Flowing Your Way Through Equations: Putting The Decisions In The Hands Of The Students

In the teaching of thermodynamics and heat transfer, there are two subject matters that baffle and bewilder students, obscuring the education process. In thermodynamics it is property evaluation and in heat transfer it is transient conduction. Property evaluation becomes a mass of tables and interpolation. Transient conduction is several different sets of differential equations and dimensionless numbers that look like a bunch of z’s and w’s all strung together. In an attempt to clarify this for the students a set of flowcharts and decision trees have been designed to guide the selection of the appropriate model for both property evaluation and transient conduction. This further fosters the solution methodology that is emphasized in both courses. It also emphasizes a pattern to problem solving that is essential for successful engineering. In the paper that follows, the methodological approach to both these befuddled topics is outlined. Introduction Some students look back on their courses and recall only the mundane; for instance the response to a question of a 5-year graduate concerning what they remember of thermodynamics, might be the interpolation and not the modeling decisions they were making with regards to the properties. The same may be said of transient heat conduction, the alum may only recall using dimensionless numbers with different characteristic length, but not why the problems were solved in that manner. The essentials of engineering education include the ability to make informed modeling decisions during problem solving. To this end, several flowcharts and decision trees have been designed to clarify these concepts to the students with regards to these to topics. Thermodynamic Property Evaluation Students need to begin to formulate decisions on modeling very early in their engineering curriculum. Thermodynamics, taken in either the sophomore or junior year, is probably the first course for many students where these decisions are expected to be made by the individual and probably one of the greatest reasons that students initially dislike the course. For instance, students must be able to decide when something can be modeled as an ideal gas. This is typically the only equation of state that they are familiar with when they enter the course and would prefer to apply it for all circumstances. To assist students in learning decision making, we have found the flowchart in Appendix 1 to be very helpful. The flowchart is used in conjunction with the information presented in Appendix 2, to complete the learning of property evaluation. The flowchart emphasizes the thought process students should be following as they approach thermodynamics P ge 915.1 2 problems and are making modeling choices. The flowchart aids in developing the decision making processes that must go into solving engineering problems. The use of the flowchart also assists students who are more inclined to be visual learners. Appendix 2 shows a summary of equations used in property evaluation, with reference to the textbook for the course. This handout clarifies the conditions for certain assumptions, for instance what equations to be used when allowing specific heat to vary with temperature for a substance modeled as an ideal gas. Heat Transfer Transient Conduction In heat transfer, students are faced with the application of not only mathematics as they have seen in previous courses, but ordinary and partial differential equations: an intimidating prospect for students. One of the most powerful tools in heat transfer analysis is non-dimensional numbers. Specifically, in transient conduction, the Biot number and the Fourier number are significantly used in analysis. A key feature in evaluating the Biot and Fourier numbers is using the appropriate characteristic length for the problem. It has been the authors’ experience that this decision is one with which students struggle. The characteristic length is typically dependent on the derivation and solution of the energy equation. Typically, this is derived and shown to the students; however, after an hour and half lecture with the magic of mathematics, students are often left wondering what they need to know and what they can take away and use for problem solving (i.e, doing the homework). The flow chart in Appendix 3 comes into play at this point. The solution methodology that is emphasized shows that when faced with a one-dimensional transient heat conduction problem, the simplest approach would be to use the lumped capacitance model. This also provides the easiest solution. If the Biot number fails the litmus test, then the flow chart indicates a move on to the next simplest solution, the one-term approximation. Finally, before trying to use the full series solution of the PDE, the possible use of the semi-infinite media solution is considered. The handout presented in Appendix 4, gives the same information as the flowchart, with a few more details and emphasis on boundary conditions. Student Feedback Two sets of students were surveyed with regards to the use of the flowchart for thermodynamics property evaluation: students at the University of Portland in ME 331, Introduction to Thermodynamics, a junior level course consisting of mechanical and electrical disciplines and graduate students at Michigan State University taking ME 802, Advanced Classical Thermodynamics. In the graduate course, the flowchart is used during the review of undergraduate thermodynamics in the beginning of the course. The survey form can be found in Appendix 5. Overall comments were very positive. From the undergraduate students written comments were minimal. Students either felt that approach was very logical and helpful or the visual method didn’t appeal to them and they preferred the handout in Appendix 2. This is attributed to the different learning P ge 915.2 3 styles of students as to which they prefer, thus reinforcing the authors approach to supply to different forms of the same handout. The numerical scores are found in Table 1. Table 1 Undergraduate student response ME 331 Q1 Q2 Q3 Q4 Average 2.83 4.03 3.27 3.57 One interesting result of the numerical data is that the average response to question 3 (Do you think the flow chart approach to the decision making associated with learning engineering problem solving is useful?) is higher then question 1 (Did you find the flow chart helpful in identifying the substance model to be used in the evaluation of thermodynamic properties for different substance?). And the response to question 2 is the highest (How useful did you find the handout on evaluating the properties for certain substance types in learning thermodynamics property evaluation?). The authors believe that the students find the flowchart model useful for understanding problem solving; however, when it comes to working out problems they are referencing the handout from Appendix 2 since it is a comprehensive summary of the appropriate equations to be utilized. The graduate students found the flowcharts to be very useful and in general rated the methodology very high. For the 20 respondents, the averages are shown in Table 2. The most positive results are in response to question 3 (How do you think undergraduate students would react to this flow chart...) and question 4 (Would you use the flow chart in teaching....). The averages are approximately 4.5 out of 5 for both questions. The written comments from the graduate students are mostly positive. In general, the approach is found to be very logical and educational. Negative comments focused on the approach being the equivalent to ‘spoon feeding’ and the perception that students would become too dependent on the handouts and not learn the material. Table 2 Graduate student response ME 802 Q1 Q2 Q3 Q4 Average 4.2 4.65 4.55 4.45 Student survey results are not available for the transient conduction flow chart at this time. Anecdotally, undergraduate students have found the flowchart approach to be very logical and helpful in clarifying the mathematics. Conclusions The flow chart methodology presented works well with the applicable topics, property evaluation and transient heat conduction. Student response to the approach has been positive. The authors feel that the flowcharts enhance the P ge 915.3 4 educational process and reinforce the thought processes and problem solving methodology emphasized in lecture. There may be even more opportunities in engineering to use the flow chart as a valuable tool in the teaching of decision making and problem solving. References Moran, Michael and Howard Shapiro, Fundamentals Of Engineering Thermodynamics, 5 Edition, Wiley 2004. Incropera, Frank and De Witt Introduction to Heat Transfer 4 Edition, Wiley 2002. CRAIG W. SOMERTON Craig W. Somerton is an Associate Professor of Mechanical Engineering and Associate Chair of Mechanical Engineering at Michigan State University. He teaches in the area of thermal engineering including thermodynamics, heat transfer, and thermal design. Dr. Somerton has research interests in computer design of thermal systems, transport phenomena in porous media, and application of continuous quality improvement principles to engineering education. He received his B.S. in 1976, his M.S. in 1979, and his Ph.D. in 1982, all in engineering from UCLA. LAURA J. GENIK Laura J. Genik is an Assistant Professor of Mechanical Engineering at the University of Portland. She teaches in the area of thermal engineering, including thermodynamics, heat transfer, and thermal system design. Dr. Genik has research interests in transport phenomena in porous media, inverse problems and parameter estimation in heat transfer processes, and computer design of thermal systems. She received her B.S. in 1991, her M.S. in 1994, and her Ph.D. in 1998, all in mechanical engineering from Michigan State University.