Conference Session

Program and Curriculum Design Initiatives

Collection

2014 ASEE Annual Conference & Exposition

Authors

Malini Natarajarathinam, Texas A&M University

Tagged Divisions

Manufacturing

classes, a simulationgame was played in class. This idea stemmed from feedback from students whotook this class in the past. They wanted an opportunity to apply the knowledgegained from class to real life situation in a more fun way than doing a classproject. The simulation was a better way to have students acquire learning byapplying than by doing a group project. With the simulation game, the entire classhad an uniform experience and the faculty could control the concepts that studentsneed to be able to use. In a group project, this was not always possible becausewith the real world problem, the group and the faculty are not always sure of allthe concepts that will manifest in the project. B. Changes in CommunicationCommunication is key in

Conference Session

Socio-cultural Elements of Learning through Service

Collection

2014 ASEE Annual Conference & Exposition

Authors

Carla B. Zoltowski, Purdue University, West Lafayette; Antonette T. Cummings P.E., Purdue University; William C. Oakes, Purdue University, West Lafayette

Tagged Divisions

Community Engagement Division

Paper ID #10076Immersive Community Engagement ExperienceDr. Carla B. Zoltowski, Purdue University, West Lafayette Carla B. Zoltowski, Ph.D., is Co-Director of the EPICS Program at Purdue University. She received her B.S. and M.S. in electrical engineering and Ph.D. in engineering education, all from Purdue University. She has served as a lecturer in Purdue’s School of Electrical and Computer Engineering. Dr. Zoltowski’s academic and research interests include human-centered design learning and assessment, service-learning, ethical reasoning development and assessment, leadership, and assistive technology.Ms. Antonette T

Conference Session

Thermodynamics, Fluids, and Heat Transfer I

Collection

2014 ASEE Annual Conference & Exposition

Authors

Timothy J. Jacobs, Texas A&M University; Jerald A. Caton, Texas A&M University; Jeffrey E. Froyd, Texas A&M University; Kumbakonam Ramamani Rajagopal, Texas A&M University

Tagged Divisions

Mechanical Engineering

. R. A. Streveler, B. M. Olds, R. L. Miller and M. A. Nelson. Using a delphi study to identify the mostdifficult concepts for students to master in thermal and transport science. in American Society for EngineeringEducation Annual Conference & Exposition. 2003. Nashville, TN.2. B. M. Olds, R. A. Streveler, R. L. Miller and M. A. Nelson. Preliminary results from the development of aconcept inventory in thermal and transport science. in American Society of Engineering Education AnnualConference & Exposition. 2004. Salt Lake City, Utah.3. M. J. Cochran and P. R. L. Heron, Development and assessment of research-based tutorials on heat

Conference Session

Enhancing the Underrepresented Student Experience

Collection

2014 ASEE Annual Conference & Exposition

Authors

Catherine Michelle Mazak, University of Puerto Rico, Mayaguez; Cristopher B. Font-Santiago; Aidsa I. Santiago-Román, University of Puerto Rico, Mayaguez

Tagged Divisions

Minorities in Engineering

thisword from German to English, translators must either decide to: (a) take the word directly as aloanword or (b) write its meaning periphrastically to attempt to grasp its sense structure to thebest of English’s extent. Likewise, when translating CATS to CATS-S, this also became anoticeable issue upon inspection. Consider questions one through three of CATS-S where “is tobe drawn” from CATS is phrased as “se dibujará” in Spanish, which translates to “will bedrawn” (see Figure 1). Although not dramatically, the imperative sense of “is to be drawn” islost, which could bring momentary confusion to a student undergoing the testing process.There were also inconsistencies with regards to the translation of terminology from CATS toCATS-S. Some words

Conference Session

Best of Computers in Education Division

Collection

2014 ASEE Annual Conference & Exposition

Authors

Cameron H. G. Wright P.E., University of Wyoming; Thad B. Welch P.E., Boise State University; Michael G. Morrow, University of Wisconsin, Madison

Tagged Divisions

Computers in Education

Division of ASEE (1998, 2005, and 2010), and the Brigadier General Roland E. Thomas Award for outstanding contribution to cadet education (both 1992 and 1993) at the U.S. Air Force Academy. He is an active ABET evaluator and an NCEES PE exam committee member.Dr. Thad B. Welch P.E., Boise State University Dr. Thad B. Welch, P.E., Boise State University Thad B. Welch, Ph.D., P.E. received the B.E.E., M.S.E.E., E.E., and Ph.D. degrees from the Georgia Institute of Technology, Naval Postgraduate School, Naval Postgraduate School, and the University of Colorado in 1979, 1989, 1989, and 1997, respectively. He was commissioned in the U.S. Navy in 1979 and has been assigned to three submarines and a submarine repair tender

Conference Session

Trends in Engineering Education 1

Collection

2014 ASEE Annual Conference & Exposition

Authors

Lisa R. Lattuca, University of Michigan; David B Knight, Virginia Tech Department of Engineering Education; Michael Geoffrey Brown, University of Michigan-CSHPE

Tagged Divisions

Educational Research and Methods

Path A Unit Level Influences Adjustment For example: • Faculty • Discipline • Student characteristics Evaluate & Adjust Environment Path B Path C Modify Perceptions & Interpretations of Educational EffectivenessThe academic plan model is also informed by two studies48, 49 that clarified the components thatToombs and Tierney identified. These studies defined the content dimension as including thosethings that faculty members bring to the table when they plan a course: their backgroundcharacteristics and experiences, their views of their

Conference Session

Addressing the NGSS, Part 3 of 3: Supporting High School Science Teachers in Engineering Pedagogy and Engineering-Science Connections

Collection

2014 ASEE Annual Conference & Exposition

Authors

J. Jill Rogers, University of Arizona; Beau R. Vezino, University of Arizona; James C. Baygents, University of Arizona; Jeffrey B. Goldberg, University of Arizona

Tagged Divisions

K-12 & Pre-College Engineering

of Education in Curriculum and Instruction (2009) and a Bachelor’s of Science in Mechanical Engineering (2005). He has received the UA Graduate Access Fellowship, the Mary & Maude Miller Scholarship, and the SRP Learning Grant. Beau’s research interest lies in understanding how students can best learn and teachers can best teach engineering in the pre-college setting.Prof. James C. Baygents, University of ArizonaDr. Jeffrey B. Goldberg, University of Arizona Dr. Jeff Goldberg is Dean, College of Engineering, and Professor in Systems and Industrial Engineering at Arizona. He was employed at Vector Research and Bell Laboratories. He is currently a Principal of Silver Oak Research Inc. which specializes in deployment

Conference Session

K-12 and Pre-College Engineering Division Poster Session

Collection

2014 ASEE Annual Conference & Exposition

Authors

Kristen B. Wendell, University of Massachusetts, Boston; Christopher George Wright, University of Tennessee, Knoxville; Patricia C. Paugh, University of Massachusetts, Boston

Tagged Divisions

K-12 & Pre-College Engineering

Practitioners.” Journal of Engineering Education, 96(4).Atman, C. J., Kilgore, D., & McKenna, A. (2008) Characterizing design learning: A mixed-methods study of engineering designers' use of language. Journal of Engineering Education, July 2008, 309-326.Aurigemma, J., Chandrasekharan, S., Nersessian, N. J., & Newstetter, W. (2013). Turning experiments into objects: The cognitive processes involved in the design of a lab-on-a-chip device. Journal of Engineering Education, 102(1), 117-140.Barton, A. C. (2003). Teaching science for social justice. New York: Teachers College Press.Bloome, D., Carter, S. P., Christian, B. M., Otto, S., & Shuart-Faris, N. (2005). Discourse analysis and the study of classroom

Conference Session

Track 1 - Session 1

Collection

2014 ASEE International Forum

Authors

Michael B. Cutlip, University of Connecticut; Mordechai Shacham, Ben-Gurion University of the Negev; Michael Elly, Ben-Gurion University of the Negev

Tagged Topics

Curriculum and Lab Development

Paper ID #11027Enabling Extensive Numerical Problem Solving on Smartphones and TabletsDr. Michael B. Cutlip, University of Connecticut Michael B. Cutlip is an Emeritus Professor within the Chemical and Biomolecular Engineering Depart- ment at the University of Connecticut and has served as department head and director of the university’s Honors Program. He has B. Ch. E. and M. S. degrees from Ohio State and a Ph. D. from the University of Colorado. He has been the Chair and National Program Chair for the ASEE Chemical Engineering Division plus he co-chaired the ASEE Summer School for Chemical Engineering faculty in 2002

Conference Session

Engineering Physics & Physics Division Technical Session 2

Collection

2014 ASEE Annual Conference & Exposition

Authors

Warren A. Turner, Westfield State University; Glenn W. Ellis, Smith College; Robert J. Beichner, North Carolina State University

Tagged Divisions

Engineering Physics & Physics

markedly different. Of particular note are questions where an incorrectanswer is chosen with more frequency than the expected answer, even after instruction.Table 2: Percentage of students choosing a particular answer for each examination item. The whitecolumns on the left for each question refer to TUG-R and the grey shaded columns on the right foreach question are adapted from Beichner4 for the TUG-K. The correct answer is indicated inboldface.Question 1 2 3 4 5 6 7 A 11 41 0 2 22 8 6 2 2 3 22 45 28 31 B 28 16 10 10 0 0 23 14 4 2 46 25 24 20 C 1 4 15 24 27 20 32 23 52 73 5 6 12 10 D 28 22 4 2 44 62 25

Collection

2014 ASEE Zone 1 Conference

Authors

Ruoxu Jia; Junling Hu; Xingguo Xiong; Linfeng Zhang

restrictions ondoor sizes compared to door frame or door way bars. Besidesthe function of the pull-up bars, price and weight of the barsare very important factors for user to select a pull-up bar. Fig.3 Beam model of a pull up bar The supporting beam can be modeled as a cantilever beam with a standard squire cross section of thickness b and length L, as shown in Fig. 3. The design requirements are

Conference Session

Entrepreneurship & Engineering Innovation Programs and Courses Session 5

Collection

2014 ASEE Annual Conference & Exposition

Authors

Perry Samson, University of Michigan

Tagged Divisions

Entrepreneurship & Engineering Innovation

betweenleadership and management, understand and develop ethical principles of entrepreneurialleadership, and recognize various entrepreneurial strategies and apply them as appropriate.MethodsThis course provides an analytical framework to improve understanding of individual and sharedownership models in entrepreneurial organizations, and the way alternative ownership decisionsaffect organizational dynamics. It also looks at the mechanisms that entrepreneurs can use tocreate specific ownership structures and organizational cultures.This course is a half-semester long (7 weeks) covering: 1. Introductions a. Present current state of equity for your project b. Introduction to the pluses and minuses of equity dilution for founders c

Conference Session

Trends in Engineering Education 1

Collection

2014 ASEE Annual Conference & Exposition

Authors

Maura J. Borrego, Virginia Tech; Michael J. Prince, Bucknell University; Christopher Evan Nellis, Virginia Tech; Prateek Shekhar, Virginia Tech; Cindy Waters, North Carolina A&T State University; Cynthia J. Finelli, University of Michigan

Tagged Divisions

Educational Research and Methods

solve a problem? When afaculty tries something that requires student involvement in class, does it usually work? What ifit doesn’t work? Site B is a smaller public institution in the Southeast designated a Historically Black Collegeor University (HBCU). It is designated as the nation’s leading producer of African-Americanengineers. Focus groups were conducted with 9 participants in 3 sessions. Students were allrecruited through their introductory materials science and engineering course by their instructor.The focus groups were conducted by researchers visiting from another institution. Mostparticipants were underrepresented minorities, consistent with the HBCU mission of Site B.Sample items from the focus group protocol include:Q. How would

Conference Session

K-12 and Pre-College Engineering Division Poster Session

Collection

2014 ASEE Annual Conference & Exposition

Authors

Brianna L. Dorie, Purdue University, West Lafayette; Monica E Cardella, Purdue University, West Lafayette; Gina Navoa Svarovsky, Science Museum of Minnesota

Tagged Divisions

K-12 & Pre-College Engineering

; feasibility analysis; evaluation; decision; communication andimplementation) distributed across three major phases (problem scoping; developing alternativesolutions; project realization).10 Because this model is based in engineering textbooks, but has alsobeen used to describe the processes that students and practitioners engage in5, it is considered to beboth prescriptive and descriptive. Building on the work of Atman and her colleagues, as well asother design researchers11-12, in addition to models set out by pre-college educators, the focus ofthis work is to describe a model of engineering design that is (a) developmentally appropriate forchildren, (b) grounded in theory, and (c) grounded in empirical findings. To accomplish this, wehave reviewed

Conference Session

NSF Grantees’ Poster Session

Collection

2014 ASEE Annual Conference & Exposition

Authors

Niaz Latif, Purdue University Calumet (College of Technology); Mohammad A. Zahraee, Purdue University Calumet (College of Technology); Aco Sikoski, Ivy Tech Community College; Branislav Rosul, College of DuPage

Tagged Topics

NSF Grantees Poster Session

Tagged Divisions

Division Experimentation & Lab-Oriented Studies

4 1 0 3.25(b) I/O Addressing Format Exam I(c) Addressing Mode2. Understand and ConstructLadder Logic Programs NSF -ATE Labs 2, 3,(a) Instruction Set Relay, Timer, Module 1-10: 70.7 Final Exam 82 82.2 3 4 1 0 3.25 4,6,7Counter, Arithmatic, Exam IIComparison, File Instruction,3. Manipulate data using PLCinstruction sets NSF -ATE(a) Relay, Timer

Conference Session

Computer Programming and Simulation

Collection

2014 ASEE Annual Conference & Exposition

Authors

John R. Baker, University of Kentucky

Tagged Divisions

Computers in Education

for only 7% of a graduate student’sgrade. So, it is certainly possible that some who submitted flawed programs and/or reportswould have fared better on the project if a larger proportion of the course grade depended on thisproject. Page 24.889.10Table 1: Results of Graduate Student Projects 2011-2013 (24 Students)Student Modal Analysis Harmonic Response Analysis Report A OK OK OK B OK Results Incorrect OK C OK OK

Conference Session

A Focus on Non-Traditional Students and Non-Traditional Course Delivery Methods

Collection

2014 ASEE Annual Conference & Exposition

Authors

Armineh Noravian, San Francisco State University; Patricia Irvine, San Francisco State University

Tagged Divisions

Two Year College Division

Paper ID #9757Building technical capital in the technology educationMs. Armineh Noravian, San Francisco State University Armineh Noravian currently works as an adjunct faculty in engineering at San Francisco State University and as an educational research associate. Noravian holds a MS in engineering and MA in applied anthro- pology (cultural) from San Jose State University. She is currently completing her Ed.D. at San Francisco State University. Correspondence regarding this article should be addressed to Armineh Noravian at armineh@mail.sfsu.edu.Dr. Patricia Irvine, San Francisco State University Dr. Irvine is

Conference Session

A Focus on Non-Traditional Students and Non-Traditional Course Delivery Methods

Collection

2014 ASEE Annual Conference & Exposition

Authors

Elaine L. Craft, Florence-Darlington Technical College; Liesel Ashley Ritchie, Institute of Behavioral Science; Sandra Janette Mikolaski

Tagged Divisions

Two Year College Division

Paper ID #8631Leadership Development for Engineering Technology Faculty: Becoming anEducational Leader through Knowledge Generation, Application, and Con-tributionMs. Elaine L. Craft, Florence-Darlington Technical College Elaine L. Craft (Florence-Darlington Technical College, Florence, SC) holds a baccalaureate degree in chemical engineering from the University of Mississippi and a MBA from the University of South Car- olina with additional graduate studies in mathematics. Her experience includes working as an engineer in industry as well as teaching and administration at community college and state levels. She has

Conference Session

California on the Move: A Robust Array of Student Success Initiatives

Collection

2014 ASEE Annual Conference & Exposition

Authors

Anna Marbella Camacho, The STEM Center, Cañada College; Danni Redding Lapuz, The STEM Center at Cañada College

Tagged Divisions

Two Year College Division

Paper ID #9202The STEM Center: Creating a Model for Success in Community CollegeSTEM Education ˜Anna Marbella Camacho, The STEM Center, Canada College Anna Camacho joined Ca˜nada College in 2012 in the capacity of Assistant Project Director of Hispanic- Serving Institution-STEM Grant (CalSTEP). In this position, Anna manages all financial aspects of the grant’s $1.1 million yearly budget. In addition to handling fiscal matters, Anna also collaborates in pro- gram implementation & development and new grant proposals. Prior to joining Ca˜nada College, Anna was a Program Officer

Collection

2014 ASEE Zone 1 Conference

Authors

Jeng-Nan Juang; Ramachandran Radharamanan

the output voltage needed to power American appliances. The solar energy system designed and developed includes a • Collect, process and display real-time data of the systemsolar panel, a battery, and an inverter. The solar panel is on an LCD screen: The system must also be able to collectdesigned with a tracking mechanism that directs the panel real-time data from the system, process it, and display thistowards the area of high sunlight intensity. It also has a data on an LCD screen.method of concentrating the sunlight onto the photoreceptors B. Merit Criteriaon the solar panel. All of these maximize the amount of solar A merit criterion was developed to compare

Collection

2014 ASEE Zone 1 Conference

Authors

Ashenafi Lambebo; Sasan Haghani

sensor code.programming interface (API) is used to display the data. • Transmit the processed data to the base station periodically for further analysis and display. Fig. 1: Network architecture Fig. 2(a): Structure of transmitter node.A. Transmitter Node To achieve a power efficient network, open source andlow-power consumption hardware were used to implement thetransmitter. The structure of the transmitting nodes and thefinal product are shown in Fig. 2(a) and Fig. 2(b),respectively. Each transmitting node consists of one

Conference Session

Diversity Redefined: Nontraditional Views in Traditional Environments

Collection

2014 ASEE Annual Conference & Exposition

Authors

Kendra Woodberry Brinkley, Virginia Commonwealth University; Falcon Rankins, Virginia Commonwealth University; Stevara Clinton, Virginia Commonwealth University Department of Chemistry; Rosalyn Hobson Hargraves, Virginia Commonwealth University

Tagged Divisions

Minorities in Engineering

2 1 0 A B C D F W Math 4 5 4 0 1 0 Chemistry 2 5 2 2 1 1Figure 1B Online Bridge Student Grade Distribution. Note that 17 of the 23 of the onlineSummer Bridge students enrolled in a math and 16 of the 23 students enrolled in chemistry classtheir first semester. Math includes students who have taken college algebra, precalculus, andcalculus (Math 141,151, and 200). Chemistry includes students who have taken introductorychemistry I, general chemistry II (Chemistry 100, 101

Conference Session

Multidisciplinary Courses and Projects

Collection

2014 ASEE Annual Conference & Exposition

Authors

M. Brian Thomas, Trine University; Andrea Mitofsky, Trine University; Vukica M. Jovanovic, Old Dominion University; John Eiler

Tagged Divisions

Multidisciplinary Engineering

24.122.114. J. E. Froyd, P. C. Wankat, K. A. Smith, Five Major Shifts in 100 Years of Engineering Education, Proc. of the IEEE 100, 1344-1360, 2012.5. Y. Wong, K. Siu, A Model of Creative Design Process for Fostering Creativity of Students in Design Education, Intl. J. Technology & Design Education, 2012. 22(4): p. 437-450.6. N. Anderson, Design Thinking: Employing an Effective Multidisciplinary Pedagogical Framework to Foster Creativity and Innovation in Rural and Remote Education, Australian & International J. Rural Education, 2012. 22(2): p. 43-52.7. B. Blair, Elastic Minds? Is the Interdisciplinary/Multidisciplinary Curriculum Equipping our Students for the Future: A Case Study, Art, Design &

Collection

2014 ASEE Zone 1 Conference

Authors

Joseph Betthauser; Daniel Benavides; Jeff Schornick; Neal O'Hara; Jimit Patel; Jeremy Cole; Edgar Lobaton

Model B The design has been optimized to be compact, highly Proc. Type ARM Cortex A8 ARM 11maneuverable using an omni-directional drive system, and Proc. Speed 1 GHz 700 MHzpossesses a suite of inertial, visual, and environmental sensors RAM 512 MB DDR3L 512 MBon-board. Fig. 2 and 3 shows CAD model views and actual GPY SGX530 3D Videocore 4views of the WolfBot. The main features considered during VFP version NEON VFPv2

Conference Session

K-12 Teacher Pre-Service and Undergraduate Instructor Training

Collection

2014 ASEE Annual Conference & Exposition

Authors

Rafic Bachnak, Penn State Harrisburg; Sofía Carolina Maldonado, Texas A&M International University; Gerardo J. Pinzon PE, Texas A&M International University; Rohitha Goonatilake, Texas A&M International University, Laredo, Texas

Tagged Divisions

K-12 & Pre-College Engineering

questions of these surveys.   b. Workshop Evaluation A final workshop evaluation was performed to get feedback from the participants on the entire workshop. Participants rated the questions on a scale of 1 (disappointing) to 5 (wonderful). Figures 3 and 4 illustrate the results for the individual questions. The majority of the participants rated the questions with a 5. This feedback helps us improve future workshops. Figure 3: Feedback on Questions 1 and 2 Page 24.525.7 Figure 4: Feedback on Questions 3 to 8Two open-ended questions were included at the

Conference Session

Nuclear and Radiological Division Technical Session 2

Collection

2014 ASEE Annual Conference & Exposition

Authors

Mark A. Prelas, University of Missouri, Columbia; Matthew L. Watermann, NSEI - University of Missouri; Denis Alexander Wisniewski; Janese Annetta Neher, Nuclear Science and Engineering Institute-University of Missouri Columbia; Charles Lyndell Weaver III, University of Missouri - Columbia

Tagged Divisions

Nuclear and Radiological

] 2x1016 thermal neutronsSteady-State Research 4x1014 fast neutrons ∞ [6] Reactor 5x1014 thermal neutrons Table 2. Comparison of the absolute efficiency for the nuclear pumping source. A B C DPump Source Charged Charged Nuclear Addition Pump Source Particle Particle Energy Energy to Efficiency Energy Energy Produced by Produce ηNP=B/(C+D) Produced Available the Source Neutron (MeV) (MeV

Conference Session

Curricular Issues in Computing and Information Technology Programs II

Collection

2014 ASEE Annual Conference & Exposition

Authors

Osvaldo Mangual, Honeywell Aerospace; Marvi Teixeira, Polytechnic University of Puerto Rico; Reynaldo Lopez-Roig, Polytechnic University of Puerto Rico; Felix Javier Nevarez-Ayala, Polytechnic University of Puerto Rico

Tagged Divisions

Computing & Information Technology

Further examples can be found in the literature6,7. It is clear that each sub-convolution can beseparately processed, followed by a reconstruction stage to provide the final result. Parallelalgorithms can be developed by factorization of the Block Pseudocirculant matrix shown in (9),(12) and (13) into diagonal blocks. The general tensor product formulation for a block diagonalfactorization of the Block Pseudocirculant Matrix is6, y r = R r0 (A r0 ⊗ I N/r )D H (B r0 ⊗ I N/r )x r0 (15) 0 0 r0 0where xr0 and yr0 are the decimated-by-r0 input and output sequences and Ar0 and Br0 are thepost/pre-processing matrices, which are determined by each

Conference Session

Multidisciplinary Engineering Division Poster Session

Collection

2014 ASEE Annual Conference & Exposition

Authors

David M. Feinauer P.E., Norwich University; Michael W. Prairie, Norwich University

Tagged Divisions

Multidisciplinary Engineering

. Page 24.178.5Project EvolutionA concise summary of the previously reported4 lessons learned in the first implementation of theproject is provided below in Table 1. For convenience, a letter has been assigned to each of theinsights. In the discussion that follows laying out the modified execution of the project in theSpring of 2013, each change that is detailed will reference the associated lesson that motivatedthe change by listing the corresponding letter afterward in parentheses.Table 1 - Lessons learned from the initial execution of the hydroelectric generator design project. Identifier Lesson Learned / Insight LL-a Narrow the problem definition LL-b Multiply component design options to increase tasks for added

Collection

2014 ASEE Zone 1 Conference

Authors

Thomas Goddard; Konstantin Litovskiy; Nathan Nichols-Roy; Matthew Reed; Igor Shvartser; Nicholas Smith; David Zeppa; Linda Werner; Julia E. Rice; Hans W. Horn; Amanda C. Engler

diagram In addition to learning background material, the student B. Difficulty defining data-modelsteam decided that it would be beneficial to maintain contactwith an intermediary to assist with answering chemistry Chemists and computer scientists communicate in tworelated questions that arose during the implementation phase. different ways. Chemists talk in terms of the applicationThe course professor sought a student with an organic domain, while the computer scientists talk in terms of thechemistry background to assist with the initial student team by implementation domain. We needed to bridge that gap byserving as an intermediary between the student team and the creating a

Collection

2014 ASEE Zone 1 Conference

Authors

Ruoxu Jia; Junling Hu; Abubaker E.M. Elbalsohi

boundaryrelative to the velocity boundary and a longer thermal entrancelength compared to the hydrodynamic length. The normalized centerline velocities in two channels areshown in Fig. 10. Centerline velocities increase rapidly in the underdeveloped flow region near the flow entrances and the changes slow as it approaches to the fully developed region. Fig. 10 Centerline velocities in two channels normalized by the inlet velocities T v p T v p (a) (b) Fig.11 Contour