo Leckner Avelningen för Energiteknik Chlmers University of Technology Göteborg, Sween 1
2 CORRELATIONS: SINGLE PHASE FLOW Reltionships for single sphericl prticles in single phse flow hve been etermine by Frössling (1938), Rnz Mrshll (1952), Rowe (1965) Nu =2+0.69Re 0.5 Pr 0.33 Sh =2+0.69Re 0.5 Sc 0.33 Gs conuction n gs convection terms, relte to the prticle imeter, re nlogous for het n mss trnsfer in this cse. Contribution from rition hs to be e in the het trnsfer cse. Het trnsfer Nu =h /k Pr= c p /k Mss trnsfer Sh = /D Sc= /D 2
3 HEAT AND MASS TRANSFER BETWEEN THE GAS AND ACTIVE PARTICLES IN THE BED Gs psses through the spce between the prticles with velocity u mf /ε i Two lrge ctive prticles surroune by smller inert prticles in be with fluiiztion velocity u. 3
4 APPLICATIONS Vrious chemicl engineering processes in fluiize be, e.g. in fuel conversion Drying n pyrolysis of fuel prticles Combustion of chr 4
5 CORRELATIONS: FLUIDIZED BED There re mny correltions giving ifferent results hving similr structure (Shown for het trnsfer (Nu) but nlogous for mss trnsfer (Sh)) n Nu const const(re / ) Pr, mf mf where or n Nu const ( / ) i i m where Nu h / k n g ( ) / 0.33 Nu h / k Re u / c g, mf mf g 3 2 i c i g i g s g Trnsformtions Nu Nu / i i Re Re / imf, mf, i 0.5 Re imf, /( ) 5
6 Bskkov Plchonok s pproch: HEAT AND MASS TRANSFER INTERPOLATED BETWEEN = i n >> i Sh 1 or Nu 1 is the low limit = i Sh i, or Nu i, is the lrge limit >> i Sh i or Nu i re in between the limits The interpoltion formule: Nu Nu i Sh i, 1 i, i Sh Nu Nu Sh Sh i, 1 i, ( / ) i ( / ) i n m Nusselt or Sherwoo number, Nu, Sh Mss n het trnsfer coefficients relte to be prticles Shi or Nui Nu, =i Nu, >>i Sh, =i Sh, >>i chimees number, Thin lines / i = Thick full lines --- Sh Thick she lines---nu chimees number 6
7 THE i = LIMIT = i ----Plchonok's correltion + Turton n Levenspiel * Bskkov et l. (10-->6) o Plchonok n Tmrin Scott et l.(2-->6) = i, Plchonok's correltion * Bskkov et l. + Hsiung n Thoos Plchonok n Tmrin Nu 1 Sh fit to t in the limit = i (Plchonok et l., 1992) Nu 1 = i 0.39 Pr 0.33 Sh 1 =2ε mf i 0.39 Sc
8 THE LARGE ACTIVE PARTICLE LIMIT >> i Trnsfer to lrge, fixe, n roune object in fluiize be, Bskkov (1973), Nu i, Pr Sh i, Sc The mss (n het) trnsfer coefficient goes to symptotic vlues s Limiting mss trnsfer coefficient m/s Lines ccoring to Bskkov. o symptotic vlue: Prins igrm x limiting vlue of -->infinity: Prins correltion Lrge prticle symptote ccoring to Bskkov 0.5 tmes the bove h symptot, W/m 2 K o Prins het trnsfer t, --> infinity ----Lrge-prticle limit, Bskkov (t from Prins 1987) x x
9 AVAILABLE HEAT TRANSFER CORRELATIONS Scott et l Tsuk n Horio, 1992 Prins, 1987 Bbos 1985 Shh, 1983 Plchonok n Tmrin,
10 HT: Scott et l. 2004; Nu 2 1.0Re ( ) mf, i Scott's t (moifie) Lines for / i =1, 2 n 2.75 (thick--within rnge, thin--extrpolte) Nu i
11 HT: Brbos et l., 1995; Nui,mx 5.33 ( ) 0.09 i 0.25 Brbos et l. t Lines for = (thick--within rnge, thin--extrpolte) o(upper) extpolte for = i o(lower) extrpolte for =0.08 m Nu i
12 HT: Tsuk n Horio, 1992: Nu ( / ) ; Nu ( PrRe )( / ) ,mx i i,mx mf i Tsuk n Horio's t Lines for = (thick--within rnge, thin--extrpolte) o(upper) extrpolte for = i o(lower) extrpolte for =0.08 m Nu i
13 HT: Prins, 1987; Nui,mx ( ) where n 0.105( ) n i i Prins't Lines for = (thick--within rnge, thin--extrpolte) o(upper) extpolte for = i o(lower) extrpolte for =0.08 m Nu i
14 HT:Plchonok n Tmrin, 1983; Nui,mx 0.41 ( ) ( ) 0.3 i 0.2 i Plchonok n Tmrin's t Lines for = , thick lines within rnge, thin--extrpolte Nu i
15 HT: Shh, 1983; Nu Nu i,mx i,mx c i p Re opt ( ) ( ) for cpi i Re opt ( ) for Shh's t Lines for = within rnge o (upper) = i o (lower) =0.08 m Nu i
16 OVERVIEW OF THE PUBLISHED HEAT TRANSFER DATA Scott's t (moifie) Lines for / =1, 2 n 2.75 i (thick--within rnge, thin--extrpolte) Nu i
17 Fit of het trnsfer t Nu Nu ( Nu Nu )( / ) i i, 1 i, i
18 SELECTED MASS TRANSFER CORRELATIONS Scl 2007 Hyhurst n Prmr 2002 Prins
19 MT: Prins 1987; m 1 m 1 Re mf mf, i Shi Sc ( ( i / ) ) mf mf m n u ( i / ) Re mf, i mf i / Prins' correltion Lines for =2, 4, 8, 10, 14, 20 mm T= K, eps=0.4 Sh i = i 0.5 Sh ( lrge)
20 MT: Scl, 2007; ,.. Scl's t re * mesure =4.6 mm green * mesure i =0.55 mm o correltion =0.2; 1; 4.6; 8.2 mm within rnge + correltion =20 mm, > outsie rnge = i (extrpolte) Sh i 0.5*Sh (lrge ) 10-1 Dt: T= K ensity 2500 kg/m 3 D= * (T/273) 1.75 m 2 /s (Sc=2.5) eps=
21 OVERVIEW OF THE MASS TRANSFER CORRELATIONS 21
22 Prins =2; 4; 10 mm Scl =2.5; 4; 10 mm Scl's conitions COMPARISON PRINS SCALA Scl s conitions in both correltions Prins conitions in both correltions Prins =2; 4; 10 mm Scl =2.5; 4; 10 mm Prins' conitions Sh i Sh i Quntity Scl Prins Temperture, K Be prticle ensity, kg/m Voige, Diffusivity, m 2 /s T T Sc
23 Fit of mss trnsfer t Sh Sh ( Sh Sh )( / ) i i, 1 i, i 1.0 T= 723 K Density 2650 kg/m 3 Diffusivity for oxygen in ir i =1.0 mm Prins c b e Sh i 10-1 i =0.1 mm Scl 10-2 Prins f Scl Active prticle size mm 23
24 CONCLUSIONS The greement between vilble correltions on het n mss trnsfer to ctive prticles in fluiize bes is not extremely high. However, the t in the mesure rnges re t lest within the limits of the Bskkov Plchonok pproch. Therefore, n estimte of coefficients is obtine by Nu Nu ( Nu Nu )( / ) i i, 1 i, i Sh Sh ( Sh Sh )( / ) i i, 1 i, i A seemingly more ccurte estimtion woul be given by the correltion of choice, pplie within its mesure rnge. It ws shown tht most correltions (exception Prins for mss trnsfer) give erroneous vlues when extrpolte to lrge ctive prticles Also, espite the imensionless representtion, the correltions epen on the properties of the mei, e.g. the Schmit number in the cse of mss trnsfer. 24
25 Appenix: HEAT TRANSFER TO AN ACTIVE PARTICLE () IN A BED OF INERT PARTICLES (i): Moel free correltions Some vilble correltions: Tmrin et l. (1982) Tmrin et l. (1985) Shh (1983) Cobbinh et l. (1984) Prins (1985) Brbos et l. (1993) Scott et l. (2004), Collier et l. (2004) (Cmbrige) Nui 5 ( ) i Nui,mx 0.41 ( ) ( ) Nu Nu mx mx i i c p Re opt ( ) ( ) for Reopt 170 cpi i Re opt ( ) for Reopt 170 i Nu,mx ( ) i n Nui,mx ( ) where n 0.105( ) Nu mx Nu c 0.61 ( ) ( ) c i pi. i 0.17 i p, g g 2 1.0Re ( ) mf, i i 25
26 References Aerov ME, Toes OM, Hyrulic n Therml Funmentls on the Opertion of Apprtus with Sttic n Fluiize Prticle Be (In Russin), Chimi, Leningr, (1968). Aveesin MM, Dvison JF, Combustion of crbon prticles in fluiize be, Trns. Inst. Chem. Eng., 51, , Brbos AL, Steinmetz D., Angelino H, Het trnsfer roun sphericl probes t high tempertures in fluiize be, pp , Fluiiztion VIII, Es J F Lrge n C Lguérie, Engineering Fountion Bskkov AP, Berg BV, Vitt OK, Filippovsky NF, Kirkosyn VA, Golobin JM, Mskev VK, Het trnsfer to objects immerse in fluiize bes, Power Technology 8 (1973) Bskkov AP, Filippovskii NF, Munts VA, Ashikhmin AA, Temperture of prticles hete in fluiize be of inert mteril, Journl of Engineering Physics 52, , Frössling, N. (1938) The evportion of flling rops [in Germn], Gerlns Beiträge zur Geophysik, 52, Hsiung TH, Thoos G, Mss trnsfer in gs fluiize bes: mesurements of ctul riving forces, Chem Engn Sci 32, (1977). Plchonok GI, Tmrin AI, Stuy of het exchnge between moel prticle n fluiize be (Trnslte), pp , J. Eng Phys Plchonok GI, Doliovich AF, Anersson S, Leckner B, Clcultion of true het n mss trnsfer coefficients between prticles n fluiize be, Fluiiztion VII, Engineering Fountion, Prins W, Fluiize be combustion of single crbon prticle, Thesis, Twente University, Rnz, WE., Mrshll Jr., WR., Evportion from rops, Chem. Engn. Progress, 48, (prt I) n (prt II) , (1952). Scl F, Mss trnsfer roun freely moving ctive prticles in the ense phse of gs fluiize be of inert prticles, Chem. Eng. Sci., 62, 4159, Shh M, Generlize preiction of mximum het trnsfer to single cyliners n spheres in gs fluiize be, Het Trnsfer Engn. 4, , Tsuk M, Horio M, Mximum het trnsfer coefficient for n immerse boy in bubbling fluiize be, In Eng Chen Res 31, , Turton R, Colkyn M, Levenspiel O, Het trnsfer from fluiize bes to immerse fine wires, Power Technology 53,
Conservation Law. Chapter Goal. 6.2 Theory
Chpter 6 Conservtion Lw 6.1 Gol Our long term gol is to unerstn how mthemticl moels re erive. Here, we will stuy how certin quntity chnges with time in given region (sptil omin). We then first erive the
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More informationGas Bypass and Solids Circulation Rate of an i-cfb Reactor with Coarse Particles
Engineering Conferences Interntionl ECI Digitl Archives The 14th Interntionl Conference on Fluiiztion From Funmentls to Proucts eferee Proceeings 213 Gs Bypss n Solis Circultion te of n i-cfb ector with
More informationTopics Review Fuel Conversion Efficiency Fuel Air Ratio Volumetric Efficiency Road Load Power Relationships between performance parameters
ME 410 Dy 5 Topics Reiew Fuel Conersion Eiciency Fuel Air Rtio Volumetric Eiciency Ro Lo Power Reltionships between perormnce prmeters Fuel Conersion Eiciency This is the rtio o power ctully prouce to
More informationMass Creation from Extra Dimensions
Journl of oern Physics, 04, 5, 477-48 Publishe Online April 04 in SciRes. http://www.scirp.org/journl/jmp http://x.oi.org/0.436/jmp.04.56058 ss Cretion from Extr Dimensions Do Vong Duc, Nguyen ong Gio
More informationSimulated Performance of Packed Bed Solar Energy Storage System having Storage Material Elements of Large Size - Part I
The Open Fuels & Energy Science Journl, 2008, 1, 91-96 91 Open Access Simulted Performnce of Pcked Bed Solr Energy Storge System hving Storge Mteril Elements of Lrge Size - Prt I Rnjit Singh *,1, R.P.
More informationTHERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION
XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es
More informationModule 2: Rate Law & Stoichiomtery (Chapter 3, Fogler)
CHE 309: Chemicl Rection Engineering Lecture-8 Module 2: Rte Lw & Stoichiomtery (Chpter 3, Fogler) Topics to be covered in tody s lecture Thermodynmics nd Kinetics Rection rtes for reversible rections
More informationPhysics Lecture 14: MON 29 SEP
Physics 2113 Physics 2113 Lecture 14: MON 29 SEP CH25: Cpcitnce Von Kleist ws le to store electricity in the jr. Unknowingly, he h ctully invente novel evice to store potentil ifference. The wter in the
More informationPH 102 Exam I Solutions
PH 102 Exm I Solutions 1. Three ienticl chrges of = 5.0 µc lie long circle of rius 2.0 m t ngles of 30, 150, n 270 s shown below. Wht is the resultnt electric fiel t the center of the circle? By symmetry,
More information1.1. Linear Constant Coefficient Equations. Remark: A differential equation is an equation
1 1.1. Liner Constnt Coefficient Equtions Section Objective(s): Overview of Differentil Equtions. Liner Differentil Equtions. Solving Liner Differentil Equtions. The Initil Vlue Problem. 1.1.1. Overview
More information- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
- 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting
More informationRel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited
More informationcha1873x_p06.qxd 4/12/05 11:50 AM Page 568 PART SIX
ch1873x_p6.qx 4/12/5 11:5 AM Pge 568 PART SIX NUMERICAL DIFFERENTIATION AND INTEGRATION PT6.1 MOTIVATION Clculus is the mthemtics of chnge. Becuse engineers must continuously el with systems n processes
More informationELETROSTATICS Part II: BASICS
GROWING WITH ONPTS: Physics LTROSTTIS Prt II: SIS Presence of chrge on ny oject cretes n electrosttic fiel roun it n in turn n electricl potentil is experience roun the oject. This phenomenon hs foun ppliction
More informationPhys 7221, Fall 2006: Homework # 6
Phys 7221, Fll 2006: Homework # 6 Gbriel González October 29, 2006 Problem 3-7 In the lbortory system, the scttering ngle of the incident prticle is ϑ, nd tht of the initilly sttionry trget prticle, which
More informationThermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report
Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block
More informationStudies on Nuclear Fuel Rod Thermal Performance
Avilble online t www.sciencedirect.com Energy Procedi 1 (1) 1 17 Studies on Nucler Fuel od herml Performnce Eskndri, M.1; Bvndi, A ; Mihndoost, A3* 1 Deprtment of Physics, Islmic Azd University, Shirz
More informationMultiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution
Multiple Integrls eview of Single Integrls eding Trim 7.1 eview Appliction of Integrls: Are 7. eview Appliction of Integrls: Volumes 7.3 eview Appliction of Integrls: Lengths of Curves Assignment web pge
More informationA027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data
A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.
More informationState space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies
Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response
More informationCBE 291b - Computation And Optimization For Engineers
The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b - Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn
More informationFreely propagating jet
Freely propgting jet Introduction Gseous rectnts re frequently introduced into combustion chmbers s jets. Chemicl, therml nd flow processes tht re tking plce in the jets re so complex tht nlyticl description
More informationExam 1 September 21, 2012 Instructor: Timothy Martin
PHY 232 Exm 1 Sept 21, 212 Exm 1 September 21, 212 Instructor: Timothy Mrtin Stuent Informtion Nme n section: UK Stuent ID: Set #: Instructions Answer the questions in the spce provie. On the long form
More informationBlack oils Correlations Comparative Study
Reservoir Technologies Blck oils Correltions Comprtive Study Dr. Muhmmd Al-Mrhoun, Mnging Director Sturdy, 26 April, 2014 Copyright 2008, NExT, All rights reserved Blck oils Correltions Introduction to
More informationEstablishment of Intensity-Duration-Frequency Curves for Precipitation in the Monsoon Area of Vietnam
京都大学防災研究所年報 第 49 号 B 平成 8 年 4 月 Annuls of Diss. Prev. Res. nst., Kyoto Univ., No. 49 B, 2006 Estblishment of ntensity-durtion-frequency Curves for Precipittion in the Monsoon Are of Vietnm Le MNH NHA*,
More informationPart I: Basic Concepts of Thermodynamics
Prt I: Bsic Concepts o Thermodynmics Lecture 4: Kinetic Theory o Gses Kinetic Theory or rel gses 4-1 Kinetic Theory or rel gses Recll tht or rel gses: (i The volume occupied by the molecules under ordinry
More informationThermal Performance of Electrocaloric Refrigeration using Thermal Switches of Fluid Motion and Changing Contact Conductance
Americn Journl of Physics nd Applictions 2016; 4(5): 134-139 http://www.sciencepublishinggroup.com/j/jp doi:.11648/j.jp.20160405.12 ISSN: 2330-4286 (Print); ISSN: 2330-4308 (Online) Therml Performnce of
More informationLecture 20: Numerical Integration III
cs4: introduction to numericl nlysis /8/0 Lecture 0: Numericl Integrtion III Instructor: Professor Amos Ron Scribes: Mrk Cowlishw, Yunpeng Li, Nthnel Fillmore For the lst few lectures we hve discussed
More information1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More information13: Diffusion in 2 Energy Groups
3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups
More informationThe International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O
IAPWS R-7 The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem
More informationELE B7 Power Systems Engineering. Power System Components Modeling
Power Systems Engineering Power System Components Modeling Section III : Trnsformer Model Power Trnsformers- CONSTRUCTION Primry windings, connected to the lternting voltge source; Secondry windings, connected
More informationINTERNATIONAL CENTRE FOR THEORETICAL PHYSICS THE ALGEBRAIC APPROACH TO THE SCATTERING PROBLEM ABSTRACT
IC/69/7 INTERNAL REPORT (Limited distribution) INTERNATIONAL ATOMIC ENERGY AGENCY INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS THE ALGEBRAIC APPROACH TO THE SCATTERING PROBLEM Lot. IXARQ * Institute of
More informationTHE INTERVAL LATTICE BOLTZMANN METHOD FOR TRANSIENT HEAT TRANSFER IN A SILICON THIN FILM
ROMAI J., v.9, no.2(2013), 173 179 THE INTERVAL LATTICE BOLTZMANN METHOD FOR TRANSIENT HEAT TRANSFER IN A SILICON THIN FILM Alicj Piseck-Belkhyt, Ann Korczk Institute of Computtionl Mechnics nd Engineering,
More informationName Class Date. Match each phrase with the correct term or terms. Terms may be used more than once.
Exercises 341 Flow of Chrge (pge 681) potentil difference 1 Chrge flows when there is between the ends of conductor 2 Explin wht would hppen if Vn de Grff genertor chrged to high potentil ws connected
More informationMaterials Analysis MATSCI 162/172 Laboratory Exercise No. 1 Crystal Structure Determination Pattern Indexing
Mterils Anlysis MATSCI 16/17 Lbortory Exercise No. 1 Crystl Structure Determintion Pttern Inexing Objectives: To inex the x-ry iffrction pttern, ientify the Brvis lttice, n clculte the precise lttice prmeters.
More informationarxiv:cond-mat/ v1 17 Jun 1997
Sov. Phys. Semicon. 25 (12), December 1991, p. 1268 1271 c 1992 Americn Institute of Physics Problem of formtion of n emf in semiconuctor n its trnsfer to n externl circuit Yu. G. Gurevich n V. B. Yurchenko
More informationFirst Law of Thermodynamics. Control Mass (Closed System) Conservation of Mass. Conservation of Energy
First w of hermodynmics Reding Problems 3-3-7 3-0, 3-5, 3-05 5-5- 5-8, 5-5, 5-9, 5-37, 5-0, 5-, 5-63, 5-7, 5-8, 5-09 6-6-5 6-, 6-5, 6-60, 6-80, 6-9, 6-, 6-68, 6-73 Control Mss (Closed System) In this section
More informationMultiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution
Multiple Integrls eview of Single Integrls eding Trim 7.1 eview Appliction of Integrls: Are 7. eview Appliction of Integrls: olumes 7.3 eview Appliction of Integrls: Lengths of Curves Assignment web pge
More informationPHYS102 - Electric Energy - Capacitors
PHYS102 - lectric nerg - Cpcitors Dr. Suess Februr 14, 2007 Plcing Chrges on Conuctors................................................. 2 Plcing Chrges on Conuctors II................................................
More informationADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS
ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:
More informationLast Time emphasis on E-field. Potential of spherical conductor. Quick quiz. Connected spheres. Varying E-fields on conductor.
Lst Time emphsis on Efiel Electric flux through surfce Guss lw: Totl electric flux through close surfce proportionl to chrge enclose Q " E = E = 4$k e Q % o Chrge istribution on conuctors Chrge ccumultes
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More informationSection 14.3 Arc Length and Curvature
Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in
More informationCONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD
CONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD Svetozár Mlinrič Deprtment of Physics, Fculty of Nturl Sciences, Constntine the Philosopher University, Tr. A. Hlinku, SK-949 74 Nitr, Slovki Emil:
More information4.5 THE FUNDAMENTAL THEOREM OF CALCULUS
4.5 The Funmentl Theorem of Clculus Contemporry Clculus 4.5 THE FUNDAMENTAL THEOREM OF CALCULUS This section contins the most importnt n most use theorem of clculus, THE Funmentl Theorem of Clculus. Discovere
More informationFBR Neutronics: Breeding potential, Breeding Ratio, Breeding Gain and Doubling time
FBR eutronics: Breeding potentil, Breeding Rtio, Breeding Gin nd Doubling time K.S. Rjn Proessor, School o Chemicl & Biotechnology SASTRA University Joint Inititive o IITs nd IISc Funded by MHRD Pge 1
More informationA HELLY THEOREM FOR FUNCTIONS WITH VALUES IN METRIC SPACES. 1. Introduction
Ttr Mt. Mth. Publ. 44 (29), 159 168 DOI: 1.2478/v1127-9-56-z t m Mthemticl Publictions A HELLY THEOREM FOR FUNCTIONS WITH VALUES IN METRIC SPACES Miloslv Duchoň Peter Mličký ABSTRACT. We present Helly
More informationProblem Set 3 Solutions
Chemistry 36 Dr Jen M Stndrd Problem Set 3 Solutions 1 Verify for the prticle in one-dimensionl box by explicit integrtion tht the wvefunction ψ ( x) π x is normlized To verify tht ψ ( x) is normlized,
More informationLecture 14: Quadrature
Lecture 14: Qudrture This lecture is concerned with the evlution of integrls fx)dx 1) over finite intervl [, b] The integrnd fx) is ssumed to be rel-vlues nd smooth The pproximtion of n integrl by numericl
More informationHarman Outline 1A1 Integral Calculus CENG 5131
Hrmn Outline 1A1 Integrl Clculus CENG 5131 September 5, 213 III. Review of Integrtion A.Bsic Definitions Hrmn Ch14,P642 Fundmentl Theorem of Clculus The fundmentl theorem of clculus shows the intimte reltionship
More informationFEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS
XIX IMEKO orld Congress Fundmentl nd Applied Metrology September 6 11, 2009, Lisbon, Portugl FEM ANALYSIS OF ROGOSKI COILS COUPLED ITH BAR CONDUCTORS Mirko Mrrcci, Bernrdo Tellini, Crmine Zppcost University
More informationTests for the Ratio of Two Poisson Rates
Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson
More informationData Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading
Dt Assimiltion Aln O Neill Dt Assimiltion Reserch Centre University of Reding Contents Motivtion Univrite sclr dt ssimiltion Multivrite vector dt ssimiltion Optiml Interpoltion BLUE 3d-Vritionl Method
More informationUNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY. CH237 - Chemical Thermodynamics and Kinetics. Tutorial Sheet VIII
UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY CH237 - Chemicl Thermodynmics nd Kinetics Tutoril Sheet VIII 1 () (i) The rte of the rection A + 2B 3C + D ws reported s 1.0 mol L -1 s -1. Stte the rtes of
More informationTerminal Velocity and Raindrop Growth
Terminl Velocity nd Rindrop Growth Terminl velocity for rindrop represents blnce in which weight mss times grvity is equl to drg force. F 3 π3 ρ L g in which is drop rdius, g is grvittionl ccelertion,
More informationCLASS XII PHYSICS. (a) 30 cm, 60 cm (b) 20 cm, 30 cm (c) 15 cm, 20 cm (d) 12 cm, 15 cm. where
PHYSICS combintion o two thin lenses with ocl lengths n respectively orms n imge o istnt object t istnce cm when lenses re in contct. The position o this imge shits by cm towrs the combintion when two
More informationP 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)
1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this
More informationNUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.
NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with
More informationNumerical Integration
Chpter 5 Numericl Integrtion Numericl integrtion is the study of how the numericl vlue of n integrl cn be found. Methods of function pproximtion discussed in Chpter??, i.e., function pproximtion vi the
More information1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon
2001 1. ) Describe the principle chrcteristics nd uses of the following types of PV cell: Single Crystl Silicon Poly Crystl Silicon Amorphous Silicon CIS/CIGS Gllium Arsenide Multijunction (12 mrks) b)
More informationChapter 3 Polynomials
Dr M DRAIEF As described in the introduction of Chpter 1, pplictions of solving liner equtions rise in number of different settings In prticulr, we will in this chpter focus on the problem of modelling
More informationOn the Generalized Weighted Quasi-Arithmetic Integral Mean 1
Int. Journl of Mth. Anlysis, Vol. 7, 2013, no. 41, 2039-2048 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/10.12988/ijm.2013.3499 On the Generlized Weighted Qusi-Arithmetic Integrl Men 1 Hui Sun School
More informationChapter Direct Method of Interpolation More Examples Electrical Engineering
Chpter. Direct Method of Interpoltion More Emples Electricl Engineering Emple hermistors re used to mesure the temperture of bodies. hermistors re bsed on mterils chnge in resistnce with temperture. o
More informationApplied. Grade 9 Assessment of Mathematics. Released assessment Questions
Applie Gre 9 Assessment of Mthemtics 21 Relese ssessment Questions Recor your nswers to the multiple-choice questions on the Stuent Answer Sheet (21, Applie). Plese note: The formt of this booklet is ifferent
More informationApplications of Bernoulli s theorem. Lecture - 7
Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.
More informationReview Topic 14: Relationships between two numerical variables
Review Topi 14: Reltionships etween two numeril vriles Multiple hoie 1. Whih of the following stterplots est demonstrtes line of est fit? A B C D E 2. The regression line eqution for the following grph
More informationSUPPLEMENTARY NOTES ON THE CONNECTION FORMULAE FOR THE SEMICLASSICAL APPROXIMATION
Physics 8.06 Apr, 2008 SUPPLEMENTARY NOTES ON THE CONNECTION FORMULAE FOR THE SEMICLASSICAL APPROXIMATION c R. L. Jffe 2002 The WKB connection formuls llow one to continue semiclssicl solutions from n
More informationG. MATEESCU 1 A. MATEESCU 1 C. SAMOILĂ 2 D. URSUŢIU 2
PRELIMINARY EXPERIMENTS OF THE NEW FACILITY AND TECHNOLOGY FOR VACUUM DRYING AND THERMAL POLIMERIZATION OF THE TURBOGENERATORS STATOR BARS INSULATION (INTEPOL) G. MATEESCU 1 A. MATEESCU 1 C. SAMOILĂ 2
More informationA Matrix Algebra Primer
A Mtrix Algebr Primer Mtrices, Vectors nd Sclr Multipliction he mtrix, D, represents dt orgnized into rows nd columns where the rows represent one vrible, e.g. time, nd the columns represent second vrible,
More informationLecture 13 - Linking E, ϕ, and ρ
Lecture 13 - Linking E, ϕ, nd ρ A Puzzle... Inner-Surfce Chrge Density A positive point chrge q is locted off-center inside neutrl conducting sphericl shell. We know from Guss s lw tht the totl chrge on
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationCMDA 4604: Intermediate Topics in Mathematical Modeling Lecture 19: Interpolation and Quadrature
CMDA 4604: Intermedite Topics in Mthemticl Modeling Lecture 19: Interpoltion nd Qudrture In this lecture we mke brief diversion into the res of interpoltion nd qudrture. Given function f C[, b], we sy
More informationHQPD - ALGEBRA I TEST Record your answers on the answer sheet.
HQPD - ALGEBRA I TEST Record your nswers on the nswer sheet. Choose the best nswer for ech. 1. If 7(2d ) = 5, then 14d 21 = 5 is justified by which property? A. ssocitive property B. commuttive property
More informationA smoothed particle hydrodynamics method for evaporating. multiphase flows
A smoothed prticle hydrodynmics method for evporting multiphse flows Xiufeng Yng*, nd Song-Chrng Kong** Deprtment of Mechnicl Engineering, Iow Stte University, Ames, IA 50011, USA * xyng@istte.edu ** kong@istte.edu
More informationNUCLEAR SYSTEMS I (2 nd Printing): THERMAL HYDRAULIC FUNDAMENTALS ERRATA
NUCLEAR SYSTEMS I ( nd Printing): THERMAL HYDRAULIC FUNDAMENTALS Neil E. Todres nd Mujid S. Kzimi ERRATA /10/04 48 (Eq. 3-0)... = q S n... = q n S n 69 (Fig. 3-11, Cption)... for irrdition time of 10 13
More informationDefinite integral. Mathematics FRDIS MENDELU
Definite integrl Mthemtics FRDIS MENDELU Simon Fišnrová Brno 1 Motivtion - re under curve Suppose, for simplicity, tht y = f(x) is nonnegtive nd continuous function defined on [, b]. Wht is the re of the
More informationSection 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40
Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since
More informationControllable Microfluidic Production of Multicomponent Multiple Emulsions
Supplementry Mteril (ESI) or L on Chip This journl is The Royl Society o Chemistry 0 Controllle Microluiic Prouction o Multicomponent Multiple Emulsions Supplementry Mteril Wei Wng, Rui Xie *, Xio-Jie
More informationDefinite integral. Mathematics FRDIS MENDELU. Simona Fišnarová (Mendel University) Definite integral MENDELU 1 / 30
Definite integrl Mthemtics FRDIS MENDELU Simon Fišnrová (Mendel University) Definite integrl MENDELU / Motivtion - re under curve Suppose, for simplicity, tht y = f(x) is nonnegtive nd continuous function
More informationA Brief Note on Quasi Static Thermal Stresses In A Thin Rectangular Plate With Internal Heat Generation
Americn Journl of Engineering Reserch (AJER) 13 Americn Journl of Engineering Reserch (AJER) e-issn : 3-847 p-issn : 3-936 Volume-, Issue-1, pp-388-393 www.jer.org Reserch Pper Open Access A Brief Note
More informationConservation Laws and Poynting
Chpter 11 Conservtion Lws n Poynting Vector In electrosttics n mgnetosttics one ssocites n energy ensity to the presence of the fiels U = 1 2 E2 + 1 2 B2 = (electric n mgnetic energy)/volume (11.1) In
More informationDepartment of Electrical and Computer Engineering, Cornell University. ECE 4070: Physics of Semiconductors and Nanostructures.
Deprtment of Electricl nd Computer Engineering, Cornell University ECE 4070: Physics of Semiconductors nd Nnostructures Spring 2014 Exm 2 ` April 17, 2014 INSTRUCTIONS: Every problem must be done in the
More informationVector potential quantization and the photon wave-particle representation
Vector potentil quntiztion nd the photon wve-prticle representtion Constntin Meis, Pierre-Richrd Dhoo To cite this version: Constntin Meis, Pierre-Richrd Dhoo. Vector potentil quntiztion nd the photon
More informationAppendix A: HVAC Equipment Efficiency Tables
Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER
More informationSection 6.3 The Fundamental Theorem, Part I
Section 6.3 The Funmentl Theorem, Prt I (3//8) Overview: The Funmentl Theorem of Clculus shows tht ifferentition n integrtion re, in sense, inverse opertions. It is presente in two prts. We previewe Prt
More informationDETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE
Determintion RevAdvMterSci of mechnicl 0(009) -7 properties of nnostructures with complex crystl lttice using DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING
More informationS. S. Dragomir. 2, we have the inequality. b a
Bull Koren Mth Soc 005 No pp 3 30 SOME COMPANIONS OF OSTROWSKI S INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS S S Drgomir Abstrct Compnions of Ostrowski s integrl ineulity for bsolutely
More informationA5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s
4. Cosmic Dynmics: The Friedmnn Eqution Reding: Chpter 4 Newtonin Derivtion of the Friedmnn Eqution Consider n isolted sphere of rdius R s nd mss M s, in uniform, isotropic expnsion (Hubble flow). The
More informationBend Forms of Circular Saws and Evaluation of their Mechanical Properties
ISSN 139 13 MATERIALS SCIENCE (MEDŽIAGOTYRA). Vol. 11, No. 1. 5 Bend Forms of Circulr s nd Evlution of their Mechnicl Properties Kristin UKVALBERGIENĖ, Jons VOBOLIS Deprtment of Mechnicl Wood Technology,
More informationTable of Content. c 1 / 5
Tehnil Informtion - t nd t Temperture for Controlger 03-2018 en Tble of Content Introdution....................................................................... 2 Definitions for t nd t..............................................................
More informationTransient Aspects of Heat Flux Bifurcation in Porous Media: An Exact Solution
Kun Yng School of Energy nd Power Engineering, Huzhong University of Science nd Technology, Wuhn 430074, PR Chin; Deprtment of Mechnicl Engineering, University of Cliforni, Riverside, Riverside, CA 95-045
More informationDefinition of Continuity: The function f(x) is continuous at x = a if f(a) exists and lim
Mth 9 Course Summry/Study Guide Fll, 2005 [1] Limits Definition of Limit: We sy tht L is the limit of f(x) s x pproches if f(x) gets closer nd closer to L s x gets closer nd closer to. We write lim f(x)
More informationStrategy: Use the Gibbs phase rule (Equation 5.3). How many components are present?
University Chemistry Quiz 4 2014/12/11 1. (5%) Wht is the dimensionlity of the three-phse coexistence region in mixture of Al, Ni, nd Cu? Wht type of geometricl region dose this define? Strtegy: Use the
More informationEstimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural Network Models
eserch Journl of ecent Sciences ISSN 77-5 es.j.ecent Sci. Estimtion of Globl Solr dition t Onitsh with egression Anlysis nd Artificil Neurl Network Models Abstrct Agbo G.A., Ibeh G.F. *nd Ekpe J.E. Fculty
More informationPsychrometric Applications
Psychrometric Applictions The reminder of this presenttion centers on systems involving moist ir. A condensed wter phse my lso be present in such systems. The term moist irrefers to mixture of dry ir nd
More informationMATH SS124 Sec 39 Concepts summary with examples
This note is mde for students in MTH124 Section 39 to review most(not ll) topics I think we covered in this semester, nd there s exmples fter these concepts, go over this note nd try to solve those exmples
More informationThermal energy 2 U Q W. 23 April The First Law of Thermodynamics. Or, if we want to obtain external work: The trick of using steam
April 08 Therml energy Soures of het Trnsport of het How to use het The First Lw of Thermoynmis U W Or, if we wnt to otin externl work: U W 009 vrije Universiteit msterm Close yle stem power plnt The trik
More informationNew Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
More information