by
Frank Bowman and Brian Tande
Department of Chemical Engineering
University of North Dakota, Grand Forks, ND
At Thanksgiving dinner, Uncle Bubba and Uncle Bill are arguing over whose house is more expensive to heat or cool: Bubba’s Georgia home in the summer or Bill’s North Dakota home in winter. Student teams play the role of Bubba and Bill’s niece or nephew, an engineering student who attempts to resolve their argument.
This interrupted case was developed for use in sophomore- and junior-level chemical engineering classes dealing with heat transfer applications and theory. It could also be adapted for use in introductory physics and engineering courses. It is designed to (1) teach students about conduction heat transfer and (2) guide students through the process of engineering model development.
Upon completing the case, students should be able to:
For this case, students work together in small groups. We like to divide the class up randomly, having them form groups based on common shirt color, birth month, number of letters in their middle name, etc. The case is organized in four sections, with one or more questions at the end of each section. Students are given one section at a time to read through and answer the questions with their group. After each section, there is a class-wide discussion before moving on to the next section. The case takes approximately 40 minutes to complete.
Students are divided into groups of three and given Part I. After reading Part I, the groups discuss the question about whose house uses more energy, Uncle Bubba’s or Uncle Bill’s. Group answers are recorded on the board in front of the classroom and their reasoning is briefly discussed. (~5 minutes)
Groups are then given three minutes to make a list of factors that could affect a house’s heating or cooling needs. The group with the longest list “wins” and has the privilege of going first in reporting to the class one factor from their list. Each group in turn then reports an item from their list until all factors have been mentioned. As students report their answers, the instructor makes a master list on the board of all responses. (~5 minutes)
The instructor then asks the class to help narrow down the list to the most important factors. In the ensuing discussion, the instructor guides the students to the four factors (wall thickness, wall surface area, inside-outside temperature difference, and thermal conductivity) that are important to conduction heat transfer and that will be examined in this case study. Other factors can be classified as either less important or beyond the scope of the current learning exercise. Many of the student ideas will likely deal with convective and radiative heat transfer, or how the house is used. These ideas should be recognized as significant and the instructor can use them as previews for future learning units. In doing this, the instructor can explain how a key element of engineering is defining a simplified model to represent a much more complex system. (5–10 minutes)
Sample discussion questions and prompts for Part I:
Students are given Part II to read and asked to answer the series of questions associated with it first individually and then together as a group. The instructor goes through each question, asking for student responses and then clarifying the correct answers as needed. Students should be able to recognize that Q will increase as A, ΔT, and k increase, but likely may not be able to choose between a linear (e.g., Q=mΔT) and a squared relationship (e.g., Q=mΔT2). The instructor should accept either choice as reasonable, and then explain that measurements of heat transfer show that the relationship is a linear one. This also provides an opportunity to explain that the mathematical model being developed should be based on measurements of the real world. (~5 minutes)
Students are given Part III, which asks them to combine their four equations into a single overall equation. During this time, the instructor moves among the groups, providing help as needed (and finding out where students may be confused). Once most groups have come up with the correct equation, the instructor writes it on the board and shows how it reduces to each of the four simple equations when different variables are held constant. (3–5 minutes)
Students are given Part IV. After reading it, they work in their groups to estimate reasonable values for area, temperature difference, and wall thickness. At this point, many students get frustrated because they want to know what the “right” answer is, and neither the case study nor the instructor provides them enough information to know precisely what values to use. Instead they have to make some assumptions about house dimensions and typical temperatures. Hopefully what happens (and it usually does) is that different groups make different assumptions and come up with very different answers for the rates of heat transfer. As groups complete their calculations, they send a representative to the board to write down their two Q values and their estimates of A, ΔT, and x for each house. Once all groups are done, the instructor reviews the results, asking group members to explain what assumptions they made. This allows students to see both the range of possible values, and their impact on the final answer. (~10 minutes)
To wrap up the case, the instructor asks several discussion questions to highlight what was learned, the limitations of the simple model, and point the way toward future topics. (~5 minutes)
Sample discussion questions and prompts for Part IV
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Acknowledgements: This case was published with support from the National Science Foundation under CCLI Award #0341279. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Date Posted: January 20, 2009.
Originally published at http://www.sciencecases.org/heat_transfer/notes.asp
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