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 four decimal places The experimental procedure is to bet on one object Then, roll three Lucky Dice and count the number of matches The number of matches will decide your profit What is the theoretical probability of one die matching the object? Choose one object to place a bet on Roll the three Lucky Dice Count the number of matches Let X = number of matches Theoretically, X ~ B( , ) Let Y = profit per game Organize the DataIn [link], fill in the y value that corresponds to each x value Next, record the number of matches picked for your class Then, calculate the relative frequency Complete the table 1/4 Discrete Distribution (Lucky Dice Experiment) x y Frequency Relative Frequency Calculate the following: ¯ x = _ sx = ¯ y = _ sy = _ ¯ Explain what x represents ¯ Explain what y represents Based upon the experiment: What was the average profit per game? Did this represent an average win or loss per game? How you know? Answer in complete sentences Construct a histogram of the empirical data Theoretical DistributionBuild the theoretical PDF chart for x and y based on the distribution from the Procedure section x y P(x) = P(y) 2/4 Discrete Distribution (Lucky Dice Experiment) x y P(x) = P(y) Calculate the following: μx = _ σx = _ μx = _ Explain what μx represents Explain what μy represents Based upon theory: What was the expected profit per game? Did the expected profit represent an average win or loss per game? How you know? Answer in complete sentences Construct a histogram of the theoretical distribution Use the Data Note RF = relative frequency Use the data from the Theoretical Distribution section to calculate the following answers Round your answers to four decimal places P(x = 3) = _ P(0 < x < 3) = _ P(x ≥ 2) = _ 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(0 < x < 3) = _ RF(x ≥ 2) = _ Discussion QuestionFor questions and 2, consider the 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 3/4 Discrete Distribution (Lucky Dice Experiment) Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions Thinking about your answers to 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? 4/4 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, BioMed Central Page 1 of 10 (page number not for citation purposes) Human Resources for Health Open Access Review A review of the application and contribution of discrete choice experiments to inform human resources policy interventions Mylene Lagarde* 1 and Duane Blaauw 2 Address: 1 Health Economics and Financing Programme, London School of Hygiene and Tropical Medicine, London, UK and 2 Centre for Health Policy, University of the Witwatersrand, Johannesburg, South Africa Email: Mylene Lagarde* - mylene.lagarde@lshtm.ac.uk; Duane Blaauw - Duane.Blaauw@wits.ac.za * Corresponding author Abstract Although the factors influencing the shortage and maldistribution of health workers have been well- documented by cross-sectional surveys, there is less evidence on the relative determinants of health workers' job choices, or on the effects of policies designed to address these human resources problems. Recently, a few studies have adopted an innovative approach to studying the determinants of health workers' job preferences. In the absence of longitudinal datasets to analyse the decisions that health workers have actually made, authors have drawn on methods from marketing research and transport economics and used Discrete Choice Experiments to analyse stated preferences of health care providers for different job characteristics. We carried out a literature review of studies using discrete choice experiments to investigate human resources issues related to health workers, both in developed and developing countries. Several economic and health systems bibliographic databases were used, and contacts were made with practitioners in the field to identify published and grey literature. Ten studies were found that used discrete choice experiments to investigate the job preferences of health care providers. The use of discrete choice experiments techniques enabled researchers to determine the relative importance of different factors influencing health workers' choices. The studies showed that non-pecuniary incentives are significant determinants, sometimes more powerful than financial ones. The identified studies also emphasized the importance of investigating the preferences of different subgroups of health workers. Discrete choice experiments are a valuable tool for informing decision-makers on how to design strategies to address human resources problems. As they are relatively quick and cheap survey instruments, discrete choice experiments present various advantages for informing policies in developing countries, where longitudinal labour market data are seldom available. Yet they are complex research instruments requiring expertise in a number of different areas. Therefore it is essential that researchers also understand the potential limitations of discrete choice experiment methods. Published: 24 July 2009 Human Resources for Health 2009, 7:62 doi:10.1186/1478-4491-7-62 Received: 27 November 2008 Accepted: 24 July 2009 This article is available from: http://www.human-resources-h COMPOSITION SUM IDENTITIES RELATED TO THE DISTRIBUTION OF COORDINATE VALUES IN A DISCRETE SIMPLEX. R. MILSON DEPT. MATHEMATICS & STATISTICS DALHOUSIE UNIVERSITY HALIFAX, N.S. B3H 3J5 CANADA MILSON@MATHSTAT.DAL.CA Submitted: March 27, 2000; Accepted: April 13, 2000. AMS Subject Classifications: 05A19, 05A20. Abstract. Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first and second order, ordinary, linear differential equations. Regarding the first class, the corresponding identities amount to a proof of the exponential formula of labelled counting. The identities in the second class can be used to establish certain geometric properties of the simplex of bounded, ordered, integer tuples. We present three theorems that support the conclusion that the inner dimensions of such an order simplex are, in a certain sense, more ample than the outer dimensions. As well, we give an algebraic proof of a bijection between two families of subsets in the order simplex, and inquire as to the possibility of establishing this bijection by combinatorial, rather than by algebraic methods. 1. Introduction The present paper is a discussion of composition sum identities that may be obtained by utilizing spectral residues of parameterized, recursively defined sequences. Here we are using the term “composition sum” to refer to a sum whose index runs over all ordered lists of positive integers p 1 ,p 2 , ,p l that such that for a fixed n, p 1 + + p l = n. Spectral residues will be discussed in detail below. Compositions sums are a useful device, and composition sum identities are frequently encountered in combinatorics. For example the Stirling numbers (of both kinds) have a This research supported by a Dalhousie University grant. 1 the electronic journal of combinatorics 7 (2000), #R20 2 natural representation by means of such sums: [4, §51, §60]: s l n = n! l! p 1 + +p l =n 1 p 1 p 2 p l ; S l n = n! l! p 1 + +p l =n 1 p 1 ! p 2 ! p l ! . There are numerous other examples. In general, it is natural to use a composition sum to represent the value of quantities f n that depend in a linearly recursive manner on quantities f 1 ,f 2 , ,f n−1 . By way of illustration, let us mention that this point of view leads imme- diately to the interpretation of the n th Fibonacci number as the cardinality of the set of compositions of n by {1, 2} [1, 2.2.23] To date, there are few systematic investigations of composition sum identities. The ref- erences known to the present author are [2] [3] [6]; all of these papers obtain their results through the use of generating functions. In this article we propose a new technique based on spectral residues, and apply this method to derive some results of an enumerative nature. Let us begin by describing one of these results, and then pass to a discussion of spectral residues. Let S 3 (n) denote the discrete simplex of bounded, ordered triples of natural numbers: S 3 (n)={(x, y, z) ∈ N 3 :0≤ x<y<z≤ n}. In regard to this simplex, we may inquire as to what is more probable: a selection of points with distinct y coordinates, or a selection of points with distinct x coordinates. The answer is given by the following. Theorem 1.1. For every cardinality l between 2 and n − 1, there are more l-element sub- sets of S 3 (n) with distinct y coordinates, than there are l-element subsets with distinct x coordinates. Let us consider this result from the point of view of generating functions. The number of points with y = j is j(n − j). Hence the generating function for subsets with distinct y-values is Y (t)= n−1 j=1 (1 + j(n −j)t), where t counts the selected points. The number of points with x = n − j is j(j − 1)/2. Hence, the generating function for subsets with distinct x-values is X(t)= n j=2 1+ j(j − 1) 2 t . The above theorem is ... data Theoretical DistributionBuild the theoretical PDF chart for x and y based on the distribution from the Procedure section x y P(x) = P(y) 2/4 Discrete Distribution (Lucky Dice Experiment) x... similarities between the graphs and distributions of the theoretical and empirical distributions Use complete sentences 3/4 Discrete Distribution (Lucky Dice Experiment) Describe the three most.. .Discrete Distribution (Lucky Dice Experiment) x y Frequency Relative Frequency Calculate the following: ¯ x =