Chapter 2: Conversion and Reactor Sizing
|
|
|
- Warren Greer
- 5 years ago
- Views:
Transcription
1 CHEMICL RECTIO EGIEERIG (SK3223) Chapte 2: Convesion and Reacto Sizing W ORHRYTI W SLLEH hayati@petoleum.utm.my RIZI MD. KSMI afiziana@petoleum.utm.my
2 Convesion, To quantify how fa a eaction has pogessed How many moles of C ae fomed fo evey mole consumed Conside : a bb cc dd The basis of calculation is always the limiting eactant b a B c a C d a D Ievesible eaction: max =. (complete convesion) Revesible eaction: max = equilibium (equilibium convesion)
3 COERSIO = moles of eacted / consumed moles of fed Batch system (,t) low system (,/W) - ( mol) ( = moles of consumed / eacted ) ( mol / s) ( = mola flow ate at which is consumed / eacted )
4 BTCH RECTOR o batch eacto, we ae inteested in detemining how long to leave the eactants in the eacto to achieve a cetain convesion om mole balance: d dt om the convesion: This is how the Design Equation deived fom mole balance equation in tems of convesion Diffeentiating with espect of time: d dt d dt = : constant with espect of time d dt d dt t d 4
5 GS LOW SYSTEM The enteing mola flow ate, (mol/s) C mol s C C mol 3 dm fo gas P RT 3 dm. s system yp RT C = enteing concentation, mol/dm 3 Y a = enteing mole faction of P = enteing total pessue, kpa T =enteing tempeatue, K P a = enteing patial pessue R= ideal gas constant = 8.34k.Pa.dm 3 /mol.k
6 CSTR ) ( om mole balance: Design Equation: om the convesion:
7 PR om mole balance: d d om the convesion: Design Equation: Diffeentiating with espect of volume: d d d d = : constant with espect of volume d d d d d
8 PBR om mole balance: d dw ' om the convesion: Design Equation: Diffeentiating with espect of weight of catalyst: d dw d dw ' d dw ' d dw W d '
9 DESIG EQUTIOS Design Equations fo Isothemal Reactos RECTOR DIEREETIL LGEBRIC ITEGRL ORM ORM ORM BTCH d O ( ) dt t O d CSTR ( O ( ) ) Exit PR O d d ( ) d PBR O ( ' ) dw W O d d O ' 9
10 RECTOR SIZIG By sizing a chemical eacto we mean we'e eithe detemine the eacto volume to achieve a given convesion o detemine the convesion that can be achieved in a given eacto type and size. omally, the pocess / expeimental data will be given (, - ) PR Simpson's One-Thid Rule is one of the moe common numeical methods. Othe numeical methods (see ppendix.4, pp 3-5): (i) Tapezoidal Rule (2 data points) (ii) Simpson's Thee-Eighth's Rule (4 data points) (iii) ive-point Quadatue omula (5 data points)
11 Reacto Sizing Levenspiel Plot CSTR PR
12 RECTORS I SERIES Why? Sometimes 2 CSTR eacto volumes in seies is less than the volume of CSTR to achieve the same convesion. Can model a PR with a lage numbe of CSTR in seies. In the case of PR, whethe you place 2 PR in seies o have PR, the total eacto volume equied to achieve the same convesion is identical.
13 RECTORS I SERIES = = convesion achieved in the PR PR 2 = convesion achieved in the PR & CSTR 2 alid only fo O side steams: CSTR 3 PR 3 3 = total convesion achieved by all 3 eactos
14 (i) CSTR in seies: ( 2 2 ) - 2 (ii) PR in seies: d d - 2
15 (iii) CSTR + PR in seies: d ( )
16 SPCE TIME, The time necessay to pocess one eacto volume by the volumetic ate enteing the eacto lso called the holding time o mean esidence time time volume volume/ time whee is entance volumetic ate 6
17 SPCE ELOCITY (S) S Recipocal of the space time, Two S commonly used in industy: GHS Gas Houly Space elocity, h - v at STP (standad temp. and pessue) LHS Liquid Houly Space elocity, h - v at some efeence tempeatue
18 REERECES Main Refeence:. ogle,h.s., Elements of Chemical Reaction Engineeing, 4 th Edition,Pentice Hall, ew Jesey, 26. Othe Refeences:. Davis, M.E and Davis, R.J, undamentals of Chemical Reaction Engineeing, Mc-Gaw-Hill, ew Yok, Schmidt, L.D, The Engineeing of Chemical Reactions, Oxfod, ew Yok, Levenspiel,O., Chemical Reaction Engineeing, 3 d Edition, Wiley,ew Yok, Smith,J., Chemical Engineeing Kinetics, 3 d Edition, McGaw- Hill, ew Yok, 98
Chapter 1: Mole Balances
CHEMICL RECTION ENGINEERING (SK3223) Chapte : Mole Balances WN NORHRYTI WN SLLEH hayati@petoleum.utm.my RIZIN MD. KSMNI afiziana@petoleum.utm.my Rate of Reaction The eaction ate is the ate at which a species
CSTR - PFR - PBR
1. Mole Balances o The Rate of Reaction, - o The Geneal Mole Balance Equation o Continuous low Reactos - CSTR (Continuous-Stied Tank Reacto) - PR (Tubula Reacto) - PBR (Packed-Bed Reacto) o Industial Reactos
Youn-Woo Lee School of Chemical and Biological Engineering Seoul National University , 599 Gwanangro, Gwanak-gu, Seoul, Korea
hemical Reacto esign Y W L Youn-Woo Lee School of hemical and iological Engineeing 55-74, 599 Gwanango, Gwana-gu, Seoul, Koea ywlee@snu.ac. http://sfpl.snu.ac. hapte 6 Multiple Reactions hemical Reaction
Chemical Reaction Engineering
Lectue hemical Reaction Engineeing (RE) is the field that studies the ates and mechanisms of chemical eactions and the design of the eactos in which they take place. Web Lectue lass Lectue 8-husday Multiple
Chemical Reaction Engineering
Lectue 3 hemical Reaction Engineeing (RE) is the field that studies the ates and mechanisms of chemical eactions and the design of the eactos in which they take place. Web Lectue 3 lass Lectue 9-Thusday
If there are multiple rxns, use concentrations not conversions. These might occur in combination or by themselves.
hapte 6 MLTIPLE RETIONS If thee ae multiple xns, use concentations not convesions. intemediate. Seies Reactions onsecutive xns. Paallel Reactions. omplex Reactions: Seies and Paallel 4. Independent None
Entropy and Free Energy: Predicting the direction of spontaneous change The approach to Chemical equilibrium
Lectue 8-9 Entopy and Fee Enegy: Pedicting the diection of spontaneous change The appoach to Chemical equilibium Absolute entopy and the thid law of themodynamics To define the entopy of a compound in
Study of C5/C6 isomerization on Pt/H-zeolite catalyst in industrial conditions
Ovidius Univesity Annals of Chemisty Volume, Numbe, pp. -6, Study of / isomeization on Pt/H-zeolite catalyst in industial conditions Claudia Iina KONCSAG*, Ioan Alexandu TUTUN and Cistian SAFTA Ovidius
Substances that are liquids or solids under ordinary conditions may also exist as gases. These are often referred to as vapors.
Chapte 0. Gases Chaacteistics of Gases All substances have thee phases: solid, liquid, and gas. Substances that ae liquids o solids unde odinay conditions may also exist as gases. These ae often efeed
9.2 Reaction rate and rate equation
9.2.1 Expession of eaction ate The ate () of a chemical eaction is defined as the concentation change of a eactant o a poduct pe unit time. mean ate [A] c c = t t t 2 1 2 1 c c 1 instantaneous ate: Physical
Design of a Fuel Processor System for
ChE class and home poblems The object of this column is to enhance ou eades collections of stimulating poblems in chemical engineeing education. Ideal poblems, which may be open-ended, ae those that motivate
Supporting information
Electonic Supplementay Mateial (ESI) fo Physical Chemisty Chemical Physics. This jounal is the Owne Societies 18 Suppoting infomation Nonstoichiometic oxides as a continuous homologous seies: linea fee-enegy
Lecture 2 - Thermodynamics Overview
2.625 - Electochemical Systems Fall 2013 Lectue 2 - Themodynamics Oveview D.Yang Shao-Hon Reading: Chapte 1 & 2 of Newman, Chapte 1 & 2 of Bad & Faulkne, Chaptes 9 & 10 of Physical Chemisty I. Lectue Topics:
Downloaded from
Chapte Notes Subject: Chemisty Class: XI Chapte: Themodynamics Top concepts 1. The banch of science which deals with study of diffeent foms of enegy and thei inteconvesion is called themodynamics. 2. A
x 1 b 1 Consider the midpoint x 0 = 1 2
1 chapte 2 : oot-finding def : Given a function f(), a oot is a numbe satisfying f() = 0. e : f() = 2 3 = ± 3 question : How can we find the oots of a geneal function f()? 2.1 bisection method idea : Find
Visit us on the Web : Copyright 2011 Pearson Education,Inc.
The authos and the publishe have taken cae in the pepaation of this book but make no expessed o implied waanty of any kind and assume no esponsibility fo eos o omissions. No liability is assumed fo the
Chemical Reaction Engineering
Lecture 2 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. 1 Lecture 2 Review of Lecture
Synthesis of Epichlorohydrin from Glycerol. Hydrochlorination of Glycerol
Synthesis of Epichloohydin fom yceol. Hydochloination of yceol Geogy Dmitiev S.*, Leonid Zanaveskin N. Fedeation State Unitay Oganization "Kapov Institute of Physical hemisty" Russia, Moscow, Minusinskaya
Physics 2A Chapter 10 - Moment of Inertia Fall 2018
Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.
Chemistry Exam I 28 February 2018
Chemisty - Exam I 8 Feuay 018 Name Show all wok o cedit. State any assumptions made to solve a polem. State all answes with the coect nume o signiicant igues. All answes in scientiic notation must e in
Modeling of trickle bed reactor for hydrotreating of vacuum gas oils: effect of kinetic type on reactor modeling
17 th Euopean ymposium on Compute Aided Pocess Engineeing ECAPE17 V. Plesu and P.. Agachi (Editos) 007 Elsevie B.V. All ights eseved. 1 Modeling of tickle bed eacto fo hydoteating of vacuum gas oils: effect
Carbon Canister Modeling. Jon Brown Staff Engineer Exhaust Aftertreatment & Emissions CLEERS Workshop 2017
Cabon Caniste Modeling Jon Bown Staff Enginee Exhaust Afteteatment & Emissions CLEERS Wokshop 2017 Agenda Cabon caniste and EVAP system oveview Motivation, Backgound, and Objective Adsoption isothem Reaction
Modeling of the fermentation in an internal loop airlift reactor
17 th Euopean Symposium on Compute Aided Pocess Engineeing ESCAPE17 V. Plesu and P.S. Agachi (Editos) 7 Elsevie B.V. All ights eseved. 1 Modeling of the fementation in an intenal loop ailift eacto Ivan
Macromolecular Chemistry
Macomolecula Chemisty R R O H 2 C CH + CO CH 2 CH C Lectue 13 Fee Radical Co-polymeization Fee Radical Copolymeization ~ ~ ~ ~ ~ ~ ~ ~ Assume chain end concentations ae constant at steady state If If 1
4. Some Applications of first order linear differential
August 30, 2011 4-1 4. Some Applications of fist ode linea diffeential Equations The modeling poblem Thee ae seveal steps equied fo modeling scientific phenomena 1. Data collection (expeimentation) Given
Solution to HW 3, Ma 1a Fall 2016
Solution to HW 3, Ma a Fall 206 Section 2. Execise 2: Let C be a subset of the eal numbes consisting of those eal numbes x having the popety that evey digit in the decimal expansion of x is, 3, 5, o 7.
Numerical solution of diffusion mass transfer model in adsorption systems. Prof. Nina Paula Gonçalves Salau, D.Sc.
Numeical solution of diffusion mass tansfe model in adsoption systems Pof., D.Sc. Agenda Mass Tansfe Mechanisms Diffusion Mass Tansfe Models Solving Diffusion Mass Tansfe Models Paamete Estimation 2 Mass
Math /8/2014. Richard McGehee, University of Minnesota 1. Math 5490 October 8, Isotopes as Climate Proxies
Math 5490 Octobe 8, 04 Topics in Applied Mathematics: Intoduction to the Mathematics of Climate Mondays and Wednesdays :30 3:45 http://www.math.umn.edu/~mcgehee/teaching/math5490-04-fall/ Steaming video
Chemical Reaction Engineering. Dr. Yahia Alhamed
Chemical Reaction Engineering Dr. Yahia Alhamed 1 Kinetics and Reaction Rate What is reaction rate? It is the rate at which a species looses its chemical identity per unit volume. The rate of a reaction
Example
Chapte.4 iffusion with Chemical eaction Example.4- ------------------------------------------------------------------------------ fluiize coal eacto opeates at 45 K an atm. The pocess will be limite by
The Catalytic Hydrogenation of Aromatic Nitro Ketone in a Microreactor: Reactor Performance and Kinetic Studies
TERATOAL JOURAL OF EMAL REATOR EGEERG Volume 6 008 Aticle A The atalytic ydogenation of Aomatic ito etone in a Micoeacto: Reacto Pefomance and inetic Studies Sunitha Tadepalli Adeniyi Lawal Stevens nstitute
Solving Problems of Advance of Mercury s Perihelion and Deflection of. Photon Around the Sun with New Newton s Formula of Gravity
Solving Poblems of Advance of Mecuy s Peihelion and Deflection of Photon Aound the Sun with New Newton s Fomula of Gavity Fu Yuhua (CNOOC Reseach Institute, E-mail:fuyh945@sina.com) Abstact: Accoding to
, the tangent line is an approximation of the curve (and easier to deal with than the curve).
114 Tangent Planes and Linea Appoimations Back in-dimensions, what was the equation of the tangent line of f ( ) at point (, ) f ( )? (, ) ( )( ) = f Linea Appoimation (Tangent Line Appoimation) of f at
CASCADE OPTIMIZATION AND CONTROL OF BATCH REACTORS
CASCADE OPIMIZAION AND CONROL OF BACH REACORS Xiangming Hua, Sohab Rohani and Athu Jutan* Depatment of Chemical and Biochemical Engineeing Univesity of Westen Ontaio, London, Canada N6A B9 * ajutan@uwo.ca
Thermodynamic Head Loss in a Channel with Combined Radiation and Convection Heat Transfer
Jounal of Poe and Enegy Engineeing, 04,, 57-63 Published Online Septembe 04 in SciRes. http://.scip.og/jounal/jpee http://dx.doi.og/0.436/jpee.04.9009 hemodynamic Head Loss in a Channel ith Combined Radiation
On the Quasi-inverse of a Non-square Matrix: An Infinite Solution
Applied Mathematical Sciences, Vol 11, 2017, no 27, 1337-1351 HIKARI Ltd, wwwm-hikaicom https://doiog/1012988/ams20177273 On the Quasi-invese of a Non-squae Matix: An Infinite Solution Ruben D Codeo J
ac p Answers to questions for The New Introduction to Geographical Economics, 2 nd edition Chapter 3 The core model of geographical economics
Answes to questions fo The New ntoduction to Geogaphical Economics, nd edition Chapte 3 The coe model of geogaphical economics Question 3. Fom intoductoy mico-economics we know that the condition fo pofit
PHEN 612 SPRING 2008 WEEK 1 LAURENT SIMON
PHEN 612 SPRING 2008 WEEK 1 LAURENT SIMON Chapter 1 * 1.1 Rate of reactions r A A+B->C Species A, B, and C We are interested in the rate of disappearance of A The rate of reaction, ra, is the number of
MECHANICAL PULPING REFINER MECHANICAL PULPS
MECHANICAL PULPING REFINER MECHANICAL PULPS Histoy of efine mechanical pulping Fo many yeas all mechanical pulp was made fom stone goundwood (SGW). This equied whole logs. Stating in the 950s, but eally
EELE 3331 Electromagnetic I Chapter 4. Electrostatic fields. Islamic University of Gaza Electrical Engineering Department Dr.
EELE 3331 Electomagnetic I Chapte 4 Electostatic fields Islamic Univesity of Gaza Electical Engineeing Depatment D. Talal Skaik 212 1 Electic Potential The Gavitational Analogy Moving an object upwad against
LECTURER: PM DR MAZLAN ABDUL WAHID PM Dr Mazlan Abdul Wahid
M 445 LU: M D MZL BDUL WID http://www.fkm.utm.my/~mazlan hapte teady-tate tate One Dimensional eat onduction M bdul Wahid UM aculty of Mechanical ngineeing Univesiti eknologi Malaysia www.fkm.utm.my/~mazlan
2.25 Advanced Fluid Mechanics
MIT Depatment of Mechanical Engineeing 2.25 Advanced Fluid Mechanics Poblem 4.27 This poblem is fom Advanced Fluid Mechanics Poblems by A.H. Shapio and A.A. Sonin u(,t) pg Gas Liquid, density Conside a
Chem 453/544 Fall /08/03. Exam #1 Solutions
Chem 453/544 Fall 3 /8/3 Exam # Solutions. ( points) Use the genealized compessibility diagam povided on the last page to estimate ove what ange of pessues A at oom tempeatue confoms to the ideal gas law
Basic Bridge Circuits
AN7 Datafoth Copoation Page of 6 DID YOU KNOW? Samuel Hunte Chistie (784-865) was bon in London the son of James Chistie, who founded Chistie's Fine At Auctionees. Samuel studied mathematics at Tinity
DonnishJournals
DonnishJounals 041-1189 Donnish Jounal of Educational Reseach and Reviews. Vol 1(1) pp. 01-017 Novembe, 014. http:///dje Copyight 014 Donnish Jounals Oiginal Reseach Pape Vecto Analysis Using MAXIMA Savaş
Test 2, ECON , Summer 2013
Test, ECON 6090-9, Summe 0 Instuctions: Answe all questions as completely as possible. If you cannot solve the poblem, explaining how you would solve the poblem may ean you some points. Point totals ae
Math Section 4.2 Radians, Arc Length, and Area of a Sector
Math 1330 - Section 4. Radians, Ac Length, and Aea of a Secto The wod tigonomety comes fom two Geek oots, tigonon, meaning having thee sides, and mete, meaning measue. We have aleady defined the six basic
Do not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Mathematics Main Seies UG Examination 2015 16 FLUID DYNAMICS WITH ADVANCED TOPICS MTH-MD59 Time allowed: 3 Hous Attempt QUESTIONS 1 and 2, and THREE othe questions.
MSE 561, Atomic Modeling in Material Science Assignment 1
Depatment of Mateial Science and Engineeing, Univesity of Pennsylvania MSE 561, Atomic Modeling in Mateial Science Assignment 1 Yang Lu 1. Analytical Solution The close-packed two-dimensional stuctue is
ENVE 302 Environmental Engineering Unit Processes. Bacterial Growth Kinetics
ENVE 302 Envionmental Enineein Unit Pocesses CHAPTER: 3 Bacteial Gowth Kinetics Assist. Pof. Bile Alpaslan Kocamemi Mamaa Univesity Depatment of Envionmental Enineein Istanbul, Tuey 1 Micobial Gowth Kinetics
Chemical Reaction Engineering
Chemical Reaction Engineering Dr. Yahia Alhamed Chemical and Materials Engineering Department College of Engineering King Abdulaziz University General Mole Balance Batch Reactor Mole Balance Constantly
When two numbers are written as the product of their prime factors, they are in factored form.
10 1 Study Guide Pages 420 425 Factos Because 3 4 12, we say that 3 and 4 ae factos of 12. In othe wods, factos ae the numbes you multiply to get a poduct. Since 2 6 12, 2 and 6 ae also factos of 12. The
Chemical Reaction Engineering
Lectue 25 hemical Reaction Enineein (RE) is the field that studies the ates and mechanisms of chemical eactions and the desin of the eactos in which they take place. Web Lectue 25 lass Lectue 21 4/2/2013
Newton s Laws, Kepler s Laws, and Planetary Orbits
Newton s Laws, Keple s Laws, and Planetay Obits PROBLEM SET 4 DUE TUESDAY AT START OF LECTURE 28 Septembe 2017 ASTRONOMY 111 FALL 2017 1 Newton s & Keple s laws and planetay obits Unifom cicula motion
Bifurcation Analysis for the Delay Logistic Equation with Two Delays
IOSR Jounal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue 5 Ve. IV (Sep. - Oct. 05), PP 53-58 www.iosjounals.og Bifucation Analysis fo the Delay Logistic Equation with Two Delays
A scaling-up methodology for co-rotating twin-screw extruders
A scaling-up methodology fo co-otating twin-scew extudes A. Gaspa-Cunha, J. A. Covas Institute fo Polymes and Composites/I3N, Univesity of Minho, Guimaães 4800-058, Potugal Abstact. Scaling-up of co-otating
Non-Equilibrium Thermodynamics Formalism for Marcus cross-exchange electron transfer reaction rates Richa Sethi and M.V.Sangaranarayanan * Department
Non-Equilibium Themodynamics Fomalism fo Macus coss-exchange electon tansfe eaction ates Richa Sethi and M.V.Sangaanaayanan * Depatment of hemisty Indian Institute of Technology, Madas hennai-600036 India
Internet Appendix for A Bayesian Approach to Real Options: The Case of Distinguishing Between Temporary and Permanent Shocks
Intenet Appendix fo A Bayesian Appoach to Real Options: The Case of Distinguishing Between Tempoay and Pemanent Shocks Steven R. Genadie Gaduate School of Business, Stanfod Univesity Andey Malenko Gaduate
F-IF Logistic Growth Model, Abstract Version
F-IF Logistic Gowth Model, Abstact Vesion Alignments to Content Standads: F-IFB4 Task An impotant example of a model often used in biology o ecology to model population gowth is called the logistic gowth
KR- 21 FOR FORMULA SCORED TESTS WITH. Robert L. Linn, Robert F. Boldt, Ronald L. Flaugher, and Donald A. Rock
RB-66-4D ~ E S [ B A U R L C L Ii E TI KR- 21 FOR FORMULA SCORED TESTS WITH OMITS SCORED AS WRONG Robet L. Linn, Robet F. Boldt, Ronald L. Flaughe, and Donald A. Rock N This Bulletin is a daft fo inteoffice
1. Introductory Material
CHEE 321: Chemical Reaction Engineering 1. Introductory Material 1b. The General Mole Balance Equation (GMBE) and Ideal Reactors (Fogler Chapter 1) Recap: Module 1a System with Rxn: use mole balances Input
Annihilation of Relativistic Positrons in Single Crystal with production of One Photon
Annihilation of Relativistic Positons in Single Cystal with poduction of One Photon Kalashnikov N.P.,Mazu E.A.,Olczak A.S. National Reseach Nuclea Univesity MEPhI (Moscow Engineeing Physics Institute),
MATH 417 Homework 3 Instructor: D. Cabrera Due June 30. sin θ v x = v r cos θ v θ r. (b) Then use the Cauchy-Riemann equations in polar coordinates
MATH 417 Homewok 3 Instucto: D. Cabea Due June 30 1. Let a function f(z) = u + iv be diffeentiable at z 0. (a) Use the Chain Rule and the fomulas x = cosθ and y = to show that u x = u cosθ u θ, v x = v
CONVERSION AND REACTOR SIZING (2) Marcel Lacroix Université de Sherbrooke
CONVERSION ND RECTOR SIZING (2) Marcel Lacroix Université de Sherbrooke CONVERSION ND RECTOR SIZING: OBJECTIVES 1. TO DEINE CONVERSION j. 2. TO REWRITE THE DESIGN EQUTIONS IN TERMS O CONVERSION j. 3. TO
ABSTRACT SIMULATION OF DYNAMIC PRESSURE- Professor Timothy A. Barbari Department of Chemical Engineering
ABSTRACT Title: SIMULATION OF DYNAMIC PRESSURE- SWING GAS SORPTION IN POLYMERS Heathe Jane St. Piee, Maste of Science, 2005 Diected By: Pofesso Timothy A. Babai Depatment of Chemical Engineeing A tanspot
Solving Some Definite Integrals Using Parseval s Theorem
Ameican Jounal of Numeical Analysis 4 Vol. No. 6-64 Available online at http://pubs.sciepub.com/ajna///5 Science and Education Publishing DOI:.69/ajna---5 Solving Some Definite Integals Using Paseval s
Engineering Genetic Circuits
Engineeing Genetic Cicuits Chis J. Myes Lectue 5: Reaction-Based Abstaction Chis J. Myes (Lectue 5: Abstaction) Engineeing Genetic Cicuits 1 / 68 Albet Einstein The gand aim of all science is to cove the
In many engineering and other applications, the. variable) will often depend on several other quantities (independent variables).
II PARTIAL DIFFERENTIATION FUNCTIONS OF SEVERAL VARIABLES In man engineeing and othe applications, the behaviou o a cetain quantit dependent vaiable will oten depend on seveal othe quantities independent
Entropy and reaction spontaneity
A quote of the week (o camel of the week): Minds ae like paachutes they only function when open Thomas Dewa 1 Entopy and eaction spontaneity Back to the II law ot themodynamics A spontaneous change is
The Combined Effect of Chemical reaction, Radiation, MHD on Mixed Convection Heat and Mass Transfer Along a Vertical Moving Surface
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-966 Vol. 5, Issue (Decembe ), pp. 53 53 (Peviously, Vol. 5, Issue, pp. 63 6) Applications and Applied Mathematics: An Intenational Jounal (AAM)
CBE Transport Phenomena I Final Exam. December 19, 2013
CBE 30355 Tanspot Phenomena I Final Exam Decembe 9, 203 Closed Books and Notes Poblem. (20 points) Scaling analysis of bounday laye flows. A popula method fo measuing instantaneous wall shea stesses in
established in the case of the model surfactant AM Br
Topic 279 Sufactants and Miceles; Ionics An intense debate concens the stuctue of micelles, paticulaly those fomed by ionic sufactants such as SDS and CTAB. It seems geneally ageed that micelles ae essentially
Current, Resistance and
Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity
Heat transfer has direction as well as magnitude. The rate of heat conduction
cen58933_ch2.qd 9/1/22 8:46 AM Page 61 HEAT CONDUCTION EQUATION CHAPTER 2 Heat tansfe has diection as well as magnitude. The ate of heat conduction in a specified diection is popotional to the tempeatue
Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,
R Pena Towe, Road No, Contactos Aea, Bistupu, Jamshedpu 8, Tel (657)89, www.penaclasses.com IIT JEE Mathematics Pape II PART III MATHEMATICS SECTION I Single Coect Answe Type This section contains 8 multiple
THERMODYNAMIC OPTIMIZATION OF TUBULAR HEAT EXCHANGERS BASED ON MINIMUM IRREVERSIBILITY CRITERIA
THERMODYNAMIC OPTIMIZATION OF TUBULAR HEAT EXCHANGER BAED ON MINIMUM IRREVERIBILITY CRITERIA As. dd. ing. Adina GHEORGHIAN, Pof. d. ing. Alexandu DOBROVICECU, As. dd. ing. Andeea MARIN,.l. d. ing. Claudia
A Backward Identification Problem for an Axis-Symmetric Fractional Diffusion Equation
Mathematical Modelling and Analysis Publishe: Taylo&Fancis and VGTU Volume 22 Numbe 3, May 27, 3 32 http://www.tandfonline.com/tmma https://doi.og/.3846/3926292.27.39329 ISSN: 392-6292 c Vilnius Gediminas
Fundamentals of Heat Transfer Muhammad Rashid Usman
Fundamentals of Heat ansfe Muhammad Rashid Usman Institute of Chemical Engineeing and echnology Univesity of the Punjab, ahoe. Figue taen fom: http:heatexchange-design.com0006heat-exchanges-6 Dated: 7-Jan-0
What molecular weight polymer is necessary to provide steric stabilization? = [1]
![What molecular weight polymer is necessary to provide steric stabilization? = [1]](/thumbs/90/104312314.jpg "What molecular weight polymer is necessary to provide steric stabilization? = [1]")
1/7 What molecula weight polyme is necessay to povide steic stabilization? The fist step is to estimate the thickness of adsobed polyme laye necessay fo steic stabilization. An appoximation is: 1 t A d
Lecture 28: Convergence of Random Variables and Related Theorems
EE50: Pobability Foundations fo Electical Enginees July-Novembe 205 Lectue 28: Convegence of Random Vaiables and Related Theoems Lectue:. Kishna Jagannathan Scibe: Gopal, Sudhasan, Ajay, Swamy, Kolla An
3.1 Random variables
3 Chapte III Random Vaiables 3 Random vaiables A sample space S may be difficult to descibe if the elements of S ae not numbes discuss how we can use a ule by which an element s of S may be associated
Chapter 1: Introduction to Polar Coordinates
Habeman MTH Section III: ola Coodinates and Comple Numbes Chapte : Intoduction to ola Coodinates We ae all comfotable using ectangula (i.e., Catesian coodinates to descibe points on the plane. Fo eample,
Non-Ideal Gas Behavior P.V.T Relationships for Liquid and Solid:
hemodynamis Non-Ideal Gas Behavio.. Relationships fo Liquid and Solid: An equation of state may be solved fo any one of the thee quantities, o as a funtion of the othe two. If is onsideed a funtion of
Vectors, Vector Calculus, and Coordinate Systems
Apil 5, 997 A Quick Intoduction to Vectos, Vecto Calculus, and Coodinate Systems David A. Randall Depatment of Atmospheic Science Coloado State Univesity Fot Collins, Coloado 80523. Scalas and vectos Any
Galactic Contraction and the Collinearity Principle
TECHNISCHE MECHANIK, Band 23, Heft 1, (2003), 21-28 Manuskipteingang: 12. August 2002 Galactic Contaction and the Collineaity Pinciple F.P.J. Rimott, FA. Salusti In a spial galaxy thee is not only a Keplefoce
Introduction and Vectors
SOLUTIONS TO PROBLEMS Intoduction and Vectos Section 1.1 Standads of Length, Mass, and Time *P1.4 Fo eithe sphee the volume is V = 4! and the mass is m =!V =! 4. We divide this equation fo the lage sphee
5.8 Trigonometric Equations
5.8 Tigonometic Equations To calculate the angle at which a cuved section of highwa should be banked, an enginee uses the equation tan =, whee is the angle of the 224 000 bank and v is the speed limit
Bernoulli equation. Frictionless incompressible flow: Equation of motion for a mass element moving along a streamline. m dt
Benoulli equation Fictionless incompessible flow: Equation of motion fo a mass element moing along a steamline F = ma= d m dt In the diection of a steamline a = d = ds s => as = dt s dt s and pependicula
Universal Gravitation
Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between
The Substring Search Problem
The Substing Seach Poblem One algoithm which is used in a vaiety of applications is the family of substing seach algoithms. These algoithms allow a use to detemine if, given two chaacte stings, one is
Using Laplace Transform to Evaluate Improper Integrals Chii-Huei Yu
Available at https://edupediapublicationsog/jounals Volume 3 Issue 4 Febuay 216 Using Laplace Tansfom to Evaluate Impope Integals Chii-Huei Yu Depatment of Infomation Technology, Nan Jeon Univesity of
SOME GENERAL NUMERICAL RADIUS INEQUALITIES FOR THE OFF-DIAGONAL PARTS OF 2 2 OPERATOR MATRICES
italian jounal of pue and applied mathematics n. 35 015 (433 44) 433 SOME GENERAL NUMERICAL RADIUS INEQUALITIES FOR THE OFF-DIAGONAL PARTS OF OPERATOR MATRICES Watheq Bani-Domi Depatment of Mathematics
Variables and Formulas
64 Vaiales and Fomulas Vaiales and Fomulas DEFINITIONS & BASICS 1) Vaiales: These symols, eing lettes, actually epesent numes, ut the numes can change fom time to time, o vay. Thus they ae called vaiales.
The Millikan Experiment: Determining the Elementary Charge
LAB EXERCISE 7.5.1 7.5 The Elementay Chage (p. 374) Can you think of a method that could be used to suggest that an elementay chage exists? Figue 1 Robet Millikan (1868 1953) m + q V b The Millikan Expeiment:
Control Chart Analysis of E k /M/1 Queueing Model
Intenational OPEN ACCESS Jounal Of Moden Engineeing Reseach (IJMER Contol Chat Analysis of E /M/1 Queueing Model T.Poongodi 1, D. (Ms. S. Muthulashmi 1, (Assistant Pofesso, Faculty of Engineeing, Pofesso,
Figure 1. We will begin by deriving a very general expression before returning to Equations 1 and 2 to determine the specifics.
Deivation of the Laplacian in Spheical Coodinates fom Fist Pinciples. Fist, let me state that the inspiation to do this came fom David Giffiths Intodction to Electodynamics textbook Chapte 1, Section 4.
A dual-reciprocity boundary element method for axisymmetric thermoelastodynamic deformations in functionally graded solids
APCOM & ISCM 11-14 th Decembe, 013, Singapoe A dual-ecipocity bounday element method fo axisymmetic themoelastodynamic defomations in functionally gaded solids *W. T. Ang and B. I. Yun Division of Engineeing
Problem 1. Part b. Part a. Wayne Witzke ProblemSet #1 PHY 361. Calculate x, the expected value of x, defined by
Poblem Pat a The nomal distibution Gaussian distibution o bell cuve has the fom f Ce µ Calculate the nomalization facto C by equiing the distibution to be nomalized f Substituting in f, defined above,
CHAPTER 3. Section 1. Modeling Population Growth
CHAPTER 3 Section 1. Modeling Population Gowth 1.1. The equation of the Malthusian model is Pt) = Ce t. Apply the initial condition P) = 1. Then 1 = Ce,oC = 1. Next apply the condition P1) = 3. Then 3
Related Rates - the Basics
Related Rates - the Basics In this section we exploe the way we can use deivatives to find the velocity at which things ae changing ove time. Up to now we have been finding the deivative to compae the