The procedures developed of automatic cascade non-azeotropic. refrigerant selection and matching

Size: px
Start display at page:

Download "The procedures developed of automatic cascade non-azeotropic. refrigerant selection and matching"

Transcription

1 5th Internatonal onference on Avance Desgn an Manufacturng Engneerng (IADME 15) The proceures evelope of automatc cascae non-azeotropc refrgerant selecton an matchng Zheng Da-yu (a), B. hen u-yan (b), B. Gao L-png (b),.lu-le (c). hen-shuo (c), D. L Xang (), D. Yu Ha-feng (), D. L Je () (a) School of Energy an vl Engneerng of Harbn ommercal Unversty Harbn, 158, hna Fax , zhengayu@16.com (b)(c)() School of Energy an vl Engneerng of Harbn ommercal Unversty Harbn, 158, hna Fax , superteacher73@16.com KEYWORDS: automatc cascae, non-azeotropc refrgerant selecton, matchng ABSTRAT: Draw the commonly refrgerants table for wrtng n the program selector workng par n tune content. Selecton accorng to the evaporaton temperature of low temperature refrgerant, base on tratonal non-azeotropc refrgerant select automatc cascae prncple, the preparaton metho of choce of refrgerant an wrtten proceures, the use of the program to select the approprate refrgerant refrgerant par. Meanwhle calculate by the heat balance prncple to raw a flow chart an wrte a program to calculate, usng the program raw on the rato of the refrgerants. VLE calculate usng the number of moles of the components, the use of the program to optmze the rato of the refrgerant. Makng savng automatc cascae refrgerant selecte tme, choose refrgeraton system s more effcent an more economc an envronmental protecton.fnally ths paper analyzes the reason of the automatc cascae OP value s low, to mprove after automatc cascae system scheme s put forwar. INTRODUTION Wth the avancement of technology, the ncreasng growth of the peoples lvng stanars. Whether n the bomecal communty, or n the tratonal manufacturng nustry, more an more eman for low temperature, whch s ncreasng the eman for equpment. Wth coolng temperatures requre lower temperatures, the effcency of the tratonal way of usng a sngle throttle refrgeraton refrgerant s reuce, can not acheve the requrements of energy conservaton, but also can not reach the esre low temperature [1]. n-azeotropc refrgerant for refrgeraton sector proves a new lower coolng worl, whle sngle machne mult-level automatc cascae makes movng parts whle reucng the esre temperature s reache, an get smple safe operaton of the refrgeraton system. n azeotropc ue to the fferent bolng pont n the process of heat transfer component changes, the proporton of non azeotropc evaporaton temperature of the workng meum s lower than any other sngle workng meum evaporaton temperature, then can get cryogenc refrgeraton temperature. In orer to acheve ts best OP, automatc cascae refrgeraton system refrgerant rato s the prmary problem, base on prevous experments show that the best rato can mprove the OP of the system []. 15. The authors - Publshe by Atlants Press 648

2 Rato of the refrgerant Select the correct non-azeotropc refrgerant par, an calculate ther rato. Reasonable rato can reuce the equpment operaton s amage, longer equpment lfe an safer. omparson of the rato of the conventonal metho of theoretcal an expermental results, only the combnaton of the fne-tune the rato of the refrgerant to get the best rato. onsere stable operaton of the automatc cascae refrgeraton system of nternal refrgerant n vapor-lqu equlbrum. Each of the refrgeraton cycle s assume that no pressure loss n the ppelne, wthout heat exchange, the compresson process s aabatc sentropc compresson, the gas-lqu separator lqu s pure lqu, an a unform temperature over the gas-lqu state uner a smplfe refrgeraton cycle. Draw ts varous contons of low temperature coolng effect parameters accorng want to acheve. Auto cascae refrgeraton are one by a compressor cycle, wth the classc cascae refrgeraton cycle thermoynamc calculaton as [4] : G = (1) q Equaton: G - cryogenc refrgerant mass flow rate (kg/s); - the requre coolng capacty (kw); q - ryogenc coolng capacty per unt mass (kj /kg). After the low-temperature refrgerant mass flow rate calculate by the estmaton of the amount of heat exchange evaporator conensate to etermne the low-temperature refrgerant conense refrgerant mass flow rate. = G ( q ) () k, + w Equaton: k, - cryogenc refrgerant conensng loa (kw); G - Low-temperature refrgerant mass flow rate (kg / s); w - Theory cryogenc unt power n low temperature (kj / kg). o, x 1. k, = (3) Equaton: o, x - cryogenc refrgerant conensng refrgerant evaporator loa (kw); Above, n the calculaton of the mass flow rate of refrgerant conensng low temperature refrgerant, by the estmaton of conensate evaporator heat transfer, an to etermne the next refrgerant flow of refrgeraton, the mole fracton of each component for VLE theoretcal calculaton of the nee theory ata. n-azeotropc mxe refrgerant bolng pont no common element n each group. Evaporaton or conensaton n certan contons, the vapor an lqu phases of fferent composton an temperature are constantly changng. 649

3 Vapor Dew pont curve Bubble pont curve Bq Temperature T Bl B Two-phase regon A Lqu Mole fracton Fgure1 n-azeotropc refrgerant(t-ε) fgure n-azeotropc mxe refrgerant occurs n the temperature change when the change n the phase constant pressure, the conensaton temperature ncreases at constant pressure to the bubble pont temperature of the ew pont temperature, the evaporaton pressure s fxe to the ew pont temperature becomes from the bubble pont temperature. Accorng to the characterstcs of the mxe refrgerant s wely use n the temperature fference between heat source to match the occason, n orer to acheve approxmate Lorentz cycle n orer to acheve the energy savng effect. The nature of the mxe refrgerant approxmates the average propertes of each component [4]. Vapor-lqu equlbrum s an nterrelate an mutually nepenent co-ecology. For the mult-component system, heat balance refers to the equlbrum force balance an equlbrum contons are satsfe, that s, each phase of the temperature, pressure an chemcal potental of the components n the respectve phases are equal. Metho for calculatng vapor-lqu equlbrum stll scusse, but t s stll the most commonly use metho s stll more precse use of the equaton of state of pure refrgerant to be ntrouce nto a sutable mxng ngreents varable to stuy the rules of the VLE features. Select fugacty coeffcents calculate PR equaton of state, that s, from the P-V-T relatonshp or measure ata of the substance calculate wth hgh accuracy [5]. PR equaton of state s: RT a( T ) P = (4) V b v( v + b) + b( V b) Where a( T) = aa( T), a c c R T RT =.4574, b =. 778 P P 1 + ( ω.699ω ) a( T) = T.5 1 ( ) T Equaton R s the unversal gas constant, T s the temperature, V s the molar volume, a functon of the temperature, b s a functon of the volume. Mxng rule to select fferent computng has a great mpact on the fugacty coeffcent of component. Frst select a classc mx of sngle-class rule Vaner Waals mxng rule [6] : a X = X a (5) b X = X b (6) 65

4 a 1 = 1 K )( a a ) (7) ( The (3-5) nto (3-) have: b = b + b )/ (8) m ( n b = x b = 1 Accorng to the unque nature of mxe refrgerants, vapor-lqu equlbrum theory can be use to calculate the bubble pont, seekng vapor phase components; ew pont calculaton, seekng lqu components; calculaton of two-phase regon, seekng equlbrum vapor an lqu phases group ryness, equlbrum constants, quanttatve stanars for each component of volatlty. Table 1 The metho to calculate VLE by equaton of state Known varables The unknown varables ueston classfcaton P, X T, y Bubble pont temperature P, y T, X Dew pont temperature T, X P, X Bubble pont pressure T, y P, X Dew pont pressure (9) The specfc calculaton shoul have a small amount of expermental ata, frst usng the theory of tratonal matchng of components nstea of ata generaton nto the process. Accorng to the above formula for calculaton program block agram [7] : 1 - Gven P an x values, entfe calculate the requre physcal constants. Temperature an phase composton of the unknown. - Selecte equaton of state to erve fugacty coeffcent equatons, an calculate vapor-lqu equlbrum rato; 3 - From the new calculate value obtane, the values are normalze wth the prevous teraton untl the fference s less than a preetermne allowable value (.1); 4 - Jugment the fference s less than a preetermne value, f less than the en of the calculaton process, output, f more than, nee to contnue to aust the temperature, untl meets the requrement. Prnt X, Y, T Gven P an X Estmate T an y uery physcal constants Austment T alculaton KX Gross whether??? = 1 alculate Y oeffcent alculatey Whether calculate KX gross change Interacton coeffcent s calculate alculatng new lqu components Whether teraton Fgure VLE calculaton flowchart 651

5 ONLUSIONS Automatc cascae refrgeraton energy effcency rato of the sze of the refrgerant has a great mpact on energy conservaton to reuce the amount of refrgerant charge whle not reucng the coolng capacty s the most mportant current research. The fllng shoul have the flexblty to master refrgerant refrgeraton equpment use fferent rules n certan proceures to quckly select a refrgerant par an proporton, save tme an be more accurate. That s accorng to the requre refrgeraton temperature, the refrgeraton capacty can rectly select the qualty an levels of non-azeotropc rato. An can be base on obectve factors gven n a varety of refrgerants par targete selecton, not only to meet the eman for coolng, but may well reuce the use of refrgerants, mprove ts effcency, economy an reuce the nfluence of refrgerants on the envronment. Effect of non-azeotropc refrgerant automatc cascae OP of the refrgeraton cycle as well as an mportant reason for the refrgerant heat exchanger separaton factor. Wth ecreasng evaporaton temperature, but the temperature of the evaporator to reuce the slp, whch shows the value of the refrgerant n the ryness of the throttle s large, a serous loss of latent heat of vaporzaton, n orer to avo ths stuaton, shoul ncrease the egree of subcoolng. Acknowlegements Helongang Provnce Natural Scence Fun Proect: NumberE131 Helongang Provnce Grauate Innovaton Fun Proect: NumberYJSX13-4HSD REFERENES [1] Weang Lu. Ternary non-azeotropc automatc cascae cryogenc equpment research [D]. Harbn Unversty of ommerce, 1. [] Bngfeng Yu. Refrgeraton an ar contonng applcaton of new technology [M]. hemcal Inustry Press,. [3] Yta Ma, Zhmng Gao, Dong hen. Multvarate mxe refrgerants screenng an matchng prncple [J] Engneerng Thermophyscs, 1997, 18 (1): 17-. [4] Yezheng Wu. Refrgeraton prncples an equpment [M]. Xan Jaotong Unversty Press, [5] Junsheng Wu. hemcal Separaton Engneerng [M]. Scence Press,. [6] Zqang Zhu, Youtng Wu. hemcal Thermoynamcs [M]. hemcal Inustry Press, 1. [7] Jun Wang, Mn L, Erx heng. Mxe refrgerant chller esgn prncple an calculaton [J] Journal of Beng Unversty of Aeronautcs an Astronautcs, 198, 4: 5. 65

Energy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model

Energy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model Lecture 4. Thermodynamcs [Ch. 2] Energy, Entropy, and Avalablty Balances Phase Equlbra - Fugactes and actvty coeffcents -K-values Nondeal Thermodynamc Property Models - P-v-T equaton-of-state models -

More information

y i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem

y i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem SOLUTION TO HOMEWORK #7 #roblem 1 10.1-1 a. In order to solve ths problem, we need to know what happens at the bubble pont; at ths pont, the frst bubble s formed, so we can assume that all of the number

More information

Operating conditions of a mine fan under conditions of variable resistance

Operating conditions of a mine fan under conditions of variable resistance Paper No. 11 ISMS 216 Operatng condtons of a mne fan under condtons of varable resstance Zhang Ynghua a, Chen L a, b, Huang Zhan a, *, Gao Yukun a a State Key Laboratory of Hgh-Effcent Mnng and Safety

More information

Supplementary Notes for Chapter 9 Mixture Thermodynamics

Supplementary Notes for Chapter 9 Mixture Thermodynamics Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects

More information

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law: CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and

More information

A Robust Method for Calculating the Correlation Coefficient

A Robust Method for Calculating the Correlation Coefficient A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal

More information

Adiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram

Adiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram Adabatc Sorpton of Ammona-Water System and Depctng n p-t-x Dagram J. POSPISIL, Z. SKALA Faculty of Mechancal Engneerng Brno Unversty of Technology Techncka 2, Brno 61669 CZECH REPUBLIC Abstract: - Absorpton

More information

SIMPLIFIED MODEL-BASED OPTIMAL CONTROL OF VAV AIR- CONDITIONING SYSTEM

SIMPLIFIED MODEL-BASED OPTIMAL CONTROL OF VAV AIR- CONDITIONING SYSTEM Nnth Internatonal IBPSA Conference Montréal, Canaa August 5-8, 2005 SIMPLIFIED MODEL-BASED OPTIMAL CONTROL OF VAV AIR- CONDITIONING SYSTEM Nabl Nassf, Stanslaw Kajl, an Robert Sabourn École e technologe

More information

on the improved Partial Least Squares regression

on the improved Partial Least Squares regression Internatonal Conference on Manufacturng Scence and Engneerng (ICMSE 05) Identfcaton of the multvarable outlers usng T eclpse chart based on the mproved Partal Least Squares regresson Lu Yunlan,a X Yanhu,b

More information

Optimization of the thermodynamic model of a solar driven Aqua - ammonia absorption refrigeration system

Optimization of the thermodynamic model of a solar driven Aqua - ammonia absorption refrigeration system nd WSEAS/IASME Internatonal Conference on RENEWABLE ENERGY SOURCES (RES') Corfu, Greece, October -, Optmzaton of the thermodynamc model of a solar drven Aqua - ammona absorpton refrgeraton system J. ABDULATEEF,

More information

New Liu Estimators for the Poisson Regression Model: Method and Application

New Liu Estimators for the Poisson Regression Model: Method and Application New Lu Estmators for the Posson Regresson Moel: Metho an Applcaton By Krstofer Månsson B. M. Golam Kbra, Pär Sölaner an Ghaz Shukur,3 Department of Economcs, Fnance an Statstcs, Jönköpng Unversty Jönköpng,

More information

Visualization of 2D Data By Rational Quadratic Functions

Visualization of 2D Data By Rational Quadratic Functions 7659 Englan UK Journal of Informaton an Computng cence Vol. No. 007 pp. 7-6 Vsualzaton of D Data By Ratonal Quaratc Functons Malk Zawwar Hussan + Nausheen Ayub Msbah Irsha Department of Mathematcs Unversty

More information

Thermodynamics General

Thermodynamics General Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,

More information

I wish to publish my paper on The International Journal of Thermophysics. A Practical Method to Calculate Partial Properties from Equation of State

I wish to publish my paper on The International Journal of Thermophysics. A Practical Method to Calculate Partial Properties from Equation of State I wsh to publsh my paper on The Internatonal Journal of Thermophyscs. Ttle: A Practcal Method to Calculate Partal Propertes from Equaton of State Authors: Ryo Akasaka (correspondng author) 1 and Takehro

More information

Assignment 4. Adsorption Isotherms

Assignment 4. Adsorption Isotherms Insttute of Process Engneerng Assgnment 4. Adsorpton Isotherms Part A: Compettve adsorpton of methane and ethane In large scale adsorpton processes, more than one compound from a mxture of gases get adsorbed,

More information

Name: SID: Discussion Session:

Name: SID: Discussion Session: Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 141 -- Fall 007 Thursday, November 15, 007 Mdterm II SOLUTIONS - 70 mnutes 110 Ponts Total Closed Book and Notes (0 ponts) 1. Evaluate whether

More information

#64. ΔS for Isothermal Mixing of Ideal Gases

#64. ΔS for Isothermal Mixing of Ideal Gases #64 Carnot Heat Engne ΔS for Isothermal Mxng of Ideal Gases ds = S dt + S T V V S = P V T T V PV = nrt, P T ds = v T = nr V dv V nr V V = nrln V V = - nrln V V ΔS ΔS ΔS for Isothermal Mxng for Ideal Gases

More information

Regulating Characteristics Analysis of Boiler Feed-water Pump when 600MW Unit Sliding-pressure Operating

Regulating Characteristics Analysis of Boiler Feed-water Pump when 600MW Unit Sliding-pressure Operating Aalable onlne at www.scencerect.com Energy rocea 7 (0 ) 5 60 0 Internatonal Conference on Future Electrcal ower an Energy Systems Regulatng Characterstcs Analyss of Boler Fee-water ump when 600MW Unt Slng-pressure

More information

modeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products

modeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products modelng of equlbrum and dynamc mult-component adsorpton n a two-layered fxed bed for purfcaton of hydrogen from methane reformng products Mohammad A. Ebrahm, Mahmood R. G. Arsalan, Shohreh Fatem * Laboratory

More information

Problem Set #6 solution, Chem 340, Fall 2013 Due Friday, Oct 11, 2013 Please show all work for credit

Problem Set #6 solution, Chem 340, Fall 2013 Due Friday, Oct 11, 2013 Please show all work for credit Problem Set #6 soluton, Chem 340, Fall 2013 Due Frday, Oct 11, 2013 Please show all work for credt To hand n: Atkns Chap 3 Exercses: 3.3(b), 3.8(b), 3.13(b), 3.15(b) Problems: 3.1, 3.12, 3.36, 3.43 Engel

More information

INTRODUCTION TO CHEMICAL PROCESS SIMULATORS

INTRODUCTION TO CHEMICAL PROCESS SIMULATORS INTRODUCTION TO CHEMICAL PROCESS SIMULATORS DWSIM Chemcal Process Smulator A. Carrero, N. Qurante, J. Javaloyes October 2016 Introducton to Chemcal Process Smulators Contents Monday, October 3 rd 2016

More information

The Analysis of Convection Experiment

The Analysis of Convection Experiment Internatonal Conference on Appled Scence and Engneerng Innovaton (ASEI 5) The Analyss of Convecton Experment Zlong Zhang School of North Chna Electrc Power Unversty, Baodng 7, Chna 469567@qq.com Keywords:

More information

Outline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property.

Outline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property. Unt Eght Calculatons wth Entropy Mechancal Engneerng 370 Thermodynamcs Larry Caretto October 6, 010 Outlne Quz Seven Solutons Second law revew Goals for unt eght Usng entropy to calculate the maxmum work

More information

An Improved multiple fractal algorithm

An Improved multiple fractal algorithm Advanced Scence and Technology Letters Vol.31 (MulGraB 213), pp.184-188 http://dx.do.org/1.1427/astl.213.31.41 An Improved multple fractal algorthm Yun Ln, Xaochu Xu, Jnfeng Pang College of Informaton

More information

(1) The saturation vapor pressure as a function of temperature, often given by the Antoine equation:

(1) The saturation vapor pressure as a function of temperature, often given by the Antoine equation: CE304, Sprng 2004 Lecture 22 Lecture 22: Topcs n Phase Equlbra, part : For the remander of the course, we wll return to the subject of vapor/lqud equlbrum and ntroduce other phase equlbrum calculatons

More information

CinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure

CinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure nhe roblem-solvng Strategy hapter 4 Transformaton rocess onceptual Model formulaton procedure Mathematcal Model The mathematcal model s an abstracton that represents the engneerng phenomena occurrng n

More information

Influence Of Operating Conditions To The Effectiveness Of Extractive Distillation Columns

Influence Of Operating Conditions To The Effectiveness Of Extractive Distillation Columns Influence Of Operatng Condtons To The Effectveness Of Extractve Dstllaton Columns N.A. Vyazmna Moscov State Unversty Of Envrnmental Engneerng, Department Of Chemcal Engneerng Ul. Staraya Basmannaya 21/4,

More information

General Thermodynamics for Process Simulation. Dr. Jungho Cho, Professor Department of Chemical Engineering Dong Yang University

General Thermodynamics for Process Simulation. Dr. Jungho Cho, Professor Department of Chemical Engineering Dong Yang University General Thermodynamcs for Process Smulaton Dr. Jungho Cho, Professor Department of Chemcal Engneerng Dong Yang Unversty Four Crtera for Equlbra μ = μ v Stuaton α T = T β α β P = P l μ = μ l1 l 2 Thermal

More information

Numerical modelization by finite differences of a thermoelectric refrigeration device of double jump". Experimental validation.

Numerical modelization by finite differences of a thermoelectric refrigeration device of double jump. Experimental validation. Numercal modelzaton by fnte dfferences of a thermoelectrc refrgeraton devce of double jump". Expermental valdaton. A. Rodríguez, J.G. Ván, D. Astran, Dpto. Ingenería Mecánca, Energétca y de Materales.

More information

Inductance Calculation for Conductors of Arbitrary Shape

Inductance Calculation for Conductors of Arbitrary Shape CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors

More information

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,

More information

A novel mathematical model of formulation design of emulsion explosive

A novel mathematical model of formulation design of emulsion explosive J. Iran. Chem. Res. 1 (008) 33-40 Journal of the Iranan Chemcal Research IAU-ARAK www.au-jcr.com A novel mathematcal model of formulaton desgn of emulson explosve Mng Lu *, Qfa Lu Chemcal Engneerng College,

More information

Optimal Design of Monorail Crane Spring Based on MATLAB Quanwei Wang, Wenan Kang, Shan Nie

Optimal Design of Monorail Crane Spring Based on MATLAB Quanwei Wang, Wenan Kang, Shan Nie Optmal esn of Monoral Crane Sprn Base on MATLAB Quanwe Wan, Wenan Kan, Shan Ne Shanon Unversty of Scence an Technoloy,Qnao,Shanon, 266590,Chna wqw79279@6.com Keywors: sprn; optmal esn; MATLAB; mathematcal

More information

The ChemSep Book. Harry A. Kooijman Consultant. Ross Taylor Clarkson University, Potsdam, New York University of Twente, Enschede, The Netherlands

The ChemSep Book. Harry A. Kooijman Consultant. Ross Taylor Clarkson University, Potsdam, New York University of Twente, Enschede, The Netherlands The ChemSep Book Harry A. Koojman Consultant Ross Taylor Clarkson Unversty, Potsdam, New York Unversty of Twente, Enschede, The Netherlands Lbr Books on Demand www.bod.de Copyrght c 2000 by H.A. Koojman

More information

Winter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan

Winter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments

More information

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons

More information

ENTROPIC QUESTIONING

ENTROPIC QUESTIONING ENTROPIC QUESTIONING NACHUM. Introucton Goal. Pck the queston that contrbutes most to fnng a sutable prouct. Iea. Use an nformaton-theoretc measure. Bascs. Entropy (a non-negatve real number) measures

More information

MODULE 6 HUMIDIFICATION AND AIR CONDITIONING

MODULE 6 HUMIDIFICATION AND AIR CONDITIONING MODULE 6 UMIDIFICATION AND AIR CONDITIONING LECTURE NO. 7 6.7 Evaporaton loss of water n coolng tower: Blowdown: Durng the coolng process of hot water n coolng tower, around % water evaporates [-3]. In

More information

A Fast Computer Aided Design Method for Filters

A Fast Computer Aided Design Method for Filters 2017 Asa-Pacfc Engneerng and Technology Conference (APETC 2017) ISBN: 978-1-60595-443-1 A Fast Computer Aded Desgn Method for Flters Gang L ABSTRACT *Ths paper presents a fast computer aded desgn method

More information

Module 3: The Whole-Process Perspective for Thermochemical Hydrogen

Module 3: The Whole-Process Perspective for Thermochemical Hydrogen "Thermodynamc Analyss of Processes for Hydrogen Generaton by Decomposton of Water" by John P. O'Connell Department of Chemcal Engneerng Unversty of Vrgna Charlottesvlle, VA 2294-4741 A Set of Energy Educaton

More information

On a one-parameter family of Riordan arrays and the weight distribution of MDS codes

On a one-parameter family of Riordan arrays and the weight distribution of MDS codes On a one-parameter famly of Roran arrays an the weght strbuton of MDS coes Paul Barry School of Scence Waterfor Insttute of Technology Irelan pbarry@wte Patrck Ftzpatrck Department of Mathematcs Unversty

More information

10.34 Numerical Methods Applied to Chemical Engineering Fall Homework #3: Systems of Nonlinear Equations and Optimization

10.34 Numerical Methods Applied to Chemical Engineering Fall Homework #3: Systems of Nonlinear Equations and Optimization 10.34 Numercal Methods Appled to Chemcal Engneerng Fall 2015 Homework #3: Systems of Nonlnear Equatons and Optmzaton Problem 1 (30 ponts). A (homogeneous) azeotrope s a composton of a multcomponent mxture

More information

Resource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud

Resource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud Resource Allocaton wth a Budget Constrant for Computng Independent Tasks n the Cloud Wemng Sh and Bo Hong School of Electrcal and Computer Engneerng Georga Insttute of Technology, USA 2nd IEEE Internatonal

More information

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient 58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),

More information

The Minimum Universal Cost Flow in an Infeasible Flow Network

The Minimum Universal Cost Flow in an Infeasible Flow Network Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran

More information

Design and Optimization of Fuzzy Controller for Inverse Pendulum System Using Genetic Algorithm

Design and Optimization of Fuzzy Controller for Inverse Pendulum System Using Genetic Algorithm Desgn and Optmzaton of Fuzzy Controller for Inverse Pendulum System Usng Genetc Algorthm H. Mehraban A. Ashoor Unversty of Tehran Unversty of Tehran h.mehraban@ece.ut.ac.r a.ashoor@ece.ut.ac.r Abstract:

More information

Review of Classical Thermodynamics

Review of Classical Thermodynamics Revew of Classcal hermodynamcs Physcs 4362, Lecture #1, 2 Syllabus What s hermodynamcs? 1 [A law] s more mpressve the greater the smplcty of ts premses, the more dfferent are the knds of thngs t relates,

More information

An efficient method for computing single parameter partial expected value of perfect information

An efficient method for computing single parameter partial expected value of perfect information An effcent metho for computng sngle parameter partal expecte value of perfect nformaton Mark Strong,, Jeremy E. Oakley 2. School of Health an Relate Research ScHARR, Unversty of Sheffel, UK. 2. School

More information

The Ordinary Least Squares (OLS) Estimator

The Ordinary Least Squares (OLS) Estimator The Ordnary Least Squares (OLS) Estmator 1 Regresson Analyss Regresson Analyss: a statstcal technque for nvestgatng and modelng the relatonshp between varables. Applcatons: Engneerng, the physcal and chemcal

More information

The Study of Teaching-learning-based Optimization Algorithm

The Study of Teaching-learning-based Optimization Algorithm Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute

More information

Sampling Theory MODULE VII LECTURE - 23 VARYING PROBABILITY SAMPLING

Sampling Theory MODULE VII LECTURE - 23 VARYING PROBABILITY SAMPLING Samplng heory MODULE VII LECURE - 3 VARYIG PROBABILIY SAMPLIG DR. SHALABH DEPARME OF MAHEMAICS AD SAISICS IDIA ISIUE OF ECHOLOGY KAPUR he smple random samplng scheme provdes a random sample where every

More information

CHEMICAL ENGINEERING

CHEMICAL ENGINEERING Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton

More information

UNR Joint Economics Working Paper Series Working Paper No Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?

UNR Joint Economics Working Paper Series Working Paper No Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist? UNR Jont Economcs Workng Paper Seres Workng Paper No. 08-005 Further Analyss of the Zpf Law: Does the Rank-Sze Rule Really Exst? Fungsa Nota and Shunfeng Song Department of Economcs /030 Unversty of Nevada,

More information

Chapter 9: Statistical Inference and the Relationship between Two Variables

Chapter 9: Statistical Inference and the Relationship between Two Variables Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,

More information

Exercises of Fundamentals of Chemical Processes

Exercises of Fundamentals of Chemical Processes Department of Energ Poltecnco d Mlano a Lambruschn 4 2056 MILANO Exercses of undamentals of Chemcal Processes Prof. Ganpero Gropp Exercse 7 ) Estmaton of the composton of the streams at the ext of an sothermal

More information

Credit Card Pricing and Impact of Adverse Selection

Credit Card Pricing and Impact of Adverse Selection Credt Card Prcng and Impact of Adverse Selecton Bo Huang and Lyn C. Thomas Unversty of Southampton Contents Background Aucton model of credt card solctaton - Errors n probablty of beng Good - Errors n

More information

3. Be able to derive the chemical equilibrium constants from statistical mechanics.

3. Be able to derive the chemical equilibrium constants from statistical mechanics. Lecture #17 1 Lecture 17 Objectves: 1. Notaton of chemcal reactons 2. General equlbrum 3. Be able to derve the chemcal equlbrum constants from statstcal mechancs. 4. Identfy how nondeal behavor can be

More information

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009 College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:

More information

High-Order Hamilton s Principle and the Hamilton s Principle of High-Order Lagrangian Function

High-Order Hamilton s Principle and the Hamilton s Principle of High-Order Lagrangian Function Commun. Theor. Phys. Bejng, Chna 49 008 pp. 97 30 c Chnese Physcal Socety Vol. 49, No., February 15, 008 Hgh-Orer Hamlton s Prncple an the Hamlton s Prncple of Hgh-Orer Lagrangan Functon ZHAO Hong-Xa an

More information

The influence of non-ideal vapor-liquid-equilibrium on vaporization of multicomponent hydrocarbon fuels

The influence of non-ideal vapor-liquid-equilibrium on vaporization of multicomponent hydrocarbon fuels ICLASS 202, 2 th Trennal Internatonal Conference on Lqud Atomzaton and Spray Systems, Hedelberg, Germany, September 2-6, 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent

More information

PERFORMANCE OF HEAVY-DUTY PLANETARY GEARS

PERFORMANCE OF HEAVY-DUTY PLANETARY GEARS THE INTERNATIONAL CONFERENCE OF THE CARPATHIAN EURO-REGION SPECIALISTS IN INDUSTRIAL SYSTEMS 6 th edton PERFORMANCE OF HEAVY-DUTY PLANETARY GEARS Attla Csobán, Mhály Kozma 1, 1 Professor PhD., Eng. Budapest

More information

G4023 Mid-Term Exam #1 Solutions

G4023 Mid-Term Exam #1 Solutions Exam1Solutons.nb 1 G03 Md-Term Exam #1 Solutons 1-Oct-0, 1:10 p.m to :5 p.m n 1 Pupn Ths exam s open-book, open-notes. You may also use prnt-outs of the homework solutons and a calculator. 1 (30 ponts,

More information

High resolution entropy stable scheme for shallow water equations

High resolution entropy stable scheme for shallow water equations Internatonal Symposum on Computers & Informatcs (ISCI 05) Hgh resoluton entropy stable scheme for shallow water equatons Xaohan Cheng,a, Yufeng Ne,b, Department of Appled Mathematcs, Northwestern Polytechncal

More information

A Self-Consistent Gibbs Excess Mixing Rule for Cubic Equations of State: derivation and fugacity coefficients

A Self-Consistent Gibbs Excess Mixing Rule for Cubic Equations of State: derivation and fugacity coefficients A Self-Consstent Gbbs Excess Mxng Rule for Cubc Equatons of State: dervaton and fugacty coeffcents Paula B. Staudt, Rafael de P. Soares Departamento de Engenhara Químca, Escola de Engenhara, Unversdade

More information

Markov Chain Monte Carlo (MCMC), Gibbs Sampling, Metropolis Algorithms, and Simulated Annealing Bioinformatics Course Supplement

Markov Chain Monte Carlo (MCMC), Gibbs Sampling, Metropolis Algorithms, and Simulated Annealing Bioinformatics Course Supplement Markov Chan Monte Carlo MCMC, Gbbs Samplng, Metropols Algorthms, and Smulated Annealng 2001 Bonformatcs Course Supplement SNU Bontellgence Lab http://bsnuackr/ Outlne! Markov Chan Monte Carlo MCMC! Metropols-Hastngs

More information

Annexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances

Annexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances ec Annexes Ths Annex frst llustrates a cycle-based move n the dynamc-block generaton tabu search. It then dsplays the characterstcs of the nstance sets, followed by detaled results of the parametercalbraton

More information

On Liu Estimators for the Logit Regression Model

On Liu Estimators for the Logit Regression Model CESIS Electronc Workng Paper Seres Paper No. 59 On Lu Estmators for the Logt Regresson Moel Krstofer Månsson B. M. Golam Kbra October 011 The Royal Insttute of technology Centre of Excellence for Scence

More information

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer Prncples of Food and Boprocess Engneerng (FS 31) Solutons to Example Problems on Heat Transfer 1. We start wth Fourer s law of heat conducton: Q = k A ( T/ x) Rearrangng, we get: Q/A = k ( T/ x) Here,

More information

Mass Transfer Processes

Mass Transfer Processes Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.

More information

Introduction to Computational Fluid Dynamics

Introduction to Computational Fluid Dynamics Introducton to Computatonal Flud Dynamcs M. Zanub 1, T. Mahalakshm 2 1 (PG MATHS), Department of Mathematcs, St. Josephs College of Arts and Scence for Women-Hosur, Peryar Unversty 2 Assstance professor,

More information

Kernel Methods and SVMs Extension

Kernel Methods and SVMs Extension Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general

More information

Design and Analysis of Landing Gear Mechanic Structure for the Mine Rescue Carrier Robot

Design and Analysis of Landing Gear Mechanic Structure for the Mine Rescue Carrier Robot Sensors & Transducers 214 by IFSA Publshng, S. L. http://www.sensorsportal.com Desgn and Analyss of Landng Gear Mechanc Structure for the Mne Rescue Carrer Robot We Juan, Wu Ja-Long X an Unversty of Scence

More information

Field and Wave Electromagnetic. Chapter.4

Field and Wave Electromagnetic. Chapter.4 Fel an Wave Electromagnetc Chapter.4 Soluton of electrostatc Problems Posson s s an Laplace s Equatons D = ρ E = E = V D = ε E : Two funamental equatons for electrostatc problem Where, V s scalar electrc

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data

More information

Air Age Equation Parameterized by Ventilation Grouped Time WU Wen-zhong

Air Age Equation Parameterized by Ventilation Grouped Time WU Wen-zhong Appled Mechancs and Materals Submtted: 2014-05-07 ISSN: 1662-7482, Vols. 587-589, pp 449-452 Accepted: 2014-05-10 do:10.4028/www.scentfc.net/amm.587-589.449 Onlne: 2014-07-04 2014 Trans Tech Publcatons,

More information

Journal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article

Journal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article Avalable onlne www.jocpr.com Journal of Chemcal and Pharmaceutcal Research, 014, 6(5):1683-1688 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 Multple mode control based on VAV ar condtonng system

More information

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9.

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9. 9.9 Real Solutons Exhbt Devatons from Raoult s Law If two volatle and mscble lquds are combned to form a soluton, Raoult s law s not obeyed. Use the expermental data n Table 9.3: Physcal Chemstry 00 Pearson

More information

Uncertainty and auto-correlation in. Measurement

Uncertainty and auto-correlation in. Measurement Uncertanty and auto-correlaton n arxv:1707.03276v2 [physcs.data-an] 30 Dec 2017 Measurement Markus Schebl Federal Offce of Metrology and Surveyng (BEV), 1160 Venna, Austra E-mal: markus.schebl@bev.gv.at

More information

A study on the effect of ball diameter on breakage properties of clinker and limestone

A study on the effect of ball diameter on breakage properties of clinker and limestone Indan Journal of Chemcal Technology Vol. 9, May 202, pp. 80-84 A study on the effect of ball dameter on breakage propertes of clnker and lmestone Vedat Denz* Department of Chemcal Engneerng, Htt Unversty,

More information

The Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites

The Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites 7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT

More information

Explicit bounds for the return probability of simple random walk

Explicit bounds for the return probability of simple random walk Explct bouns for the return probablty of smple ranom walk The runnng hea shoul be the same as the ttle.) Karen Ball Jacob Sterbenz Contact nformaton: Karen Ball IMA Unversty of Mnnesota 4 Ln Hall, 7 Church

More information

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth

More information

NAME and Section No. it is found that 0.6 mol of O

NAME and Section No. it is found that 0.6 mol of O NAME and Secton No. Chemstry 391 Fall 7 Exam III KEY 1. (3 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). In the reacton 3O O3 t s found that.6 mol of O are consumed. Fnd

More information

UNIFAC. Documentation. DDBSP Dortmund Data Bank Software Package

UNIFAC. Documentation. DDBSP Dortmund Data Bank Software Package UNIFAC Documentaton DDBSP Dortmund Data Ban Software Pacage DDBST Dortmund Data Ban Software & Separaton Technology GmbH Mare-Cure-Straße 10 D-26129 Oldenburg Tel.: +49 441 361819 0 Fax: +49 441 361819

More information

VQ widely used in coding speech, image, and video

VQ widely used in coding speech, image, and video at Scalar quantzers are specal cases of vector quantzers (VQ): they are constraned to look at one sample at a tme (memoryless) VQ does not have such constrant better RD perfomance expected Source codng

More information

CHAPTER 7 ENERGY BALANCES SYSTEM SYSTEM. * What is energy? * Forms of Energy. - Kinetic energy (KE) - Potential energy (PE) PE = mgz

CHAPTER 7 ENERGY BALANCES SYSTEM SYSTEM. * What is energy? * Forms of Energy. - Kinetic energy (KE) - Potential energy (PE) PE = mgz SYSTM CHAPTR 7 NRGY BALANCS 1 7.1-7. SYSTM nergy & 1st Law of Thermodynamcs * What s energy? * Forms of nergy - Knetc energy (K) K 1 mv - Potental energy (P) P mgz - Internal energy (U) * Total nergy,

More information

a b a In case b 0, a being divisible by b is the same as to say that

a b a In case b 0, a being divisible by b is the same as to say that Secton 6.2 Dvsblty among the ntegers An nteger a ε s dvsble by b ε f there s an nteger c ε such that a = bc. Note that s dvsble by any nteger b, snce = b. On the other hand, a s dvsble by only f a = :

More information

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol Georgetown Unversty From the SelectedWorks of Mark J Meyer 8 Usng the estmated penetrances to determne the range of the underlyng genetc model n casecontrol desgn Mark J Meyer Neal Jeffres Gang Zheng Avalable

More information

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to

More information

A quote of the week (or camel of the week): There is no expedience to which a man will not go to avoid the labor of thinking. Thomas A.

A quote of the week (or camel of the week): There is no expedience to which a man will not go to avoid the labor of thinking. Thomas A. A quote of the week (or camel of the week): here s no expedence to whch a man wll not go to avod the labor of thnkng. homas A. Edson Hess law. Algorthm S Select a reacton, possbly contanng specfc compounds

More information

McCabe-Thiele Diagrams for Binary Distillation

McCabe-Thiele Diagrams for Binary Distillation McCabe-Thele Dagrams for Bnary Dstllaton Tore Haug-Warberg Dept. of Chemcal Engneerng August 31st, 2005 F V 1 V 2 L 1 V n L n 1 V n+1 L n V N L N 1 L N L 0 VN+1 Q < 0 D Q > 0 B FIGURE 1: Smplfed pcture

More information

PETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium

PETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium ETE 30 Lectures # 24 & 25 Chapter 2 Gas Lqud Equlbrum Thermal Equlbrum Object A hgh T, Object B low T Intal contact tme Intermedate tme. Later tme Mechancal Equlbrum ressure essels Vale Closed Vale Open

More information

A Particle Filter Algorithm based on Mixing of Prior probability density and UKF as Generate Importance Function

A Particle Filter Algorithm based on Mixing of Prior probability density and UKF as Generate Importance Function Advanced Scence and Technology Letters, pp.83-87 http://dx.do.org/10.14257/astl.2014.53.20 A Partcle Flter Algorthm based on Mxng of Pror probablty densty and UKF as Generate Importance Functon Lu Lu 1,1,

More information

Basic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos

Basic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos Introducton to Toshhsa Ueda School of Scence for Open and Envronmental Systems Keo Unversty, Japan Combuston Mxng and reacton n hgh vscous flud Applcaton of Chaos Keo Unversty 1 Keo Unversty 2 What s reactve

More information

Gasometric Determination of NaHCO 3 in a Mixture

Gasometric Determination of NaHCO 3 in a Mixture 60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)

More information

Exponential Type Product Estimator for Finite Population Mean with Information on Auxiliary Attribute

Exponential Type Product Estimator for Finite Population Mean with Information on Auxiliary Attribute Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 193-9466 Vol. 10, Issue 1 (June 015), pp. 106-113 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) Exponental Tpe Product Estmator

More information

Lecture 12. Transport in Membranes (2)

Lecture 12. Transport in Membranes (2) Lecture 12. Transport n embranes (2) odule Flow Patterns - Perfect mxng - Countercurrent flow - Cocurrent flow - Crossflow embrane Cascades External ass-transfer Resstances Concentraton Polarzaton and

More information

Appendix II Summary of Important Equations

Appendix II Summary of Important Equations W. M. Whte Geochemstry Equatons of State: Ideal GasLaw: Coeffcent of Thermal Expanson: Compressblty: Van der Waals Equaton: The Laws of Thermdynamcs: Frst Law: Appendx II Summary of Important Equatons

More information

On Blow-Out of Jet Spray Diffusion Flames

On Blow-Out of Jet Spray Diffusion Flames 5 th ICDERS August 7, 015 Lees, UK n Blow-ut of Jet Spray Dffuson Flames N. Wenberg an J.B. Greenberg Faculty of Aerospace Engneerng, Technon Israel Insttute of Technology Hafa, Israel 1 Introucton The

More information

SOLVING NON-LINEAR SYSTEMS BY NEWTON s METHOD USING SPREADSHEET EXCEL Tay Kim Gaik Universiti Tun Hussein Onn Malaysia

SOLVING NON-LINEAR SYSTEMS BY NEWTON s METHOD USING SPREADSHEET EXCEL Tay Kim Gaik Universiti Tun Hussein Onn Malaysia SOLVING NON-LINEAR SYSTEMS BY NEWTON s METHOD USING SPREADSHEET EXCEL Tay Km Gak Unverst Tun Hussen Onn Malaysa Kek Se Long Unverst Tun Hussen Onn Malaysa Rosmla Abdul-Kahar

More information