Modern Problem Solvng Tehnques n Engneerng wth POLYMATH, Exel and MATLAB. Introduton Engneers are fundamentally problem solvers, seekng to aheve some objetve or desgn among tehnal, soal eonom, regulatory and envronmental onstrants Problem Solvng n Chemal Engneerng Mathematal Model Physal Propertes Soluton Algorthm Doumentaton
Chemal Engneer s Tools of Trade - 1965 Calulaton Doumentaton Propertes Graphal Soluton Chemal Engneer s Problem Soluton Tehnques - 1965 Analytal solutons, nludng Model smplfaton by negletng less mportant terms Model manpulaton to brng t nto a solvable form Short-ut soluton tehnques Replang the problem wth a smpler one that an be solved Graphal solutons Tral and error soluton tehnques Numeral soluton, nludng Computer language programmng and debuggng
Shortomngs of the Tradtonal Soluton Tehnques Manual and Graphal Soluton Tehnques Tedous, tme onsumng error prone proess Oversmplfaton may lead to wrong results Hghest preson s two demal dgts Tme onstrants prevent sreenng of large number of alternatves to fnd an optmal soluton Computer Language Programmng Requres experts n programmng, numeral and optmzaton methods Tedous, tme onsumng error prone proess Frst Mlestones of Computer Use for Problem Solvng Fortran Programmng and Proess Smulaton Programs 1984, frst PC based Mathematal Software Pakages POLYMATH 1.0 on four 8 or 5 dskettes
Workshop Materal Avalablty All the workshop materal s avalable on the ftp ste: ftp://ftp.bgu.a.l/shaham/psworkshoptau_08/ The omplete set of the workshop notes, presentatons, Polymath, Exel and MATLAB fles an be downloaded as one zp fle: Workshop08Partpant.zp or ndvdual fles and folders an be downloaded separately. Sequental Calulatons wth POLYMATH and Exel, Parametr Studes wth Exel A typal example s the soluton of ub equatons of state for the ompressblty fator for spefed value of the temperature T and pressure P. R = 0. 0806 T = 304. P = 7. 9 b = RT /( 8P ) a = ( 7/ 64 )(R T P = R T/(V-b) a/v /P ) Soluton s easly obtaned by Polymath for a few sets of values of T and P. Exel or MATLAB are needed to arry out the alulatons for large sets of data
Sequental Calulatons wth POLYMATH and Exel, Parametr Studes wth Exel Example 1 Molar Volume and Compressblty Fator from Redlh-Kwong Equaton Example-1.pdf Prob_4.1.pdf Example1_A.pol Example1_B1.xls Example1_B1.xls Presentaton Handouts Example problem n the book of Cutlp and Shaham Polymath soluton fle Exel soluton, ompressblty fator Exel soluton, molar volume Soluton of a Sngle Nonlnear (Implt) Algebra Equaton wth POLYMATH and MATLAB, Parametr Studes wth MATLAB A sngle nonlnear equaton an be wrtten n the form f ( x ) = 0 where f s a funton and x s the unknown. Addtonal explt equatons may also be nluded. Typal examples belongng to ths ategory nlude: Solvng varous equatons of state for molar volume and/or ompressblty fator Bubble pont, dew pont and sothermal flash alulatons for deal mult-omponent mxtures Calulaton of adabat flame temperature n ombuston. Calulaton of the flow rate n a ppelne.
Multple Lnear and Polynomal Regresson wth Statstal Analyss Gven a set of data of measured (or observed) values of a dependent varable: y versus n ndependent varables x 1, x, x n, multple lnear regresson attempts to fnd the best values of the parameters a 0, a 1, a n for the equaton ŷ ˆ + y = a0 + a1x1, + a x, + K an xn, s the alulated value of the dependent varable at pont. The best parameters have values that mnmze the squares of the errors N S = ( y yˆ ) = 1 In polynomal regresson there s only one ndependent varable, thus y ˆ = a + a x + a x + K+ a 0 1 n x n Multple Lnear Regresson wth Statstal Analyss Correlaton of Heat of Hardenng of Portland Cement versus Composton Example-3.pdf Example_3.pol RegrOvervew.pdf Presentaton Handouts Polymath data fle Equatons, Statsts, Graphs and Examples Polynomal and Nonlnear Regresson wth Statstal Analyss Correlatng Temperature Dependent Physal Propertes Example-4.pdf Prob_4.4.pdf CpEthane.pol VpEthane.pol WagnerEq.pol Presentaton Handouts Example problem n the book of Cutlp and Shaham Polymath data fle (Heat apaty) Polymath data fle (Vapor pressure) Polymath soluton fle (Wagner equaton)
Top 5 Example 5 Soluton of a System of ODEs wth POLYMATH and Exel, Parametr Studes wth Exel Adabat Operaton of a Tubular Reator for Crakng of Aetone Top 6 Example 6 Soluton of a System of Nonlnear Algebra Equatons (NLE) wth POLYMATH and MATLAB, Parametr Studes wth MATLAB Complex Chemal Equlbrum Top 7 Example 7 Top 8 Example 8 Soluton of Multple-Model, Multple-Algorthm Problems Sem-ontnuous Fed-Bath and Cyl- Fed Bath Operaton of a Boreator Estmatng Model Parameters for Dynam Models Modelng Reproduton Rate of a Mroorgansm n a Fermenter Top 9 Example 9 Constraned Mnmzaton wth POLYMATH and Exel Complex Chemal Equlbrum by Gbbs Energy Mnmzaton Top 10 Example 10 Soluton of a System of ODEs wth POLYMATH and MATLAB, Boundary Value Iteratons wth MATLAB Smultaneous Multomponent Dffuson of Gases Top 11 Example 11 Method of Lnes for Partal Dfferental Equatons Dffuson and Reaton n a Fallng Lamnar Lqud Flm Top 1 Example 1 Applatons n Envronmental Engneerng Numeral Smulatons wth the Oxygen-sag model Top 13 Example 13 Applatons n Proess Safety HAZOP Analyss of a Proess for Oxdaton of -otanol n a sembath reator
Pratal Use of the Materal Studed n the Workshop Eduatonal verson of the Polymath 6.1 program, for personal use of the Workshop partpants s avalable at http://www.polymath-software.om/tral. The followng user name and password should enable you to enter the ste: User Name: psworkshop Password: tau008 Download the fle: PolymathEduTral61.exe, save t on your omputer and run t n order to nstall Polymath 6.1 All the workshop materal s avalable on the ftp ste: ftp://ftp.bgu.a.l/shaham/psworkshoptau_08/ The omplete set of the workshop notes, presentatons, Polymath, Exel and MATLAB fles an be downloaded as one zp fle: Workshop08Partpant.zp or ndvdual fles and folders an be downloaded separately. Pratal Use of the Materal Studed n the Workshop 8. Flud Mehans 9. Heat transfer 10. Mass Transfer Chapters 1. Introduton. Bas Prnples and Calulatons 3. Regresson and Correlaton of Data 4. Problem Solvng wth Exel 5. Problem Solvng wth MATLAB 6. Advaned Tehnques n Problem Solvng. 7.Thermodynams 11. Chemal Reaton Engneerng 1. Phase Equlbra and Dstllaton 13. Proess Dynams and Control 14. Bohemal Engneerng
Book Usage n Varous Courses An ntrodutory ourse of Computer Based Problem Solvng (CBPS) Examples for Numeral Methods and Advaned Math Courses 8. Flud Mehans 9. Heat transfer 10. Mass Transfer 1. Introduton. Bas Prnples and Calulatons 3. Regresson and Correlaton of Data 4. Problem Solvng wth Exel 5. Problem Solvng wth MATLAB 6. Advaned Tehnques n Problem Solvng. 7.Thermodynams 11. Chemal Reaton Engneerng 1. Phase Equlbra and Dstllaton 13. Proess Dynams and Control 14. Bohemal Engneerng Categorzng Problems Aordng to the Soluton Tehnque Used Bas Tops Advaned Tops (a) Conseutve Calulatons (b) System of Lnear Algebra Equatons () One Nonlnear (Implt) Algebra Equaton (d) Multple Lnear and Polynomal Regressons (e) Systems of Frst-Order Ordnary Dfferental Equatons (ODE s) - Intal Value problems (f) System of Nonlnear Algebra Equatons (NLE) (g) Hgher Order ODE s (h) Systems of Frst-Order ODEs - Boundary Value Problems () Stff Systems of Frst-Order ODE s (j) Dfferental-Algebra System of Equatons (DAE s) (k) Partal Dfferental Equatons (PDE) (l) Nonlnear Regresson (m) Parameter Estmaton n Dynam Systems (n) Nonlnear Programmng (Optmzaton) wth Equty Constrants