Conference Session

Thermodynamics, Fluids, and Heat Transfer I

Collection

2009 Annual Conference & Exposition

Authors

B. Terry Beck, Kansas State University; Bill Whitson, Kansas State University; Greg Payne, Kansas State University; Trevor Heitman, Kansas State University

Tagged Divisions

Mechanical Engineering

tunnel flowvisualization, smoke injection is the usual means to visualize the flows; whereas with watertunnel flow visualization a dye injection method is typically employed. The ability to visualizeflows, and the associated boundary layer separation and vortex shedding phenomenon, forms anextremely important thrust of such introductory courses, and is an invaluable educational tool aswell as a tool for practical engineering design. Smoke Rake Converging Nozzle FLOW Illuminated Separation Bubble Smoke Streams (a) Schematic of Sharp-Edged Nozzle Flow (b) Actual Half-Section Nozzle Flow Figure 1: Wind Tunnel Flow Visualization—Internal FlowThe work presented

Conference Session

Thermodynamics, Fluids, and Heat Transfer I

Collection

2009 Annual Conference & Exposition

Authors

Andrew Foley, United States Coast Guard Academy; Michael Plumley, United States Coast Guard Academy

Tagged Divisions

Mechanical Engineering

AC 2009-1620: ENTHALPY IN A BOX: TEACHING OPEN VS. CLOSED SYSTEMWORK TERMSAndrew Foley, United States Coast Guard AcademyMichael Plumley, United States Coast Guard Academy Page 14.579.1© American Society for Engineering Education, 2009 Enthalpy in a box Teaching open v closed system work terms.Abstract In teaching a general approach to thermodynamics the authors have reduced the equationcount in their course to basically one accounting equation, the Reynolds Transport equation.While this has been well received by students it does require that they, in turn, have a greaterphysical understanding of problems as success is now

Conference Session

Trends in Mechanical Engineering I

Collection

2009 Annual Conference & Exposition

Authors

Jiang Zhou, Lamar University; Paul Corder, Lamar University; Hsing-wei Chu, Lamar University; Kendrick Aung, Lamar University

Tagged Divisions

Mechanical Engineering

simplified as a 1DOF spring-mass-damper system. Figure 1. Typical drop apparatus and mounting scheme [9]2.2 Simplified ModelThe test board supported by four screws in the drop test can be simplified a 1DOF mass-spring-damper system. The equation of motion is M &x&(t ) − B x& (t ) − Kx (t ) ? f ( t ) (1)where M is the mass, B is the damping coefficient, and K is the spring constant of the test board,x(t) is the displacement of the test board of the system, and f(t) is the applied impact impulse. Page 14.715.3The JEDEC standard suggests that the test board be subjected to

Conference Session

Outstanding Contributions to Mechanical Engineering Education

Collection

2009 Annual Conference & Exposition

Authors

John Wagner, Clemson University; Katie Knaub, National Association of Watch and Clock Collectors

Tagged Divisions

Mechanical Engineering

identical time side gears; attached lever arms and add weights on the input and output shafts to balance the mechanism. 5. Complete necessary calculations required to determine the output torque analytically and compare results with gear teeth, lever arms, and input weights. Page 14.1271.7 Figure 2: Assembled and internal components of a clock’s mechanism – (a) front view of entire assembly, and (b) front plate removed to illustrate the meshed gear trains3.2 Motion Analysis of Clock Pendulums (Lab II)The mechanical properties of a clock’s pendulum such as the moment of inertia and frequencywill be analyzed using

Conference Session

Student Learning and Assessment

Collection

2009 Annual Conference & Exposition

Authors

Andre Butler, Mercer University; William Moses, Mercer University

Tagged Divisions

Mechanical Engineering

achieved for themechanical specialization. The statement of program outcomes for the Mercer UniversitySchool of Engineering proposes that, among a number of other engineering and societalcapabilities, graduates will be able to “design and conduct experiments and analyze data.”5 This Page 14.52.4outcome and its assessment are intended specifically to address ABET engineering programcriterion 3(b)—“Engineering programs must demonstrate that their students attain the followingoutcomes: . . . (b) an ability to design and conduct experiments, as well as to analyze andinterpret data . . .”1 as well as SACS comprehensive standard 3.3.1—“The institution

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

Wael Mokhtar, Grand Valley State University

Tagged Divisions

Mechanical Engineering

, professional technical meetings, and team work.The course objectives include the following: 1. Perform and document research activities in a professional manner a. Perform literature searches b. Maintain a journal denoting all research activities c. Create a master research plan for future research direction 2. Summarize the research project’s past, present, and future goals 3. Complete research related tasks in a timely fashion with limited faculty supervision a. Create a plan for specific research activities b. Update and document progress on research activities c. Perform open-ended tasks as assigned by the instructor 4. Participate as an effective team member on the project a

Conference Session

Thermodynamics, Fluids, and Heat Transfer II

Collection

2009 Annual Conference & Exposition

Authors

Michael Maixner, United States Air Force Academy; James Baughn, UC Davis

Tagged Divisions

Mechanical Engineering

AC 2009-430: A SIMPLE, AFFORDABLE STEADY-STATE FIN HEAT TRANSFERMINI-LAB/DEMOMichael Maixner, United States Air Force Academy Michael Rex Maixner graduated with distinction from the U. S. Naval Academy, and served as a commissioned officer in the USN for 25 years; his first 12 years were spent as a shipboard officer, while his remaining service was spent strictly in engineering assignments. He received his Ocean Engineer and SMME degrees from MIT, and his Ph.D. in mechanical engineering from the Naval Postgraduate School. He served as an Instructor at the Naval Postgraduate School and as a Professor of Engineering at Maine Maritime Academy; he is currently a member of the Department

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

Nihad Dukhan, University of Detroit, Mercy; Mark Schumack, University of Detroit, Mercy

Tagged Divisions

Mechanical Engineering

probe the ability of students to a)explain the societal context of engineering, b) explain the importance of pro-active communityservice, and demonstrate an inclination to continue such service in the future, c) exhibit anappreciation of communication with non-engineers and finally, d) challenge some of thestudents’ stereotypes regarding others. The service-learning project was executed incollaboration with a local not-for-profit organization. Reflections were conducted by thestudents by answering a set of carefully-phrased questions after conducting the project. Analysisof students’ responses as well as the implications of the trends obtained, are explained in thispaper. The recorded benefits of service learning are described and can be

Conference Session

Trends in Mechanical Engineering I

Collection

2009 Annual Conference & Exposition

Authors

Freddie Davis, West Texas A&M University; Emily Hunt, West Texas A&M University; Kendra Campbell, West Texas A&M University

Tagged Divisions

Mechanical Engineering

improvements were made for participating students. For example, therewas a 16% increase in peer-to-peer connections. “The Connections with Peers Factor is based onthree response items about the degree to which the course improved the student’s (a) efforts toget to know students in classes, (b) ability to meet new people with common interests, and (c)ability to establish close friendships with peers”.12 Additionally, because of the shared courses,students felt more comfortable engaging in friendships with classmates. By establishingfriendships, students “reported a 6% higher mean score on overall satisfaction with the collegethey are attending.”12A study conducted at Georgia State University in 200613 sought quantitative evidence regardingthe efficacy

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

Rogelio Luck, Mississippi State University; B.K. Hodge

Tagged Divisions

Mechanical Engineering

, uncertainty analysis, inverse heat transfer, radiation heat transfer, applied math, theoretical and applied control systems, piezoelectric sensors, electrical power system generation and distribution, and redundant measurement systems.B. Hodge, Mississippi State University B. K. Hodge is Professor of Mechanical Engineering at Mississippi State University (MSU) where he serves as the TVA Professor of Energy Systems and the Environment and is a Giles Distinguished Professor and a Grisham Master Teacher. He is a Fellow of the American Society for Engineering Education and the American Society of Mechanical Engineers and an Associate Fellow of the American Institute of Aeronautics and Astronautics

Conference Session

Thermodynamics, Fluids, and Heat Transfer II

Collection

2009 Annual Conference & Exposition

Authors

Amir Karimi, University of Texas, San Antonio

Tagged Divisions

Mechanical Engineering

thetemperature at an arbitrary position in the fin. By using the tool menu and selecting the GoalSeek option a dialog box appears, as shown in Fig 7. The target cell (temperature in this case,cell E16) then is selected and its value is set to a desired value for that cell (175). The cell thatits value must be changed is identified (cell A16). After clicking on the Solve button, the value inthe selected cell A16 (x) automatically changes to a value that yields the desired temperature of175 oC in the target cell (E16). The solution is presented in Fig. 7-b. Page 14.17.10 Fig. 6 Solution of Example 2 by a trial and error procedure(a) Initial guess

Conference Session

Trends in Mechanical Engineering I

Collection

2009 Annual Conference & Exposition

Authors

Charles Forsberg, Hofstra University

Tagged Divisions

Mechanical Engineering

AC 2009-815: USE OF THE KNOWLEDGE AND SKILL BUILDER (KSB)FORMAT IN A SENIOR MECHANICAL ENGINEERING LABORATORYCharles Forsberg, Hofstra University Charles H. Forsberg is an Associate Professor of Engineering at Hofstra University, where he teaches courses in computer programming and the thermal/fluids area of mechanical engineering. He received a B. S. in Mechanical Engineering from the Polytechnic Institute of Brooklyn (now Polytechnic Institute of NYU), and an M. S. in Mechanical Engineering and Ph. D. from Columbia University. He is a Licensed Professional Engineer in New York State. Page

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

Enrique Barbieri, University of Houston; Raresh Pascali, University of Houston; Miguel Ramos, University of Houston; William Fitzgibbon, University of Houston

Tagged Divisions

Mechanical Engineering

semester hours for ET programs, with no specifics for E programs. SomeInstitutions defer the Humanities and Social Science electives to the senior year in order tointroduce as many technical courses as possible during the first two years. If one assumes asomewhat uniform distribution of the semester credit hours over an undergraduate careerspanning 8 semesters, the number of credits per semester will range between 15 and 18 hours.The proposed two-year template ranges between 65-68 credit hours and is given in Table 2. Table 2. A 2-year Template for ME and MET Programs. Format: Course (a, b) where a=number of lecture hours; b=number of lab hours Term 1 Term 2 Term 3 Term

Conference Session

Trends in Mechanical Engineering I

Collection

2009 Annual Conference & Exposition

Authors

Ashland Brown, University of the Pacific; Kris Wood, University of Texas; Kristen Kaufman, Grad Student Universiy ot Texas; Daniel Jensen, United States Air Force Academy; Joseph Rencis, University of Arkansas; Christina White, Columbia University

Tagged Divisions

Mechanical Engineering

BeamThese four modules, as part of the entire set of 12 Finite Element learning modules, are arefreshing first step to filling a current void in engineering education. Their benefits, along withthe assessment methodology developed in this paper, have the potential to be far reaching.Assessment FoundationsHelpful steps to assessments for the FE tutorials are: (a) gathering student demographics (i.e.academic major, educational level, grade point average, expected grade earned in current course,reason for taking course, plans after graduation, age, ethnicity, and gender); (b) gathering Felder-Silverman learning style and MBTI personality type (this analysis, along with learningobjectives, can be reviewed and fed back into improving the learning

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

Aman Yadav, Purdue University; Gregory Shaver, Purdue University; Peter Meckl, Purdue University

Tagged Divisions

Mechanical Engineering

perceptions ofbenefits of using case studies. Specifically, the survey asked participants to compare caseteaching method with traditional lecture along nine dimensions related to their learning andengagement. The survey was adapted from previous research conducted by Yadav 7.C. ProcedureThe study utilized a counterbalanced design, where two topics (thermal vs. hydraulic systems)and the method of instruction (case study vs. traditional lecture) were counterbalanced.Specifically, instructor A taught thermal systems topic with case studies while instructor Btaught the same topic using traditional lecture. This was reversed for the hydraulic systems topicso that instructor B taught using case studies and instructor A taught using traditional

Conference Session

Trends in Mechanical Engineering I

Collection

2009 Annual Conference & Exposition

Authors

Nidal Al-Masoud, Central Connecticut State University; Peter Baumann, Central Connecticut State University; Alfred Gates, Central Connecticut State University

Tagged Divisions

Mechanical Engineering

engineering courses students will acquire in-depth principles of thermo-fluid sciences, mechanical systems and control, materials, mechanical design, finite element analysis and manufacturing. a. Through the aerospace specialization, students will both broaden and deepen their knowledge in aerospace materials, structures, propulsion, flight dynamics and control. b. Through the manufacturing specialization, students will broaden and deepen their knowledge manufacturing automation, systems design, strategy and simulation. 2. Graduates will acquire industry relevant experience within the academic environment through course projects, laboratory experimentation, classroom

Conference Session

Design Projects in Mechanical Engineering II

Collection

2009 Annual Conference & Exposition

Authors

Matthias Lang, University of Texas, Austin; Dinesh Rabindran, University of Texas, Austin; Tricia Berry, University of Texas, Austin

Tagged Divisions

Mechanical Engineering

Brake Harmonic Drive Controller Actuator Output (a) Powercube robot joint module (b) Walking machine (c) 7-DOF serial robot manipulator Figure 1. Picture of PR 110 joint module and some robotic systems assembled using this module6In today’s world, most robots are controlled in position-mode, that is, their operational objectiveis to move from one point to another along a specified path with a specified motion profile.Frequently, this means the robot or one of its arms will move from the starting position to thespecified target position without regard to the forces (or

Conference Session

Design Projects in Mechanical Engineering II

Collection

2009 Annual Conference & Exposition

Authors

Brian Novoselich, United States Military Academy; Joel Dillon, United States Military Academy

Tagged Divisions

Mechanical Engineering

AC 2009-48: TWO IS BETTER THAN ONE: EXPERIENCES REVITALIZING ACAPSTONE DESIGN COMPETITION PROGRAMBrian Novoselich, United States Military Academy Brian Novoselich is a Major in the United States Army and an Assistant Professor in the Department of Civil and Mechanical Engineering at the United States Military Academy, West Point, NY. He holds a M.S. in Mechanical Engineering.Joel Dillon, United States Military Academy Joel Dillon is a Major in the United States Army and an Instructor in the Department of Civil and Mechanical Engineering at the United States Military Academy, West Point, NY. He holds a M.S. in Mechanical Engineering

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

Yaomin Dong, Kettering University; Jacqueline El-Sayed, Kettering University

Tagged Divisions

Mechanical Engineering

AC 2009-857: A METHODOLOGY FOR TEAM TEACHING A COURSE WITHINDUSTRIAL EXPERTSYaomin Dong, Kettering University Dr. Yaomin Dong is Assistant Professor of Mechanical Engineering at Kettering University. He received his Ph.D. in Mechanical Engineering at the University of Kentucky in 1998. Dr. Dong has extensive R&D experience in automotive industry and holds multiple patents. He is specialized in metalforming processes, design with composite materials, and finite element analysis.Jacqueline El-Sayed, Kettering University Dr. Jacqueline El-Sayed is a professor of mechanical engineering at Kettering University, the Richard L. Terrell Professor of Excellence in Teaching. She has been an

Conference Session

Statics and Dynamics: What's New

Collection

2009 Annual Conference & Exposition

Authors

Edward Anderson, Texas Tech; Roman Taraban, Texas Tech; Diana Hudson, Texas Tech

Tagged Divisions

Mechanical Engineering

involved in TOT or ifthey all share some of the same mechanisms, as suggested by the correlations between the threevariables, the hierarchical regression would account for that in level two and the unique,additional GRD variance explained by TOT could be assessed in level three. None of the levelone or two predictor variables were able to explain a significant proportion of GRD variance.However, the SCI posttest, entered as level three, was able to predict a significant additionalproportion of the course grade variance. The results are provided in Table 9. Page 14.119.8 B SE B β

Conference Session

Design Projects in Mechanical Engineering II

Collection

2009 Annual Conference & Exposition

Authors

Emilia Bratschitsch, Joanneum University of Applied Sciences; Adrian Millward-Sadler, Joanneum University of Applied Sciences

Tagged Divisions

Mechanical Engineering

Page 14.733.4The students receive the signed form ‘A’ and are asked to apply to the approved companies.They send a written application and a résumé and record responses in a second form (the so- -3-called form ‘B’, from German word “Bewerbungsübersicht” meaning “applicationsummary”), Figure 3.Using form ‘B’, we follow how the companies deal with the applications, how manyacceptances respectively refusal letters our juniors receive, which industry areas have themost interest in internship students, and which are the preferred disciplines. Applying thissystem consistently we obtain an overview of our students areas of interest regarding subjectsand host

Conference Session

Outstanding Contributions to Mechanical Engineering Education

Collection

2009 Annual Conference & Exposition

Authors

Dianne Pawluk, Virginia Commonwealth University; Curtis Taylor, University of Florida; Marcia Hoffman, Virginia Commonwealth University; Maria McClintock, Virginia Commonwealth University

Tagged Divisions

Mechanical Engineering

nano worlds are part of the same continuum,with more features potentially appearing as the scale ofviewing decreases. In order to communicate thisconcept we have decided to allow students tocontrollably “zoom in” on objects they are familiarwith, such as a compact disc or human hair. As thescale decreases, they will become aware of the detailsthey can feel and, for the sighted students, see in thetopology, while appreciating the fact that it is the sameobject.For the actual implementation of the haptic feedback onthe Novint Falcon, both the macro- and nanosurfacetopologies are simulated using an analog of an AFM – a Figure 7. (a) 3-D AFM image isrelatively stiff virtual spring, is used to model the haptic converted to (b) a gray

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

Kathy Schmidt, University of Texas, Austin; Juan Garcia, University of Texas, Austin; Michael Webber, University of Texas, Austin

Tagged Divisions

Mechanical Engineering

conferencing settings, Journal of Interactive Learning Research, 12, pp. 427–449. 9. Oomen-Early, J., & Sloane, B. (2007). Entering the Blogosphere: Blogs as Teaching and Learning Tools in Health Education, International Electronic Journal of Health Education, v10, pp. 186-196. 10. Berger, E. (2007). Podcasting in engineering education: A preliminary study of content, student attitudes, and impact. Journal of Online Education, v4 (1). 11. Evans, C. (2008). The effectiveness of m-learning in the form of podcast revision lectures in higher education. Computers & Education, v50 (2), pp. 491-498. Page

Conference Session

Mechanical Engineering Poster Session

Collection

2009 Annual Conference & Exposition

Authors

David Miller, Montana State University

Tagged Divisions

Mechanical Engineering

AC 2009-1866: ENGAGING FRESHMEN IN A HANDS-ON DISCOVERY OFMECHANICAL ENGINEERINGDavid Miller, Montana State University Page 14.538.1© American Society for Engineering Education, 2009 Engaging Freshmen in a Hands-on Discovery of Mechanical Engineering I. AbstractThis paper outlines a new approach in the introductory freshmen mechanical engineering courseat Montana State University to increase student retention. The objective is to utilize, within theIntroduction to Mechanical Engineering (ME101) course, a set of freshmen-level, hands-onlaboratory modules across the breadth of mechanical engineering to introduce students to

Conference Session

Design Projects in Mechanical Engineering I

Collection

2009 Annual Conference & Exposition

Authors

Tony Jones, United States Army; Daisie Boettner, United States Military Academy; Anna Lambert, University of Memphis; Brian Novoselich, United States Military Academy; Stephanie Ivey

Tagged Divisions

Mechanical Engineering

AC 2009-928: ORGANIZATIONAL LEADERSHIP AND EFFECTIVE TEAMPROBLEM-SOLVING STRATEGIES IN ENGINEERING DESIGN PROJECTS: ACASE STUDYTony Jones, United States ArmyAnna Lambert, University of MemphisDaisie Boettner, United States Military AcademyBrian Novoselich, United States Military AcademyStephanie Ivey, Page 14.936.1© American Society for Engineering Education, 2009 Organizational Leadership and Effective Team Problem Solving Strategies in Engineering Design Projects: A Case StudyAbstractThis project presents a case study examination of the problem solving strategies and discoursepatterns used by members of an Engineering Capstone Design Team. In our study, a

Conference Session

Trends in Mechanical Engineering II

Collection

2009 Annual Conference & Exposition

Authors

David Willis, Southern Methodist University; Paul Krueger, Southern Methodist University; Alice Kendrick, Southern Methodist University

Tagged Divisions

Mechanical Engineering

AC 2009-1726: THE INFLUENCE OF A RESEARCH EXPERIENCES FORUNDERGRADUATES PROGRAM ON STUDENTS’ ATTITUDES TOWARDENGINEERING RESEARCHDavid Willis, Southern Methodist University David A. Willis is an Associate Professor in the Department of Mechanical Engineering at Southern Methodist University (SMU). He received his B.S. degree from North Carolina State University and his M.S. and Ph.D. degrees from Purdue University in 2001. His areas of research interests are heat transfer, phase change, and fluid mechanics problems associated with short pulse laser-material interactions. His research involves experimental studies of laser microfabrication, high power laser-ablation, and laser-induced forward

Conference Session

Student Learning and Assessment

Collection

2009 Annual Conference & Exposition

Authors

Constantin Ciocanel, Northern Arizona University; Suzanne Pieper, Northern Arizona University

Tagged Divisions

Mechanical Engineering

AC 2009-2081: A THREE-WAY APPROACH TO INVESTIGATING STUDENTS’LEARNING STYLES IN AN ENGINEERING LABORATORYConstantin Ciocanel, Northern Arizona UniversitySuzanne Pieper, Northern Arizona University Page 14.133.1© American Society for Engineering Education, 2009 A Three-Way Approach to Investigating Student Learning Styles in an Engineering LaboratoryAbstractThis paper presents the approach taken in the Experimental Methods in the Thermal SciencesLaboratory offered by the Mechanical Engineering Department from Northern ArizonaUniversity to investigate laboratory-specific student learning styles. To support this approach,the laboratory was

Conference Session

Trends in Mechanical Engineering II

Collection

2009 Annual Conference & Exposition

Authors

Ping Ren, Virginia Tech; Janis Terpenny, Virginia Tech; Dennis Hong; Richard Goff, Virginia Tech

Tagged Divisions

Mechanical Engineering

AC 2009-671: BRIDGING THEORY AND PRACTICE IN A SENIOR-LEVELROBOTICS COURSE FOR MECHANICAL AND ELECTRICAL ENGINEERSPing Ren, Virginia Tech Ping Ren is a PhD candidate working under the direction of Dr. Dennis Hong in RoMeLa (Robotics & Mechanisms Laboratory) of the Mechanical Engineering Department at Virginia Tech. He is passionate about advancing research in robotics and innovations related to robotics education.Dennis Hong, Virginia Tech Dennis Hong is an Assistant Professor and the Director of RoMeLa (Robotics & Mechanisms Laboratory) of the Mechanical Engineering Department at Virginia Tech. His research expertise lies in the area of mobile robot locomotion, humanoid robots

Conference Session

Outstanding Contributions to Mechanical Engineering Education

Collection

2009 Annual Conference & Exposition

Authors

Steven O'Halloran, University of Portland; Timothy Doughty, University of Portland

Tagged Divisions

Mechanical Engineering

AC 2009-51: INTEGRATION OF NUMERICAL ANALYSIS AND EXPERIMENTALTESTING INVOLVING HEAT TRANSFER FOR A SMALL HEATED CYLINDERDURING COOLINGSteven O'Halloran, University of PortlandTimothy Doughty, University of Portland Page 14.777.1© American Society for Engineering Education, 2009 Integration of Numerical Analysis and Experimental Testing Involving Heat Transfer for a Small Heated Cylinder During CoolingAbstractHeat transfer projects can be focused on either experimental measurements or numericalanalysis. Due to time constraints in a class it can be difficult to solve complicated problemsusing both methods. The project

Conference Session

Trends in Mechanical Engineering II

Collection

2009 Annual Conference & Exposition

Authors

Craig Somerton, Michigan State University

Tagged Divisions

Mechanical Engineering

Craig W. Somerton 7/29/05In the mass exchanger component of a dialysis machine we have two fluid streams blood(B) and dialysate (D) with a mass transfer between them of several different species. Theprimary species of this mass transfer is urea (U). An overall urea balance on the massexchanger is &U ?m m & B (m U, B,in / m U, B,out ) (1) & U ?m m & D (m U,D,out / m U,D,in ) (2)where & i : mass flow rate (kg/s) of fluid or species i m mi: mass fraction of species I (kg of species i/kg of mixture)For a counterflow mass exchanger the mass