Discrete Distribution (Playing Card Experiment)

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I NTERNATIONAL J OURNAL OF E NERGY AND E NVIRONMENT Volume 2, Issue 5, 2011 pp.783-796 Journal homepage: www.IJEE.IEEFoundation.org ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved. Experimental investigations and CFD study of temperature distribution during oscillating combustion in a crucible furnace J. Govardhan 1 , G.V.S. Rao 2 , J. Narasaiah 3 1 Department of Mechanical Engineering, AVN Institute of Engineering & Technology, A.P., India. 2 Department of Mechanical Engineering, PIRM Engineering College, A.P., India. 3 Department of Mechanical Engineering, PRRM Engineering College, A.P., India. Abstract As part of an investigation few experiments were conducted to study the enhanced heat transfer rate and increased furnace efficiency in a diesel fired crucible furnace with oscillating combustion. The results of experimental investigations of temperature distribution inside the crucible furnace during oscillating combustion are validated with the numerical simulation CFD code. At first pragmatic study of temperature distribution inside a furnace was carried out with conventional mode of combustion at certain conditions and later transient behavior similar to that is conducted with oscillating combustion mode with the same conditions. There found to be enhanced heat transfer rate, reduced processing time and increased furnace efficiency with visibly clean emissions during the oscillating combustion mode than the conventional combustion mode. In the present paper the temperatures inside the furnace at few designated points measured by suitable K type thermo-couples are compared with the CFD code. The geometric models were created in ANSYS and the configuration was an asymmetric one for computational reason. The experimental and numerical investigations produce similar acceptable results. The presented results show that the 3D transient model appeared to be an effective numerical tool for the simulation of the crucible furnace for melting processes. Copyright © 2011 International Energy and Environment Foundation - All rights reserved. Keywords: Temperature distribution; Oscillating combustion; crucible furnace; furnace efficiency; heat transfer. 1. Introduction In view of the impact on economy due to ever increasing energy prices globally and problems associated with global warming with the methods of energy utilization especially in the melting processes, there is a clear need for the heat transfer industries to focus on energy efficient methods and implementation of new technologies. The proposed new technologies shall be capable of utilizing variety of fuel resources with optimum release of heat energy and low emissions. Conventional combustion is generally used in the heat transfer industries for various melting operations. These systems using air-fuel mixture for combustion can be changed into oscillating combustion mode by introducing oscillations in the fuel flow rate as a parameter to improve the furnace performance. The furnaces which operate at high temperature produce large quantities of emissions are sometimes less productive and less efficient. There is a need to develop a technology that reduces emissions while increasing thermal efficiency for Discrete Distribution (Playing Card Experiment) Discrete Distribution (Playing Card Experiment) By: OpenStaxCollege Discrete Distribution (Playing Card Experiment) Class Time: Names: Student Learning Outcomes • The student will compare empirical data and a theoretical distribution to determine if an everyday experiment fits a discrete distribution • The student will demonstrate an understanding of long-term probabilities Supplies • One full deck of playing cards ProcedureThe experimental procedure is to pick one card from a deck of shuffled cards The theoretical probability of picking a diamond from a deck is _ Shuffle a deck of cards Pick one card from it Record whether it was a diamond or not a diamond Put the card back and reshuffle Do this a total of ten times Record the number of diamonds picked Let X = number of diamonds Theoretically, X ~ B( _, _) Organize the Data Record the number of diamonds picked for your class in [link] Then calculate the relative frequency x Frequency Relative Frequency 1/3 Discrete Distribution (Playing Card Experiment) x Frequency Relative Frequency 10 Calculate the following: ¯ x = s = Construct a histogram of the empirical data Theoretical Distribution Build the theoretical PDF chart based on the distribution in the Procedure section x P(x) 2/3 Discrete Distribution (Playing Card Experiment) x P(x) 10 Calculate the following: μ = σ = Construct a histogram of the theoretical distribution Using the Data NOTE RF = relative frequency Use the table from the Theoretical Distribution section to calculate the following answers Round your answers to four decimal places • P(x = 3) = _ • P(1 < x < 4) = _ • P(x ≥ 8) = _ Use the data from the Organize the Data section to calculate the following answers Round your answers to four decimal places • RF(x = 3) = _ • RF(1 < x < 4) = _ • RF(x ≥ 8) = _ Discussion QuestionsFor questions and 2, think about the shapes of the two graphs, the probabilities, the relative frequencies, the means, and the standard deviations Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions Use complete sentences Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions Using your answers from questions and 2, does it appear that the data fit the theoretical distribution? In complete sentences, explain why or why not Suppose that the experiment had been repeated 500 times Would you expect [link] or [link] to change, and how would it change? Why? Why wouldn’t the other table change? 3/3 I NTERNATIONAL J OURNAL OF E NERGY AND E NVIRONMENT Volume 1, Issue 6, 2010 pp.987-998 Journal homepage: www.IJEE.IEEFoundation.org ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2010 International Energy & Environment Foundation. All rights reserved. An experimental investigation of heat transfer and fluid flow in a rectangular duct with inclined discrete ribs K. R. Aharwal 1 , B. K. Gandhi 2 , J. S. Saini 2 1 Department of Mechanical Engineering S.G.S.I.T.S. Indore (M.P.), India. 2 Department of Mechanical and Industrial Engineering I.I.T. Roorkee (U.A.), India. Abstract Artificial roughness in the form of repeated ribs is generally used for enhancement of heat transfer heated surface to the working fluid. In the present work experimental investigations has been carried out to study the effect of a gap in the inclined rib on the heat transfer and fluid flow characteristics of heated surface. A rectangular duct of aspect ratio of 5.83 has been used to conduct experiments on one rib roughened surface. Experimental data have been collected to determine Nusselt number (heat transfer coefficient) as a function of roughness and flow parameters in the form of repeated ribs. In order to understand the mechanism of heat transfer through a roughened duct having inclined rib with and without gap, the detailed analysis of the fluid flow structure is required. Therefore the detailed velocity structures of fluid flow inside a similar roughened duct as used for the heat transfer analysis were obtained by 2-Dimensional Particle Image Velocimetry (PIV) system and the heat transfer results were correlated with the flow structure. It was found that inclined rib with a gap (inclined discrete rib) had better heat transfer performance compared to the continuous inclined rib arrangement. Further the inclined discrete rib with relative gap width (g/e) of 1.0 gives the higher heat transfer performance compared to the other relative gap width. Copyright © 2010 International Energy and Environment Foundation - All rights reserved. Keywords: Artificial roughness, Relative gap position, Reynolds number, Nusselt number. 1. Introduction A Large number of studies on heat transfer and flow characteristics have been carried out to investigate the effect of rib design parameters namely rib height, angle of attack, relative roughness pitch, rib arrangement and rib cross-section. However, the artificial roughness results in higher frictional losses leading to excessive power requirement for the fluid to flow through the duct. It is therefore desirable that turbulence must be created only in a region very close to the heat-transferring surface to break the viscous sub-layer for augmenting the heat transfer and the core flow should not be unduly disturbed to limit the increase in friction losses. This can be done by keeping the height of the roughness elements small in comparison to the duct dimensions [1]. Han et al. [2] investigated the effect of angle of attack () α Copyright © 2009 by James L. Hein. All rights reserved. Prolog Experiments in Discrete Mathematics, Logic, and Computability James L. Hein Portland State University March 2009 2 Contents Preface 4 1 Introduction to Prolog 5 1.1 Getting Started 5 1.2 An Introductory Example 6 1.3 Some Programming Tools 9 2 Beginning Experiments 12 2.1 Variables, Predicates, and Clauses 12 2.2 Equality, Unification, and Computation 16 2.3 Numeric Computations 19 2.4 Type Checking 20 2.5 Family Trees 21 2.6 Interactive Reading and Writing 23 2.7 Adding New Clauses 25 2.8 Modifying Clauses 27 2.9 Deleting Clauses 28 3 Recursive Techniques 31 3.1 The Ancester Problem 31 3.2 Writing and Summing 33 3.3 Switching Pays 36 3.4 Inductively Defined Sets 38 4 Logic 42 4.1 Negation and Inference Rules 42 4.2 The Blocks World 44 4.3 Verifying Arguments in First-Order Logic 46 4.4 Equality Axioms 48 4.5 SLD-Resolution 49 4.6 The Cut Operation 51 5 List Structures 54 5.1 List and String Notation 54 5.2 Sets and Bags of Solutions to a Query 56 5.3 List Membership and Set Operations 60 5.4 List Operations 64 Contents 3 6 List Applications 68 6.1 Binary Trees 68 6.2 Arranging Objects 70 6.3 Simple Ciphers 73 6.4 The Birthday Problem 76 6.5 Predicates as Variables 77 6.6 Mapping Numeric Functions 79 6.7 Mapping Predicates 80 6.8 Comparing Numeric Functions 83 6.9 Comparing Predicates 84 7 Languages and Expressions 86 7.1 Grammar and Parsing 86 7.2 A Parsing Macro 87 7.3 Programming Language Parsing 89 7.4 Arithmetic Expression Evaluation 90 8 Computability 94 8.1 Deterministic Finite Automata 94 8.2 Nondeterministic Finite Automata 96 8.3 Mealy Machines 99 8.4 Moore Machines 102 8.5 Pushdown Automata 104 8.6 Turing Machines 106 8.7 Markov Algorithms 110 8.8 Post Algorithms 112 9 Problems and Projects 116 9.1 Lambda Closure 116 9.2 Transforming an NFA into a DFA 118 9.3 Minimum-State DFA 124 9.4 Defining Operations 128 9.5 Tautology Tester 130 9.6 CNF Generator 134 9.7 Resolution Theorem Prover for Propositions 135 10 Logic Programming Theory 140 10.1 The Immediate Consequence Operator 140 10.2 Negation as Failure 141 10.3 SLDNF-Resolution 143 Answers to Selected Experiments 145 Index 156 4 Preface This book contains programming experiments that are designed to reinforce the learning of discrete mathematics, logic, and computability. Most of the experiments are short and to the point, just like traditional homework problems, so that they reflect the daily classroom work. The experiments in the book are organized to accompany the material in Discrete Structures, Logic, and Computability, Third Edition, by James L. Hein. In traditional experimental laboratories, there are many different tools that are used to perform various experiments. The Prolog programming language is the tool used for the experiments in this book. Prolog has both commercial and public versions. The language is easy to learn and use because its syntax and semantics are similar to that of mathematics and logic. So the learning curve is steep and no prior knowledge of the language is assumed. In fact, the experiments are designed to introduce language features as tools to help explore the problems being studied. The instant feedback provided by Prolog’s interactive environment can help the process of learning. When students get immediate feedback to indicate success or failure, there is a powerful incentive to try and get the right solution. This encourages students to ask questions like, PLAYING THE GENE CARD? A Report on Race and Human Biotechnology Osagie K. Obasogie Center for Genetics and Society Preface by Dorothy Roberts Playing the gene Card? A Report on Race and Human Biotechnology By Osagie K. Obasogie Center for Genetics and Society Preface by Dorothy Roberts © 2009 Center for Genetics and Society All rights reserved. No part of this publication may be reproduced in whole or in part without the written consent of the Center for Genetics and Society except in brief quotations or summaries in articles and reviews. Center for Genetics and Society 436 14th Street, Suite 700 Oakland, CA 94612 tel 510-625-0819 www.geneticsandsociety.org www.biopoliticaltimes.org www.biopolicywiki.org To download this report: www.thegenecard.org iii C e n t e r f o r g e n e t i C s a n d s o C i e t y P l ay i n g t h e g e n e C a r d ? A Report on Race and Human Biotechnology Contents Executive Summary vii About the Author ix Acknowledgments x Preface by Dorothy Roberts, Kirkland & Ellis Professor of Law, Northwestern Law School xi Race Cards and Gene Cards: A Note About the Report's Title xiv Introduction | Are 21st Century Technologies Reviving 19th Century Theories of Race? 1 How Have New Genetic eories of Racial Dierence Developed? 1 Context: Aer the Human Genome Project 2 Key Concern: Will Commercial and Forensic Applications Revive Biological eories of Race? 4 In is Report 5 Sidebar: What Does It Mean to Say that Race Is Not Biologically Signicant or that It Is a Social Construction? 3 Chapter 1 | Race-Based Medicine: One Step Forward, Two Steps Back? 7 Pharmacogenomics: e Concept Behind Race-Based Medicines 8 First on the Scene: BiDil 9 Concerns about BiDil 11 Addressing Disparities in Health rough Race-Specic Pharmaceuticals 13 Conclusion: Evaluating Race-Based Medicine 15 Recommendations 15 Sidebars: Major Projects on Human Genetic Variation 8 Why Genetic Variations Matter 10 Top-Down Marketing to the Black Community 11 Contents iv Contents Historical eories of Race 12 Are More Race-Based Medicines Around the Corner? 13 e Slavery Hypothesis 14 Chapter 2 | Ancestry Tests: Back to the Future? 17 African American Ancestry 17 Context: Population Genetics 18 From Groups and Populations to Individuals 23 Techniques Used by Ancestry Tests 24 Concerns about the Genetic Ancestry Industry 28 Conclusion: Resisting Racial Typologies 30 Recommendations 30 Sidebars: Native Americans and Ancestry Tests 18 Race, Intelligence, and James Watson 19 Bioprospecting and Biopiracy 20 From Race to Population and Back 21 e Business of DNA Ancestry Testing 24 Special Types of DNA 28 Human Genetic Variation—A Work in Progress 29 Chapter 3 | Race and DNA Forensics in the Criminal Justice System 31 How Does It Work? 31 How Reliable Are DNA Forensic Technologies? 32 DNA Databases 33 Cold Hits and Partial Matches 34 Whose DNA Is in ese Databases? 36 Siing DNA Databases to Catch Family Members 39 Predicting Criminality 40 Using DNA to Build Racial Proles 41 Conclusion: Eects on Minority Communities 43 Recommendations 44 Sidebars: DNA Entrapment? 32 e Scandal in Houston 33 e Innocence Project 33 v C e n t e r f o r g e n e t i C s a n d s o C i e t y P l ay i n g t h e g e n e C a r d ? A Report on Race and Human Biotechnology Contents “e Informer in Your Blood” 34 Juking Stats 35 “e Birthday Problem” and the Limits of Forensic Database Matches 36 Minority Communities and the War on Drugs 38 Civil Liberties and DNA Databases 39 Phrenology, a Classic Pseudo-Science 41 Conclusion 45 Racial Categories in Human Biotechnology Research 45 Race Impact Assessments 46 Responsible Regulation 47 Endnotes 49 About the Center for Genetics and Society 80 vii C e n t e r f o r G e n e t i C s a n d s o C i e t y P l ay i n G t h e G e n e C a r d ? I NTERNATIONAL J OURNAL OF E NERGY AND E NVIRONMENT Volume 2, Issue 5, 2011 pp.783-796 Journal homepage: www.IJEE.IEEFoundation.org ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved. Experimental investigations and CFD study of temperature distribution during oscillating combustion in a crucible furnace J. Govardhan 1 , G.V.S. Rao 2 , J. Narasaiah 3 1 Department of Mechanical Engineering, AVN Institute of Engineering & Technology, A.P., India. 2 Department of Mechanical Engineering, PIRM Engineering College, A.P., India. 3 Department of Mechanical Engineering, PRRM Engineering College, A.P., India. Abstract As part of an investigation few experiments were conducted to study the enhanced heat transfer rate and increased furnace efficiency in a diesel fired crucible furnace with oscillating combustion. The results of experimental investigations of temperature distribution inside the crucible furnace during oscillating combustion are validated with the numerical simulation CFD code. At first pragmatic study of temperature distribution inside a furnace was carried out with conventional mode of combustion at certain conditions and later transient behavior similar to that is conducted with oscillating combustion mode with the same conditions. There found to be enhanced heat transfer rate, reduced processing time and increased furnace efficiency with visibly clean emissions during the oscillating combustion mode than the conventional combustion mode. In the present paper the temperatures inside the furnace at few designated points measured by suitable K type thermo-couples are compared with the CFD code. The geometric models were created in ANSYS and the configuration was an asymmetric one for computational reason. The experimental and numerical investigations produce similar acceptable results. The presented results show that the 3D transient model appeared to be an effective numerical tool for the simulation of the crucible furnace for melting processes. Copyright © 2011 International Energy and Environment Foundation - All rights reserved. Keywords: Temperature distribution; Oscillating combustion; crucible furnace; furnace efficiency; heat transfer. 1. Introduction In view of the impact on economy due to ever increasing energy prices globally and problems associated with global warming with the methods of energy utilization especially in the melting processes, there is a clear need for the heat transfer industries to focus on energy efficient methods and implementation of new technologies. The proposed new technologies shall be capable of utilizing variety of fuel resources with optimum release of heat energy and low emissions. Conventional combustion is generally used in the heat transfer industries for various melting operations. These systems using air-fuel mixture for combustion can be changed into oscillating combustion mode by introducing oscillations in the fuel flow rate as a parameter to improve the furnace performance. The furnaces which operate at high temperature produce large quantities of emissions are sometimes less productive and less efficient. There is a need to develop a technology that reduces emissions while increasing thermal efficiency for Discrete Distribution (Lucky Dice Experiment) Discrete Distribution (Lucky Dice Experiment) By: OpenStaxCollege Discrete Distribution (Lucky Dice Experiment) Class Time: Names: Student Learning Outcomes • The student will compare empirical data and a theoretical distribution to determine if a Tet gambling game fits a discrete distribution • The student will demonstrate an understanding of long-term probabilities Supplies • one “Lucky Dice” game or three regular dice Procedure Round answers to relative frequency and probability problems to ... empirical data Theoretical Distribution Build the theoretical PDF chart based on the distribution in the Procedure section x P(x) 2/3 Discrete Distribution (Playing Card Experiment) x P(x) 10 Calculate.. .Discrete Distribution (Playing Card Experiment) x Frequency Relative Frequency ... between the graphs and distributions of the theoretical and empirical distributions Use complete sentences Describe the three most significant differences between the graphs or distributions of the