Fin Shape Thermal Optimization Using Bejans Constuctal Theory

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Fin Shape Thermal Optimization Using Bejan's Constructal Theory

Author : Giulio Lorenzini
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1608456072
Total Pages : 222 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis Fin Shape Thermal Optimization Using Bejan's Constructal Theory by : Giulio Lorenzini

Download or read book Fin Shape Thermal Optimization Using Bejan's Constructal Theory written by Giulio Lorenzini and published by Morgan & Claypool Publishers. This book was released on 2011-04-29 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains research results obtained by applying Bejan's Constructal Theory to the study and therefore the optimization of fins, focusing on T-shaped and Y-shaped ones. Heat transfer from finned surfaces is an example of combined heat transfer natural or forced convection on the external parts of the fin, and conducting along the fin. Fin's heat exchange is rather complex, because of variation of both temperature along the fin and convective heat transfer coefficient. Furthermore possible presence of more fins invested by the same fluid flow has to be considered. Classical fin theory tried to reduce the coupled heat transfer problem to a one-dimensional problem by defining an average temperature of the fin and writing equations using this parameter. However, it was shown that this approach cannot be used because of the effects of two-dimensional heat transfer, especially in the presence of short fins. CFD codes offer the possibility to consider bi-dimensional (and more generally, three-dimensional) effects and then a more real approach to the physic phenomena of finned surface's heat exchange. A commercial CFD code was used to analyse the case of heat exchange in presence of T-shaped fins, following an approach suggested by Bejan's Constructal Theory. The comparative results showed a significant agreement with previous research taken as a reference, and this result allows for the application of this approach to a wider range of systems. T-shaped optimized fin geometry is the starting point for further research. Starting from the optimal results (T-shape optimized fins), we show the trend of the assessment parameter (the dimensionless conductance) in function of the angle α between the two horizontal arms of the fin. A value for α, 90°

Fin-Shape Thermal Optimization Using Bejan's Constuctal Theory

Author : Giulio Lorenzini
Publisher : Springer Nature
ISBN 13 : 3031793331
Total Pages : 205 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Fin-Shape Thermal Optimization Using Bejan's Constuctal Theory by : Giulio Lorenzini

Download or read book Fin-Shape Thermal Optimization Using Bejan's Constuctal Theory written by Giulio Lorenzini and published by Springer Nature. This book was released on 2022-05-31 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains research results obtained by applying Bejan's Constructal Theory to the study and therefore the optimization of fins, focusing on T-shaped and Y-shaped ones. Heat transfer from finned surfaces is an example of combined heat transfer natural or forced convection on the external parts of the fin, and conducting along the fin. Fin's heat exchange is rather complex, because of variation of both temperature along the fin and convective heat transfer coefficient. Furthermore possible presence of more fins invested by the same fluid flow has to be considered. Classical fin theory tried to reduce the coupled heat transfer problem to a one-dimensional problem by defining an average temperature of the fin and writing equations using this parameter. However, it was shown that this approach cannot be used because of the effects of two-dimensional heat transfer, especially in the presence of short fins. CFD codes offer the possibility to consider bi-dimensional (and more generally, three-dimensional) effects and then a more real approach to the physic phenomena of finned surface's heat exchange. A commercial CFD code was used to analyse the case of heat exchange in presence of T-shaped fins, following an approach suggested by Bejan's Constructal Theory. The comparative results showed a significant agreement with previous research taken as a reference, and this result allows for the application of this approach to a wider range of systems. T-shaped optimized fin geometry is the starting point for further research. Starting from the optimal results (T-shape optimized fins), we show the trend of the assessment parameter (the dimensionless conductance) in function of the angle a between the two horizontal arms of the fin. A value for a, 90°

FIN-SHAPE THERMAL OPTIMIZATION USING BEJAN'S CONSTUCTAL THEORY

Author : GIULIO. MORETTI LORENZINI (SIMONE. CONTI, ALESSANDRA.)
Publisher :
ISBN 13 : 9783031009297
Total Pages : pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis FIN-SHAPE THERMAL OPTIMIZATION USING BEJAN'S CONSTUCTAL THEORY by : GIULIO. MORETTI LORENZINI (SIMONE. CONTI, ALESSANDRA.)

Download or read book FIN-SHAPE THERMAL OPTIMIZATION USING BEJAN'S CONSTUCTAL THEORY written by GIULIO. MORETTI LORENZINI (SIMONE. CONTI, ALESSANDRA.) and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Systems Engineering

Author : Giulio Lorenzini
Publisher :
ISBN 13 : 9788303179333
Total Pages : 0 pages
Book Rating : 4.1/5 (793 download)

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Book Synopsis Systems Engineering by : Giulio Lorenzini

Download or read book Systems Engineering written by Giulio Lorenzini and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains research results obtained by applying Bejan's Constructal Theory to the study and therefore the optimization of fins, focusing on T-shaped and Y-shaped ones. Heat transfer from finned surfaces is an example of combined heat transfer natural or forced convection on the external parts of the fin, and conducting along the fin. Fin's heat exchange is rather complex, because of variation of both temperature along the fin and convective heat transfer coefficient. Furthermore possible presence of more fins invested by the same fluid flow has to be considered. Classical fin theory tried to reduce the coupled heat transfer problem to a one-dimensional problem by defining an average temperature of the fin and writing equations using this parameter. However, it was shown that this approach cannot be used because of the effects of two-dimensional heat transfer, especially in the presence of short fins. CFD codes offer the possibility to consider bi-dimensional (and more generally, three-dimensional) effects and then a more real approach to the physic phenomena of finned surface's heat exchange. A commercial CFD code was used to analyse the case of heat exchange in presence of T-shaped fins, following an approach suggested by Bejan's Constructal Theory. The comparative results showed a significant agreement with previous research taken as a reference, and this result allows for the application of this approach to a wider range of systems. T-shaped optimized fin geometry is the starting point for further research. Starting from the optimal results (T-shape optimized fins), we show the trend of the assessment parameter (the dimensionless conductance) in function of the angle a between the two horizontal arms of the fin. A value for a, 90°

Simplified Models for Assessing Heat and Mass Transfer

Author : Giulio Lorenzini
Publisher : Springer Nature
ISBN 13 : 3031793609
Total Pages : 106 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Simplified Models for Assessing Heat and Mass Transfer by : Giulio Lorenzini

Download or read book Simplified Models for Assessing Heat and Mass Transfer written by Giulio Lorenzini and published by Springer Nature. This book was released on 2022-06-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to supply valid and reasonable parameters in order to guide the choice of the right model of industrial evaporative tower according to operating conditions which vary depending on the particular industrial context: power plants, chemical plants, food processing plants and other industrial facilities are characterized by specific assets and requirements that have to be satisfied. Evaporative cooling is increasingly employed each time a significant water flow at a temperature which does not greatly differ from ambient temperature is needed for removing a remarkable heat load; its aim is to refrigerate a water flow through the partial evaporation of the same.

Shape and Structure, from Engineering to Nature

Author : Adrian Bejan
Publisher : Cambridge University Press
ISBN 13 : 9780521793889
Total Pages : 370 pages
Book Rating : 4.7/5 (938 download)

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Book Synopsis Shape and Structure, from Engineering to Nature by : Adrian Bejan

Download or read book Shape and Structure, from Engineering to Nature written by Adrian Bejan and published by Cambridge University Press. This book was released on 2000-10-16 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seemingly universal geometric forms unite the flow systems of engineering and nature. For example, tree-shaped flows can be seen in computers, lungs, dendritic crystals, urban street patterns, and communication links. In this groundbreaking book, Adrian Bejan considers the design and optimization of engineered systems and discovers a deterministic principle of the generation of geometric form in natural systems. Shape and structure spring from the struggle for better performance in both engineering and nature. This idea is the basis of the new constructal theory: the objective and constraints principle used in engineering is the same mechanism from which the geometry in natural flow systems emerges. From heat exchangers to river channels, the book draws many parallels between the engineered and the natural world. Among the topics covered are mechanical structure, thermal structure, heat trees, ducts and rivers, turbulent structure, and structure in transportation and economics. The numerous illustrations, examples, and homework problems in every chapter make this an ideal text for engineering design courses. Its provocative ideas will also appeal to a broad range of readers in engineering, natural sciences, economics, and business.

Tree-Shaped Fluid Flow and Heat Transfer

Author : António F. Miguel
Publisher : Springer
ISBN 13 : 3319732609
Total Pages : 108 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Tree-Shaped Fluid Flow and Heat Transfer by : António F. Miguel

Download or read book Tree-Shaped Fluid Flow and Heat Transfer written by António F. Miguel and published by Springer. This book was released on 2018-04-20 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first comprehensive state-of-the-art research on tree (dendritic) fluid flow and heat transfer. It covers theory, numerical simulations and applications. It can serve as extra reading for graduate-level courses in engineering and biotechnology. Tree flow networks, also known as dendritic flow networks, are ubiquitous in nature and engineering applications. Tree-shaped design is prevalent when the tendency of the flow (fluid, energy, matter and information) is to move more easily between a volume (or area) and a point, and vice versa. From the geophysical trees to animals and plants, we can observe numerous systems that exhibit tree architectures: river basins and deltas, lungs, circulatory systems, kidneys, vascularized tissues, roots, stems, and leaves, among others. Tree design is also prevalent in man-made flow systems, both in macro- and microfluidic devices. A vast array of tree-shaped design is available and still emerging in chemical engineering, electronics cooling, bioengineering, chemical and bioreactors, lab-on-a-chip systems, and smart materials with volumetric functionalities, such as self-healing and self-cooling. This book also addresses the basic design patterns and solutions for cooling bodies where there is heat generation. Several shapes of fin as well as assemblies of fins are addressed. An up-to-date review of cavities, i.e., inverted or negative fins, for facilitating the flow of heat is also presented. Heat trees using high thermal conductivity material can be used in the cooling of heat-generating bodies, and can also be applied to the cooling of electronics.

Advances in Heat Transfer

Author : Ephraim M. Sparrow
Publisher : Academic Press
ISBN 13 : 0124079326
Total Pages : 360 pages
Book Rating : 4.1/5 (24 download)

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Book Synopsis Advances in Heat Transfer by : Ephraim M. Sparrow

Download or read book Advances in Heat Transfer written by Ephraim M. Sparrow and published by Academic Press. This book was released on 2013-11-19 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Heat Transfer fills the information gap between regularly scheduled journals and university-level textbooks by providing in-depth review articles over a broader scope than in journals or texts. The articles, which serve as a broad review for experts in the field, will also be of great interest to non-specialists who need to keep up-to-date with the results of the latest research. This serial is essential reading for all mechanical, chemical and industrial engineers working in the field of heat transfer, graduate schools or industry. - This serial is essential reading for all mechanical, chemical and industrial engineers working in the field of heat transfer, graduate schools or industry

Thermohydrodynamic Programming and Constructal Design in Microsystems

Author : Tao Dong
Publisher : Academic Press
ISBN 13 : 0128131926
Total Pages : 198 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Thermohydrodynamic Programming and Constructal Design in Microsystems by : Tao Dong

Download or read book Thermohydrodynamic Programming and Constructal Design in Microsystems written by Tao Dong and published by Academic Press. This book was released on 2018-10-20 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thermohydrodynamic Programming and Constructal Design in Microsystems explains the direction of a morphing system configuration that is illustrated by life evolution in nature. This is sometimes referred to as the fourth law of thermodynamics, and was first applied in thermofluidic engineering, with more recent applications in physics and biology. The book specifically focuses on synthetic modeling and constructal optimization in the design of microsystemic devices, which are of particular interest to researchers and practitioners in the sphere of micro- and nanoscale physics, a mechanistically deviation from conventional theory. The book is an important reference resource for researchers working in the area of micro- and nanosystems technology and those who want to learn more about how thermodynamics can be effectively applied at the micro level. - Explains how the application of constructal theory can lead to more effective microsystems design - Offers an introduction to the fundamentals and application to different flow and heat/mass transport systems - Bridges the gap between theoretical design and optimization, from a practical point-of-view

Case Studies in Forensic Physics

Author : Gregory A. DiLisi
Publisher : Springer Nature
ISBN 13 : 3031020863
Total Pages : 146 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Case Studies in Forensic Physics by : Gregory A. DiLisi

Download or read book Case Studies in Forensic Physics written by Gregory A. DiLisi and published by Springer Nature. This book was released on 2022-06-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a forensics-style re-examination of several historical events. The purpose of these studies is to afford readers the opportunity to apply basic principles of physics to unsolved mysteries and controversial events in order to settle the historical debate. We identify nine advantages of using case studies as a pedagogical approach to understanding forensic physics. Each of these nine advantages is the focus of a chapter of this book. Within each chapter, we show how a cascade of unlikely events resulted in an unpredictable catastrophe and use introductory-level physics to analyze the outcome. Armed with the tools of a good forensic physicist, the reader will realize that the historical record is far from being a set of agreed upon immutable facts; instead, it is a living, changing thing that is open to re-visitation, re-examination, and re-interpretation.

Empowering Professional Teaching in Engineering

Author : John Heywood
Publisher : Springer Nature
ISBN 13 : 303179382X
Total Pages : 223 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Empowering Professional Teaching in Engineering by : John Heywood

Download or read book Empowering Professional Teaching in Engineering written by John Heywood and published by Springer Nature. This book was released on 2022-05-31 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each one of us has views about education, how discipline should function, how individuals learn, how they should be motivated, what intelligence is, and the structures (content and subjects) of the curriculum. Perhaps the most important beliefs that (beginning) teachers bring with them are their notions about what constitutes "good teaching". The scholarship of teaching requires that (beginning) teachers should examine (evaluate) these views in the light of knowledge currently available about the curriculum and instruction, and decide their future actions on the basis of that analysis. Such evaluations are best undertaken when classrooms are treated as laboratories of inquiry (research) where teachers establish what works best for them. Two instructor centred and two learner centred philosophies of knowledge, curriculum and instruction are used to discern the fundamental (basic) questions that engineering educators should answer in respect of their own beliefs and practice. They point to a series of classroom activities that will enable them to challenge their own beliefs, and at the same time affirm, develop, or change their philosophies of knowledge, curriculum and instruction.

The Art of Teaching Physics with Ancient Chinese Science and Technology

Author : Matt Marone
Publisher : Springer Nature
ISBN 13 : 303102088X
Total Pages : 157 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Art of Teaching Physics with Ancient Chinese Science and Technology by : Matt Marone

Download or read book The Art of Teaching Physics with Ancient Chinese Science and Technology written by Matt Marone and published by Springer Nature. This book was released on 2022-05-31 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blending physics with the study of ancient Chinese science, technology, and culture is a unique and highly effective way to present the fundamentals of physics to non-science majors. Based on the author’s course at Mercer University (Georgia, U.S.), The Art of Teaching Physics with Ancient Chinese Science and Technology exposes a wide range of students to the scientific method and techniques of experimental analysis through the eyes and discoveries of ancient Chinese “polymaths” long before the European concept of the scientific method was even considered. No other book so deftly makes the connections from ancient China to Ben Franklin to Michael Faraday while teaching physics at the same time. A distinctive characteristic of this book is the detailed hands-on laboratory experiments. This first includes making a simple magnetic compass and magnetometer. Students then use the compass/magnetometer to measure the strength of the magnetic field produced by a long straight wire. The second experiment covers two different methods of mining copper to introduce students to simple chemical principles such as displacement reactions, oxidation, reduction, and electronegativity. Originally developed for non-science students in an Asian studies environment, this book provides a valuable resource for science teachers who wish to explore the historical connections largely ignored in traditional texts. When paired with Teaching Physics through Ancient Chinese Science and Technology (Marone, 2019), these two texts provide a unique means of studying selected topics traditionally found in a two-semester Physics course.

Engineering Principles in Everyday Life for Non-Engineers

Author : Saeed Benjamin
Publisher : Springer Nature
ISBN 13 : 3031793722
Total Pages : 196 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Engineering Principles in Everyday Life for Non-Engineers by : Saeed Benjamin

Download or read book Engineering Principles in Everyday Life for Non-Engineers written by Saeed Benjamin and published by Springer Nature. This book was released on 2022-05-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the role of some engineering principles in our everyday lives. Engineers study these principles and use them in the design and analysis of the products and systems with which they work. The same principles play basic and influential roles in our everyday lives as well. Whether the concept of entropy, the moments of inertia, the natural frequency, the Coriolis acceleration, or the electromotive force, the roles and effects of these phenomena are the same in a system designed by an engineer or created by nature. This shows that learning about these engineering concepts helps us to understand why certain things happen or behave the way they do, and that these concepts are not strange phenomena invented by individuals only for their own use, rather, they are part of our everyday physical and natural world, but are used to our benefit by the engineers and scientists. Learning about these principles might also help attract more and more qualified and interested high school and college students to the engineering fields. Each chapter of this book explains one of these principles through examples, discussions, and at times, simple equations.

Generating Functions in Engineering and the Applied Sciences

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031794109
Total Pages : 99 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Generating Functions in Engineering and the Applied Sciences by : Rajan Chattamvelli

Download or read book Generating Functions in Engineering and the Applied Sciences written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-05-31 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on generating functions (GFs) and their applications. It discusses commonly encountered generating functions in engineering and applied sciences, such as ordinary generating functions (OGF), exponential generating functions (EGF), probability generating functions (PGF), etc. Some new GFs like Pochhammer generating functions for both rising and falling factorials are introduced in Chapter 2. Two novel GFs called "mean deviation generating function" (MDGF) and "survival function generating function" (SFGF), are introduced in Chapter 3. The mean deviation of a variety of discrete distributions are derived using the MDGF. The last chapter discusses a large number of applications in various disciplines including algebra, analysis of algorithms, polymer chemistry, combinatorics, graph theory, number theory, reliability, epidemiology, bio-informatics, genetics, management, economics, and statistics. Some background knowledge on GFs is often assumed for courses in analysis of algorithms, advanced data structures, digital signal processing (DSP), graph theory, etc. These are usually provided by either a course on "discrete mathematics" or "introduction to combinatorics." But, GFs are also used in automata theory, bio-informatics, differential equations, DSP, number theory, physical chemistry, reliability engineering, stochastic processes, and so on. Students of these courses may not have exposure to discrete mathematics or combinatorics. This book is written in such a way that even those who do not have prior knowledge can easily follow through the chapters, and apply the lessons learned in their respective disciplines. The purpose is to give a broad exposure to commonly used techniques of combinatorial mathematics, highlighting applications in a variety of disciplines.

Engineering Thermodynamics and 21st Century Energy Problems

Author : Donna Riley
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1608453634
Total Pages : 100 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis Engineering Thermodynamics and 21st Century Energy Problems by : Donna Riley

Download or read book Engineering Thermodynamics and 21st Century Energy Problems written by Donna Riley and published by Morgan & Claypool Publishers. This book was released on 2011-10-28 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy is a basic human need; technologies for energy conversion and use are fundamental to human survival. As energy technology evolves to meet demands for development and ecological sustainability in the 21st century, engineers need to have up-to-date skills and knowledge to meet the creative challenges posed by current and future energy problems. Further, engineers need to cultivate a commitment to and passion for lifelong learning which will enable us to actively engage new developments in the field. This undergraduate textbook companion seeks to develop these capacities in tomorrow's engineers in order to provide for future energy needs around the world. This book is designed to complement traditional texts in engineering thermodynamics, and thus is organized to accompany explorations of the First and Second Laws, fundamental property relations, and various applications across engineering disciplines. It contains twenty modules targeted toward meeting five often-neglected ABET outcomes: ethics, communication, lifelong learning, social context, and contemporary issues. The modules are based on pedagogies of liberation, used for decades in the humanities and social sciences for instilling critical thinking and reflective action in students by bringing attention to power relations in the classroom and in the world. This book is intended to produce a conversation and creative exploration around how to teach and learn thermodynamics differently. Because liberative pedagogies are at their heart relational, it is important to maintain spaces for discussing classroom practices with these modules, and for sharing ideas for implementing critical pedagogies in engineering contexts. Table of Contents: What and Why? / The First Law: Making Theory Relevant / The Second Law and Property Relations / Thinking Big Picture about Energy and Sustainability

Engineering Design

Author : George D. Catalano
Publisher : Springer Nature
ISBN 13 : 3031020901
Total Pages : 125 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Engineering Design by : George D. Catalano

Download or read book Engineering Design written by George D. Catalano and published by Springer Nature. This book was released on 2022-05-31 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: While more and more undergraduate engineering programs are moving toward a multi-disciplinary capstone experience, there remains a need for a suitable textbook. The present text seeks to meet that need by providing a student friendly step by step template for this important and culminating academic journey beginning with the student design team's first meeting with the client to the final report and presentation. The text provides a wide range of design tools, a discussion of various design methodologies, a brief history of modern engineering, and a substantive consideration of engineering ethics. In addition, chapters are included on communication, team building and dealing with the inevitable obstacles that students encounter. Throughout the text, emphasis is placed upon the issues of environmental impact and the importance of diversity.

The Captains of Energy

Author : Vincent C. Prantil
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1627055894
Total Pages : 220 pages
Book Rating : 4.6/5 (27 download)

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Book Synopsis The Captains of Energy by : Vincent C. Prantil

Download or read book The Captains of Energy written by Vincent C. Prantil and published by Morgan & Claypool Publishers. This book was released on 2015-02-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: In teaching an introduction to transport or systems dynamics modeling at the undergraduate level, it is possible to lose pedagogical traction in a sea of abstract mathematics. What the mathematical modeling of time-dependent system behavior offers is a venue in which students can be taught that physical analogies exist between what they likely perceive as distinct areas of study in the physical sciences. We introduce a storyline whose characters are superheroes that store and dissipate energy in dynamic systems. Introducing students to the overarching conservation laws helps develop the analogy that ties the different disciplines together under a common umbrella of system energy. In this book, we use the superhero cast to present the effort-flow analogy and its relationship to the conservation principles of mass, momentum, energy, and electrical charge. We use a superhero movie script common to mechanical, electrical, fluid, and thermal engineering systems to illustrate how to apply the analogy to arrive at governing differential equations describing the systems' behavior in time. Ultimately, we show how only two types of differential equation, and therefore, two types of system response are possible. This novel approach of storytelling and a movie script is used to help make the mathematics of lumped system modeling more approachable for students.