Lessons Learned: Implementing the Case

Teaching Method in a Mechanical

Engineering Course
AMAN YADAV, GREGORY M. SHAVER, AND PETER MECKL
Purdue University

BACKGROUND RESULTS
Case studies have been found to increase students’ critical thinking and Results suggested that the majority of participants felt the use of case studies
problem-solving skills, higher-order thinking skills, conceptual change, and was engaging and added a lot of realism to the class. There were no signifi-
their motivation to learn. Despite the popularity of the case study approach cant differences between traditional lecture and case teaching method on
within engineering, the empirical research on the effectiveness of case studies is students’ conceptual understanding. However, the use of case studies did no
limited and the research that does exist has primarily focused on student harm to students’ understanding while making the content more relevant to
perceptions of their learning rather than actual learning outcomes. students.

PURPOSE (HYPOTHESIS) CONCLUSIONS

This paper describes an investigation of the impact of case-based instruction Case-based instruction can be beneficial for students in terms of actively
on undergraduate mechanical engineering students’ conceptual understanding engaging them and allowing them to see the application and/or relevance of
and their attitudes towards the use of case studies. engineering to the real world.

DESIGN/METHOD
Seventy-three students from two sections of the same mechanical engineering
course participated in this study. The two sections were both taught using tradi-
tional lecture and case teaching methods. Participants completed pre-tests, post- KEYWORDS
tests, and a survey to assess their conceptual understanding and engagement. case-based instruction, conceptual understanding, mechanical engineering

I. INTRODUCTION and minorities, leading to increased under-representation of these

populations in engineering disciplines (Seymour and Hewitt, 1997).
A majority of engineering classes involve the “teaching by The issues of student retention, preparing students for the nature
telling” approach (i.e., lecture-based approach), which is still the of engineering, and lack of student motivation raises many ques-
most dominant teaching method for engineering classes tions for engineering educators. How do engineering educators
(Elshorbagy and Schönwetter, 2002). However, this traditional allow students to “comprehend the nature of workplace problem
lecture method leaves engineering graduates ill-prepared for the solving” to prepare them for the real world of practice (Jonnasen,
engineering profession (Lattuca, et al., 2006). The traditional lecture Strobel, and Lee, 2006)? How do engineering educators engage
approach falls short because it is not an effective motivator for undergraduate engineering students? Hence, engineering educators
students as they are passive recipients of information rather than face the challenges of not only preparing students for the workplace,
being actively involved in the learning process (Prince and Felder, but also engaging students in order to decrease attrition rates, espe-
2006). Furthermore, the types of problems students often solve in cially among women and minorities. The use of case studies is one
classrooms using this traditional approach do not necessarily prepare pedagogical technique that may offer a solution through its focus
them for the real-world problems they will encounter as engineers. on student-centered learning and engagement in authentic problem
Real-world problems are complex, ill-structured, without a clear solving.
solution, have conflicting goals, and can be presented in a number
of ways (Jonnasen, Strobel, and Lee, 2006).
Use of the traditional lecture method also has led to low levels of II. CASE TEACHING METHOD
student attendance and retention in the engineering disciplines
(Seymour and Hewitt, 1997). Seymour and Hewitt found that A. Case-based Instruction
students reported poor teaching method as one of the main reasons Case-based instruction has been used within other professional
for leaving or switching out of science, mathematics, and engineer- fields, such as in medicine and business, to educate students to work
ing majors. There is a 40 percent attrition rate in the engineering dis- in complex and ill-structured domains and prepare students for the
ciplines between freshmen and senior years (Seymour and Hewitt, real world of practice (Davis, 1999; Williams, 1992). Case-based
1997). The student loss is proportionally even greater among women instruction is designed to help students acquire knowledge “deeply

January 2010 Journal of Engineering Education 55

rooted” in the discipline and allow them to take part in self-directed undergraduates respond particularly well to case-based instruction
learning. Cases could be problem-based, historical in nature, pre- and positive effects of small-group learning associated with case
sent exemplary scenario, dilemma-based, and/or illustrate critical study teaching are significantly greater for under-represented popu-
issues in the field (Yadav and Barry, 2009). Cases allow students to lations such as African Americans and Latinos (Springer, Stanne,
apply their theoretical knowledge to practical situations in a sup- and Donovan, 1999).
portive environment without concerns regarding the impact of their
actions. Christopher Columbus Langdell, who has been credited B. Case-based Instruction in Engineering
with the creation of the “case method” approach, advocated the use Case studies in engineering education began in the 1960’s to
of case studies to help students develop diagnostic skills in a field 1970’s with several projects created to help develop cases for engi-
that is continuously changing, complex, and ill-structured (Garvin, neering faculty (Raju and Sankar, 1999; Richards et al., 1995).
2003; Williams, 1992). Langdell believed that the best way to study Cases in engineering present students with real or hypothetical
law is by examining appellate court decisions as cases and advocated situations that are “an account of an engineering activity, event or
that such use of cases would prepare students for the real world of problem containing some of the background and complexities en-
practice (Garvin, 2003). Similarly, engineering problems do not countered by an engineer” (Fuchs, 1970). Fuchs made an argument
have a clear-cut solution and require engineers to make complex for using cases in engineering because they bring “outside reality
decisions. Thus, cases have the potential to be an effective medium inside the classroom,” which is an important aspect of engineering
for illuminating the complex nature of engineering because they education (Fuchs, 1970). He stated that bringing outside reality
provide students with realistic contextual information to solve into the classroom sensitizes students to kinds of experiences they
workplace problems. find after leaving school, which in turn motivates them to learn the
Previous research on case-based instruction has suggested that concepts they need to master in their engineering disciplines. In
case studies make the content easier to remember, make the class addition to introducing the real world, cases illustrate what engi-
more enjoyable for students, and increase student attendance neers do, help teach basic concepts and problem-solving skills, and
(Hoag, Lillie, and Hoppe, 2005; Lundeberg, 1999). In one study, provide engineering experience to students (Henderson, Bellman,
Hoag investigated the effect of cases in a Clinical Immunology and and Furman, 1983). Richards and colleagues also proposed the use
Serology course on students’ critical thinking, class attendance, and of cases in engineering education because cases can make the cur-
course satisfaction (Hoag, Lillie, and Hoppe, 2005). Two semesters riculum relevant for students, motivate them, make learning active,
of the same course were examined; one semester taught without push students to integrate the concepts they have learned from
cases (N  56) and the next semester taught with case-based other courses, and build upon students’ prior experiences (Richards
instruction (N  67). The case-based instruction included nine et al., 1995).
cases interspersed throughout the semester with each case taking Previous research has suggested that case studies make learning
one 50-minute class period in which students worked in groups of more interesting and motivating for students while allowing them
five or six. The authors collected items of student performance on to relate to real world situations. Vesper and Adams evaluated the
five critical thinking multiple-choice exam questions and student case method in two engineering courses, one a senior machine
attendance on case study days and traditional lecture days. The design course at the University of Santa Clara and another a freshmen
authors found that the student performance on critical thinking was engineering drawing course at Stanford University (Vesper and
similar in the two semesters; however, student attendance was Adams, 1969). They asked the students to complete a questionnaire
significantly higher on the days cases were used (95.6 percent) as at the end of each course, which asked them to rate the educational
compared to when lecture was used (80.3 percent). However, 13 per- value of the various teaching methods used in each course: case
cent of the course grade was from case studies and attendance was method, traditional lecture, and laboratory sessions. The question-
mandatory to earn those points, which confounded the statistical naire also included open-ended items for students to express their
difference in attendance for case days. The end of the course evalua- opinions about each teaching method. Results suggested that the
tions suggested that students reported higher instructor involve- case method received the highest rating and students reported that
ment, student-instructor interaction, and course organization when case studies presented a realistic view of engineering. In addition,
cases were used. the authors developed a teaching objectives checklist in an attempt
Cases have also been found to increase students’ critical think- to capture the most likely objectives of the case method and three
ing and problem-solving skills (Dochy et al., 2003; Yadav and groups of participants completed the checklist: 30 professors, who
Beckerman, 2009), higher-order thinking skills (Bergland et al., participated in a case method summer institute; four professors,
2006; Dori, Tal, and Tsaushu, 2003), conceptual change (Gallucci, who taught first-year graduate course Case Studies in Mechanical
2007), and their motivation to learn (Yadav et al., 2007). For Engineering at University of California, Berkeley; and 18 students,
example, 200 non-science major students participated in a study to who took the Berkeley course. The authors found that both stu-
investigate the effects of using cases to teach biotechnology concepts dents and professors agreed that cases “convey knowledge of what
(Dori, Tal, and Tsaushu, 2003). Using a pre-post test experimental engineers do and how they work,” “develop skills in spotting key
design, the researchers measured students’ knowledge, understand- facts amid less relevant data,” and “identify and define practical
ing of concepts, application of knowledge to new contexts, and problems.”
higher-order thinking skills (i.e., question posing, argumentation Raju and Sankar also evaluated the effectiveness of a case study
skills, and system thinking). The authors found a significant in a senior level mechanical engineering project design course (Raju
improvement in students’ knowledge and higher-order thinking and Sankar, 1999). The authors found that students rated the cases
skills for students at all academic levels and the gap between students used as effective on the four dimensions (i.e., usefulness, attractive-
at the low and high academic level narrowed. In addition, female ness, challenging, and clear) being measured. Specifically, students

56 Journal of Engineering Education January 2010

found case studies to be very useful and challenging as they brought hypotheses about what might have caused the problems described
real world problems to the classroom (Raju and Sankar, 1999). In in the case studies. The case study discussion also allowed students
another study, Garg and Varma examined students’ perceptions of to consider any alternative explanations for the failures, solutions to
learning from case studies in a software engineering course when prevent it from happening again, and consider key elements of the
compared to traditional lecture approach (Garg and Varma, 2007). mathematical models. The case studies were implemented across
The authors found the case study approach was rated higher than two class periods of 50 minutes each, worked on individually by
the traditional lecture approach. Students reported that case studies students, and were not graded. These case studies presented real-
were better at helping them to improve their communication skills, life problems to allow students to develop analytical and critical
ability to think critically, and apply the concepts and skills learned in thinking skills. Specifically, these were “issue cases,” where the main
the course. focus of the case was on “what is going on here?” allowing students
Despite the popularity of case study approach within engineer- to develop hypothesis and consider alternative explanations
ing, the practice of using cases has not become widespread and most (Herreid, 1994).
educators have limited knowledge of how to implement cases into These case studies were used to challenge students thinking and
their classrooms (Raju and Sankar, 1999). Further, the empirical allow them to understand and apply course concepts to real-life
research on the effectiveness of case studies is limited and the re- scenarios. Both case studies involved developing hypotheses and
search that does exist has primarily focused on student perceptions mitigation strategies for component failure in complex systems that
of their learning rather than actual learning outcomes (Prince led to catastrophic failure. The case studies were designed to scaf-
and Felder, 2006). The increased interest in student-centered and fold students’ understanding of complex dynamic models; hence,
problem-based teaching creates a need for the field to better under- allowing them to generalize their learning to other situations.
stand case-based instruction and its benefits for engineering students During the case study work, students hypothesized about what
(Das, 2006). Specifically, the field needs to examine whether the caused the failure in the dam or the reactor core and develop a
use of case studies results in increased student learning and engage- dynamic model to explain the failure and strategies to prevent it
ment. In this study, the researchers examined the influence of case from happening again. The development of the model itself was an
studies on students’ conceptual understanding and their attitudes iterative process as the students went through multiple models
towards the use of case studies. Specifically, the research sought to taking into account various elements presented in the case studies.
answer the following research questions: (1) what is the influence of Due to the time constraint of covering a topic in two 50-minute
case-based instruction on students’ conceptual understanding com- lectures, the cases only focused on the topic at hand and were kept
pared to traditional lecture teaching method?, and (2) what are the short. We provide an overview of the case studies and have included
attitudes of students towards the use of case studies? them in Appendix A.

Hydraulics Case Study. The hydraulics modeling was

III. METHODOLOGY presented via a case study of human fatalities resulting from
two catastrophic failures of hydro-electric dam penstocks
A. Participants due to a dynamic phenomenon call “water hammer.”
Seventy-three participants from two sections of the same systems Penstocks are large pipes that carry water from a large
modeling mechanical engineering course participated in this study. reservoir to a turbine, which spins in response to the water
The course provides an introduction to modeling electrical, mechan- flow. The turbine rotates an electric generator, thereby
ical, fluid, and thermal systems containing elements, including turning the water energy into electrical energy. When the
sensors and actuators used in feedback control systems. Participants flow through the turbines is abruptly slowed via a restriction
included eight females and sixty-five males. Thirty-one participants (i.e., penstock valve/gate closing), a dynamic phenomenon
were from Instructor A’s section and 42 participants were from called “water hammer” occurs in response to the moving
Instructor B’s section. All participants were enrolled in the Mechan- water inertia. While the water flow near the restriction is
ical Engineering program at a large mid-western university and were slowed, the water mass upstream continues to move under
required to take the course. the influence of its inertia. This causes increases in water
pressure inside the penstock and may lead to penstock
B. Materials failure. The case study discussed how mathematical models
1) Case studies: The authors developed two case studies based on can predict this phenomenon and provided insight as to
actual events that related to two course topics (i.e., hydraulics and how it can be avoided.
thermal systems). The case studies were written by the last two
authors and examined to make sure they met the basic rules for Thermal Systems Case Study. The case study covering thermal
what makes a good case (Herreid, 1997). According to Herreid, a systems focused on the Three Mile Island nuclear power
good case: has pedagogical value, tells a short story, contains rele- plant disaster. After a brief overview of the plant and its
vant details about the events, and is applicable to the students’ field history, a timeline of the events on the day of the partial
of study to arouse their interest. The students were given a handout reactor meltdown was covered. The case study was
of the case study prior to its introduction in class along with the case accompanied by technical details to allow students to
discussion questions. In the following class, the instructor reviewed conduct thermal calculations to help explain the events of
the case study, describing the problems presented and discussing Three Mile Island. Specifically, students were asked to do
the case study questions. Specifically, the instructors led a class dis- an energy balance to assess how much reactor energy had to
cussion after the in-class individual case study work to brainstorm be dissipated once the steam turbines were shut down. After

January 2010 Journal of Engineering Education 57

 that, focus shifted to a closer look at the individual reactor than faculty) perspective on the influence of case studies on their
fuel rods, and once again, students were asked to use course learning, engagement, and motivation. The survey had previously
principles to determine surface and core temperatures in the been implemented with education undergraduate students to assess
fuel rods during the meltdown. Students also conducted a their perceptions of cases (Yadav, 2006). The survey was used to
transient analysis to estimate the rise in fuel rod temperature assess student attitudes towards the use of case studies in the
as a function of time, to gain a sense of how quickly the mechanical engineering classes. Participants were asked about
reactor core heated and melted. their perceptions of the influence of case studies on their learning
(e.g., “The case study was helpful in helping me synthesize ideas
2) Knowledge test: A pre-post test format was used to assess and information presented in the course”), critical thinking (e.g.,
students’ conceptual understanding of the two topics used in this “The case study allowed me to view an issue from multiple per-
study: thermal systems and fluid systems. We wanted to assess stu- spectives”), and engagement (e.g., “I was more engaged in class
dents’ conceptual understanding by measuring their ability to apply when using the case study”). See Table 4 for all survey items (Note:
their learning to solve a complex problem. Instead of using objective the items were randomized in the actual survey given to the stu-
tests, which assess students’ ability to remember facts and figures, dents). Internal reliability of the survey and each subscale was de-
open-ended problems were developed to illuminate the impact of termined by using Cronbach’s Alpha: overall (  0.91), learning
cases on students’ conceptual understanding. The tests were de- (  0.83), critical thinking (  0.65), and engagement ( 
signed to check for conceptual understanding as they consisted of 0.78); see Devillis (2003) for a detailed discussion on internal
problems that required a comprehensive understanding of the un- consistency reliability.
derlying concepts to set up the necessary equations and to properly
combine them for the final answer. The pre-tests consisted of one C. Procedure
problem statement to assess students’ prior knowledge of the corre- The present study was counter-balanced for the content (i.e.,
sponding topic (thermal systems or fluid systems). This test allowed thermal systems vs. fluid systems) and instructional method (tradi-
the researchers to consider students’ prior knowledge when assess- tional vs. case method) to account for any bias towards a particular
ing the impact of the teaching method (case-based instruction vs. content. The basic design of this study is depicted in Table 1.
traditional lecture) and allowed them to make better conclusions Instructor A used the case method for the thermal systems topic
about the impact of the teaching method. The post-test consisted and the traditional method for the fluid systems topic. In contrast,
of a similar but more complex problem as compared to the pre-test Instructor B switched the teaching method for the two topics, with
question. The rationale for increasing the difficulty of the post-test the traditional method being used for the thermal topic and the case
was to allow enhanced assessment of student learning in thermal method being used for fluid systems topic. The instructors taught
and fluid systems modeling. The students could not simply plug in each concept at the same time in their respective classes. The in-
numbers into an equation to produce the solution. An additional structors were familiarized with the case method by regular meetings
question was posed in the post-test, requiring the students to inter- with the first author to discuss implementation of case studies and
pret their previous answer and make an assessment of the broader also evaluated the case studies together. The two instructors were
implications of their analysis. Reliability of the tests was determined also provided resources from the National Center for Case Study
by using the split-half reliability method to reflect that the tests Teaching in Science on how to write cases, teach with cases, and
were measuring the constructs. The correlation coefficient was assess the case method. The two instructors also met weekly to
0.88, which indicates good reliability for the tests. Specifically, the discuss teaching strategies to ensure that the same topics were cov-
tests took the following form: ered similarly and used the same assignments and quizzes. Data
a. Thermal system test: were collected using the pre-/post-tests and the surveys. Partici-
i. Pre-test problem: mathematical modeling of a heat- pants completed each of the two knowledge pre-tests before the
generating computer chip topic was introduced in the class and then completed the post-test
ii. Post-test problem: mathematical modeling of a heat- after the topic was covered in class (either via traditional lecture or
generating computer chip with heat sink via the case method). Finally, at the end of the study, participants
b. Fluid system test: completed the attitude survey.
i. Pre-test problem: mathematical modeling of a reservoir-
driven flow through a valve restriction (fluid inertia effect D. Data Analysis
neglected) The second and third authors coded the knowledge pre-tests
ii. Post-test problem: mathematical modeling of reservoir- and post-tests on a scale of 0–3 to assess students’ conceptual un-
driven flow through a valve restriction and pump (fluid derstanding of thermal and fluid mechanics. The scale is based on
inertia effect included)
The tests are provided in Appendix B. Independent sample
t-tests conducted on the pre-test scores between the two classes
exhibited that there were no statistical differences on knowl-
edge about hydraulics topic (p  0.31) and thermal topic (p 
0.42).
3) Survey: Participants also completed a 22 Likert-item survey
that was adapted from a national survey on faculty perceptions of
benefits and challenges of case-based instruction (Yadav et al., Table 1. Research design.
2007). The survey items were changed to reflect students’ (rather

58 Journal of Engineering Education January 2010

the work of Emert and Parish who used it to obtain measures of traditional lecture was used (marginal mean  2.12) were identical
conceptual attainment in undergraduate core mathematics courses to when case studies were used as the method of instruction
(Emert and Parish, 1996). Specifically, a score of zero was given if (marginal mean  2.11). There was also no significant difference
the student was unable to solve the problem and exhibited no un- between the two topics, F(1, 70)  0.771, p  0.38, p2  0.01, r 
derstanding of the problem; one was assigned if the student showed 0.11, 1-  0.15. Participants scored an average of 2.17 for the
some grasp of the topic, but was unable to solve the problem (i.e., thermal topic, while scoring an average of 2.06 on hydraulics test.
average understanding); two was assigned if the student exhibited However, the results did reveal a statistically significant difference
good grasp of the topic, but was unable to solve the problem in a between the two classes, F(1, 70)  37.26, p  0.00, p2  0.35,
clear and succinct manner (i.e., good understanding); and a score r  0.18, 1-  0.32. Participants in Class B (marginal mean 
of three was assigned if the student accurately solved the problem in 2.41) outperformed participants in Class A (marginal mean  1.71)
a clear and succinct manner with no false starts (i.e., excellent un- (See Table 2 for a detailed descriptive statistics and Table 3 for
derstanding). A rubric was used to facilitate this coding, which ANCOVA statistics).
included representative responses from participants on each of the
four points of the scale. B. Survey
In order to establish inter-rater reliability, the two raters Results from the survey indicated that overall students had
were first trained together on the rubric by scoring a sample of positive attitudes towards the use of case studies in the mechanical
the knowledge tests from each topic. When the researchers were engineering course (see Table 4).
satisfied that both raters agreed on the rubric and how to score A vast majority of the students felt that the use of case-based
the tests, they each independently coded the same 10 percent of instruction added realism to the class (79.1 percent), was thought
the knowledge tests from each topic, which were selected ran- provoking (68.6 percent), and relevant to learning about the course
domly. This led to an inter-rater reliability of 90 percent, which concepts (64.0 percent). A majority of the students reported that
was deemed sufficient for the raters to code the remaining tests the case studies allowed for more discussion of the course ideas
independently. One rater coded the remaining thermal knowl- (60.4 percent), enabled them to view an issue from multiple per-
edge tests, while the second rater coded the fluid mechanics spectives (59.3 percent), and was applicable to their field of study
tests. (53.4 percent). Students also felt that the use of case based instruc-
The conceptual scores from the knowledge post-test were tion was beneficial for them in learning the course material. Specifi-
analyzed using a univariate analysis of covariance (ANCOVA) cally, students reported that case studies allowed them to analyze
blocking design with four factors: Condition (Traditional Lecture the basic elements of the course concepts (55.8 percent), form a
vs. Case Studies)  Topic (Thermal Systems vs. Fluid Systems)  deeper understanding (52.3 percent), synthesize ideas and informa-
Classroom (Class A vs. Class B)  Participants (the blocks in the tion presented in the course (52.3 percent), and retain more from
design). Participants’ pre-test scores were used as a covariate in the the class (47.7 percent). In addition, students reported that cases
analysis. Finally, the survey was analyzed using frequency distribu-
tion and Chi Square Tests of Association to analyze whether more
students agreed that case studies helped to increase their learning,
critical thinking, and engagement.

IV. RESULTS

A. Knowledge
The ANCOVA results revealed that condition did not have a
significant influence on the conceptual understanding of partici-
pants, F(1, 70)  0.01, p  0.92, p2  0.00, r  0.02, 1-  0.05.
The post-hoc power analysis to calculate power (1-) was conduct-
ed using G*Power 3; see (Faul et al., 2007; Grissom and Kim,
2005) for a detailed discussion on effect size (r) and power (1-). Table 2. Comparing students across conditions.
The descriptive statistics suggested that participant scores when

Table 3. Results of ANCOVA.

January 2010 Journal of Engineering Education 59

 Table 4. Student attitudes towards the use of case studies.

60 Journal of Engineering Education January 2010

 Table 4. Continued...

brought together material learned in several other mechanical engi- conceptual understanding of the course concepts being taught via
neering courses (45.4 percent) and enabled them to apply the course the case method as compared to traditional lecture. However, the
concepts to new situations (44.2 percent). Students also felt that case studies also did not harm students’ understanding and made
case studies made the class more engaging with about half of the the content relevant to the students. Considering previous re-
students (51.2 percent) reporting that they were more engaged in search has found that students report lack of relevance, implica-
class when cases were used, and only 18.6 percent disagreeing with tions, and applicability to the real world as one of the main reasons
that statement. The percentages reported here are aggregate of for switching out of engineering, this is an important finding for
agree and strongly agree. retention of undergraduate engineering students (Seymour and
Survey results also indicated that students had mixed feelings Hewitt, 1997).
towards how the case studies were implemented in the course. For A possible hypothesis for the lack of significant difference in
example, 37.2 percent of the students reported that the use of case achievement between case study and lecture approach could be a
study was more entertaining than educational, and 32.5 percent a result of how case studies were implemented in the course;
disagreed with that. About one-third of the students reported that specifically, the way case studies were implemented emphasized
the case study took more time than it was worth (32.6 percent), “theoretical representation of the real-world problem” (Raju and
while another one-third felt that case study was worth the time Sankar, 1999). Previous research in psychology has suggested
(34.7 percent). It is also interesting to note that 50.0 percent of the that higher interest levels do not necessarily lead to better student
students believed that the use of cases allowed for less content to be performance (McDaniel et al., 2000). Gallucci further argued
covered in the class. Finally, frequency of the individual survey that even though case studies provide a positive and engaging
items was aggregated to give each of the three subscales (i.e., learn- experience for students, if not implemented carefully, they might
ing, critical thinking, and engagement) a total frequency count and not promote conceptual understanding of the topic (Gallucci,
chi-square analysis was conducted on the resulting contingency 2006). She stated, “students may enjoy the case study, especially
table. The Chi Square Test of Association suggested that signifi- if it is a change from classroom routine, but we need to ask: what
cantly more students agreed that case studies increased their learn- concept understanding have they gained or developed” (Gallucci,
ing, critical thinking, and engagement, 2 (2)  10.124, p  0.038. 2006). This is highlighted by results from this study, which sug-
gest that even though students had positive feelings towards the
use of case teaching method, the implementation of case studies
V. CONCLUSION in this study did not lead to an increase in students’ conceptual
understanding.
A. Implications Previous research in motivation has suggested that “unless
Results suggest that students had an overall positive attitude teachers act in ways that promote cognitive engagement, students’
towards the use of case studies. For example, students felt that the motivation to learn will not necessarily translate into thoughtful-
case studies added significant realism to the class, were relevant to ness or greater understanding of the subject matter” (Blumenfeld,
the course concepts, and they were more engaged when case studies Mergendoller, and Puro, 1992). Blumenfield, Puro, and
were used. These findings from the survey provide support that case- Mergendoller (1992) argued that teachers need to both “bring
based instruction can be beneficial for students in terms of actively the lesson to students” and “bring students to the lesson” in order
engaging them and allowing them to see the application and/or rele- to translate motivation into thoughtfulness. The implementation
vance of engineering to the real world. Therefore, this method has of cases in this study “brought the lesson to students” by enhanc-
the potential to “address many of the problems commonly associated ing their interest and increasing their perceived value of the con-
with teaching undergraduate science and engineering” (Yadav et al., tent being covered. However, the implementation of cases failed
2007) by making the problems more relevant to students and help- to “bring students to the lesson,” which requires teaching prac-
ing them to “vicariously experience situations in the classroom that tices that cognitively engage students on the main point of the
they may face in the future and thus help bridge the gap between lesson and allow them to apply the concepts to new situations. In
theory and practice” (Raju and Sankar, 1999). our study, the cases illustrated abstract course ideas through
However, the results from this study suggest that the use of interesting stories, but did not become the focal point around
case studies did not have any significant impact on students’ which the course concepts were structured. Additionally,

January 2010 Journal of Engineering Education 61

students did not have the opportunity to apply the concepts maximized. For example, whether case studies need to be long
learned, via separate activities and assignments, between their vs. short, real vs. hypothetical, success vs. failure, or present sin-
learning from case studies and the post-test. Hence, the manner gle vs. multiple issues should be guided by the pedagogical goals
in which cases were implemented could be hypothesized for the of the instructor and what he/she wants students to grasp from
result that students did not differ on their conceptual under- the activity.
standing between the lecture and the case method. Third, it is important to use measurement tools that assess
Another possible conjecture for the finding that case studies student outcomes and provide an effective means to gauge true dif-
did not lead to a significant improvement in conceptual under- ferences between control and experimental conditions. Yadav and
standing could be because of initial student resistance with respect Barry stated, “Measuring student learning to assess the impact of an
to the amount of material covered in the class. Since students were intervention (e.g. case studies) is important because of the effect the
not familiar with case studies, this pedagogical technique might type of assessment used can have on outcome measures” (Yadav and
have faced some student resistance. Recall that only 22 percent of Barry, 2009). Hence, researchers need to carefully develop instru-
the students felt that more content was covered by using case stud- ments that assess students’ critical thinking and conceptual under-
ies, while half of the students felt that lecture covered more con- standing. Lundeberg and Yadav argued for using Mazur’s paired
tent. Consequently, students might have felt that the use of case problem testing by giving students open-ended problems and having
studies took time away from their learning, and when completing them explain their solutions qualitatively (Lundeberg and Yadav,
the knowledge test they might have felt unprepared as “the materi- 2006).
al was not covered in the class.” This is congruent with previous
research, which has suggested that faculty report initial student B. Limitations and Future Research
resistance to case studies because this method does not present a This study had a few limitations. The first limitation of this
clear solution, requires students to critically examine the situation, study was that it focused on the impact of case studies on only two
and asks them to make decisions in a complex environment (Yadav topics in a within-subjects quasi-experimental design, and within
et al., 2007). each class students experienced the case method only once. Since
Results suggested that students from Class B scored significantly this was likely the first time students encountered the case method,
higher than students from Class A. Recall that this study utilized a two topics might have not been sufficient to successfully implement
quasi-experimental research design with two instructors teaching case studies and see the benefits of this approach on students’
the two classes and students were not randomly assigned to the two conceptual understanding. In addition, this research study used two
classes. There could also have been differing teaching styles pre-/post-tests that required students to have a comprehensive
between the two instructors, which might also help explain the understanding of the underlying concepts to solve the problem;
differences between the two classes. however, the measurement tools might not have fully captured
These findings have important implications for how case studies students’ conceptual understanding. Future research needs to exam-
should be implemented within engineering courses. First, the results ine the impact of case studies by making it a dominant classroom
from this study suggest it may be important for engineering educa- experience for students using carefully constructed measures that
tors to gradually introduce case studies in order to allow students assess a broader range of student outcomes. This would allow
time to adjust to this method of instruction as well as help students researchers to more rigorously examine what concepts students have
understand the purpose of this teaching approach. Students in these gained from cases after the initial novelty or resistance from students
classes may have viewed case studies as real world stories that pro- has dissipated.
vided a “break from the routine” rather than viewing them as Another limitation of this study was that the two classes were
authentic problems that raise relevant issues the instructor wanted not statistically equivalent as there was no random assignment and
them to examine. Students, in general, view learning as only being it involved two instructors, which could have resulted in the class-
achieved through “direct instruction” due to their prior experiences room differences observed on student outcomes. In order to remove
as K-12 students and active learning processes, such as the use of such classroom effects, subsequent research needs to be conducted
case studies, challenge students’ epistemological beliefs (Yadav and with one instructor teaching two classes where students are ran-
Koehler, 2007). Students in this study reported that cases allowed domly assigned. If a comparable classroom is not available, an
for less content to be covered in the class; hence, it seems important A-B-A-B research design could be used to assess the impact of cases
that instructors highlight the relevance of case studies to course in a single classroom (Yadav and Barry, 2009). Note, this study
goals and students’ learning. This would allow students to see case- included two different instructors teaching the two sections of the
based instruction being applicable to their learning in the course same course, but we did not specifically explore any instructor
and alleviate any potential student resistance, while allowing them differences. Further research could explore instructor differences by
to develop problem-solving skills required in their future engineer- asking whether certain teaching styles are more likely to be success-
ing careers. ful at using case studies. Future research needs to also examine the
Second, the type of case studies used and how they are imple- actual implementation of cases by observing classes when cases are
mented plays an important role in the success of this approach in implemented as well as interviewing faculty who use cases for the
increasing students’ conceptual understanding. In this study, first time and faculty who have used cases previously. This research
case studies were used only once and tertiary to the course mate- did not examine how student perceptions of their learning and
rial rather than as an integral part of the course, which may not engagement matched with their actual learning outcomes. Future
have been sufficient to truly highlight the benefits of case-based research should examine whether students’ perceptions of learning
instruction. Hence, case studies need to be carefully selected and match with their actual learning outcomes. Additionally, researchers
implemented in engineering courses so that their benefits are should investigate the long-term impact of learning from case

62 Journal of Engineering Education January 2010

studies, such as retention of concepts and ability to apply concepts Herreid, C.F. 1997. What makes a good case? Some basic rules of good
in the workplace. Having students apply the concepts (learned via storytelling help teachers generate student excitement in the classroom.
case studies and/or lecture) in a 6–10 week follow-up assessment Journal of College Science Teaching 27 (3): 163–65.
would allow researchers to examine retention. However, the ability Hoag, K., J. Lillie, and R. Hoppe. 2005. Piloting case-based in-
to apply concepts in the workplace would involve a complicated struction in a didactic clinical immunology course. Clinical Laboratory
research design and include qualitative observation in the field, Science 18 (4): 213–20.
interviews with supervisors as well as quantitative performance data Jonnasen, D., J. Strobel, and C.B. Lee. 2006. Everyday problem solving
of students’ applying the concepts. in engineering: Lessons for engineering educators. Journal of Engineering
Education 95 (2): 1–14.
Lattuca, L.R., P.T. Terenzini, J.F. Volkwein, and G.D. Peterson.
REFERENCES 2006. The changing face of engineering education. The Bridge 36 (2):
6–44.
Bergland, M., M.A. Lundeberg, K. Klyczek, J. Sweet, J. Emmons, C. Lundeberg, M.A. 1999. Discovering teaching and learning through
Martin, J. Werner, and M. Jarvis-Uetz. 2006. Exploring biotechnology cases. In Who learns what from cases and how: The research base for teaching and
using case based multimedia. The American Biology Teacher 68 (2): 81–86. learning with cases, eds. M.A. Lundeberg, B.B. Levin, and H. Harrington,
Blumenfeld, P.C., J.R. Mergendoller, and P. Puro. 1992. Translating 3–23. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
motivation into thoughtfulness. In Redefining student learning, eds. H.H. Lundeberg, M.A., and A. Yadav. 2006. Assessment of case study
Marshall, 207–39. Norwood, NJ: Ablex. teaching: Where do we go from here? Part 2. Journal of College Science
Das, S. 2006. Implementing a multi-media case study in traditional Teaching 35 (6): 8–13.
laboratory class. In Proceedings of American Society for Engineering Education. McDaniel, M.A., P.J. Waddill, K. Finstad, and T. Bourg. 2000. The
Chicago, IL effects of text-based interest on attention and recall. Journal of Educational
Davis, M. 1999. Case method. In Ethics and the university, eds. M. Psychology 92 (3): 492–502.
Davis, 143–74. New York: Routledge. Prince, M.J., and R.M. Felder. 2006. Inductive teaching and learning
DeVellis, R.F. 2003. Scale development: Theory and applications. methods: Definitions, comparisons, and research bases. Journal of Engi-
Thousand Oaks, CA: Sage. neering Education 95 (2): 123–38.
Dochy, F., M. Segers, P. VandenBossche, and D. Gijbels. 2003. Ef- Raju, P.K., and C.S. Sankar. 1999. Teaching real-world issues through
fects of problem-based learning: A meta-analysis. Learning & Instruction case studies. Journal of Engineering Education 88 (4): 501–08.
13 (5): 533–68. Richards, L.G., M. Gorman, W.T. Scherer, and R.D. Landel. 1995.
Dori, Y., R. Tal, and M. Tsaushu. 2003. Teaching biotechnology Promoting active learning with cases and instructional modules. Journal of
through case studies-can we improve higher order thinking skills of non- Engineering Education 84 (4): 375–81.
science majors. Science Education 87 (6): 767–93. Seymour, E., and N.M. Hewitt. 1997. Talking about leaving: Why un-
Elshorbagy, A., and D.J. Schönwetter. 2002. Engineer morphing: dergraduates leave the sciences. Boulder, CO: Westview Press.
Bridging the gap between classroom teaching and the engineering profes- Springer, L., M.E. Stanne, and S.S. Donovan. 1999. Effects of small-
sion. International Journal of Engineering Education 18 (3): 295–300. group learning on undergraduates in science, mathematics, engineering,
Emert, J.W., and C.R. Parish. 1996. Assessing concept attainment in and technology: A meta-analysis. Review of Educational Research 69 (1):
undergraduate core course in mathematics. In Assessment in practice: Putting 21–51.
principles to work on college campuses, eds. T.W. Banta, J.P. Lund, K.E. Vesper, K.H., and J.L. Adams. 1969. Evaluating learning from the case
Black, and F.W. Oblander. San Francisco, CA: Jossey-Bass. method. Engineering Education 60 (2): 104–06.
Faul, F., E. Erdfelder, A.-G. Lang, and A. Buchner. 2007. G*power 3: Williams, S.M. 1992. Putting case-based instruction into context:
A flexible statistical power analysis program for the social, behavioral, and Examples from legal and medical education. The Journal of Learning
biomedical sciences. Behavior Research Methods 39: 175–91. Sciences 2 (4): 367–427.
Fuchs, H.O. 1970. Outside reality inside the classroom. Journal of Yadav, A. 2006. Video cases in teacher education: What role does task play in
Engineering Education 60 (7): 745–47. learning from video cases in two elementary education literacy methods courses?
Gallucci, K. 2006. Learning concepts with cases. Journal of College Doctoral Dissertation, Counseling, Educational Psychology, and Special
Science Teaching 36 (2): 16–20. Education, Michigan State University.
Gallucci, K. 2007. The case method of instruction, conceptual change and Yadav, A., and B.E. Barry. 2009. Using case-based instruction to in-
student attitude. Doctoral Dissertation, Science Education, North Carolina crease ethical understanding in engineering: What do we know? What
State University. do we need? International Journal of Engineering Education 25 (1):
Garg, K., and V. Varma. 2007. A study on the effectiveness of case 138–43.
study approach in software engineering education. In Proceedings of 20th Yadav, A., and J.L. Beckerman. 2009. Implementing case studies in a
Conference on Software Engineering Education and Training. Dublin, Ireland plant pathology course: Impact on student learning and engagement. Jour-
Garvin, D.A. 2003. Making the case: Professional education for the nal of Natural Resources and Life Sciences Education 38: 50–55.
world of practice. Harvard Magazine 106 (1): 56–65. Yadav, A., and M.J. Koehler. 2007. The role of epistemological beliefs
Grissom, R.J., and J.J. Kim. 2005. Effect sizes for research: A broad practi- in preservice teachers’ interpretation of video cases of early-grade literacy
cal approach. Mahwah, NJ: Lawrence Erlbaum Associates. instruction. Journal of Technology and Teacher Education 15 (3): 335–61.
Henderson, J.M., L.E. Bellman, and B.J. Furman. 1983. A case for Yadav, A., M.A. Lundeberg, M. DeSchryver, K.H. Dirkin, N. Schiller,
teaching engineering with cases. Engineering Education 73 (4): 288–92. K.S. Maier, and C.F. Herreid. 2007. Teaching science with case studies: A
Herreid, C.F. 1994. Case studies in science: A novel method of science national survey of faculty perceptions of the benefits and challenges of using
education. Journal of College Science Teaching 23 (4): 221–29. cases. Journal of College Science Teaching 37 (1): 34–38.

January 2010 Journal of Engineering Education 63

 AUTHORS’ BIOGRAPHIES (IFAC) Symposium on Advances in Automotive Control, and
is a recent recipient of the Kalman award for the best paper
Aman Yadav is an assistant professor of Educational Psycholo- published in the Journal of Dynamic Systems, Measurement,
gy at Purdue University. His research focuses on the use of case- and Control.
based instruction and problem-based learning in STEM Address: School of Mechanical Engineering, Purdue University,
disciplines. In addition to his Ph.D. in Educational Psychology and 585 Purdue Mall, West Lafayette, IN 47907-2088; telephone:
Educational Technology, Dr. Yadav also has Bachelors in Electrical (1) 765.494.9342; fax: (1) 765.494.0787; e-mail: gshaver@
Engineering and Masters of Science in Electrical Engineering. Dr. purdue.edu.
Yadav has undertaken both quantitative and qualitative research
projects and has a strong familiarity with both types of analyses. Peter Meckl obtained his Ph.D. in Mechanical Engineering
Address: Department of Educational Studies, Purdue University, from MIT in 1988. He joined the faculty in the School of Mechan-
100 N. University Street, West Lafayette, IN 47907; telephone: ical Engineering at Purdue University in 1988, where he is currently
(1) 765.496.2354; fax: (1) 765.496.1228; e-mail: amanyadav@ a professor. Dr. Meckl’s research interests are primarily in dynamics
purdue.edu. and control of machines, with emphasis on vibration reduction and
motion control. His teaching responsibilities include undergraduate
Greg Shaver is an assistant professor of Mechanical Engi- courses in systems modeling, measurement systems, and control,
neering at Purdue University. He is also a graduate of Purdue and graduate courses in advanced control design and microproces-
University’s School of Mechanical Engineering, having ob- sor control. Dr. Meckl was selected as an NEC Faculty Fellow from
tained a Bachelor’s degree with highest distinction. He holds a 1990 to 1992. He received the Ruth and Joel Spira Award for out-
Masters degree and a Ph.D. in Mechanical Engineering from standing teaching in 2000. He is a member of the American Society
Stanford University. His research interests and background in- of Mechanical Engineers (ASME), the Institute for Electrical and
clude the modeling and control of advanced combustion Electronics Engineers (IEEE), and the American Society for Engi-
processes. Greg is an active member of the American Society of neering Education (ASEE).
Mechanical Engineering (ASME), participating in the ASME Address: School of Mechanical Engineering, Purdue University,
Dynamic Systems and Controls Division and the ASME Auto- 585 Purdue Mall, West Lafayette, IN 47907-2088; telephone:
motive and Transportation Systems Panel. He is the editor of (1) 765.494.5686; fax: (1) 765.494.0539; e-mail: meckl@
the 2007 International Federation of Automatic Control purdue.edu.

64 Journal of Engineering Education January 2010

 APPENDIX A: CASE STUDIES

Thermal Case Study: Three Mile Island Nuclear The Three Mile Island Reactor 2 (shown schematically in
Generating Station Figure 1) experienced a loss of coolant accident on March 28th,
This case study uses concepts from thermal systems to describe 1979. The timeline for the accident is as follows:
the Three Mile Island nuclear power plant disaster. The three-mile • 4:00:37 AM: Due to maintenance for a recurring problem
island nuclear generating station contained two pressurized water with the demineralizer, condensate pumps trip, main feedwa-
reactors, each of which generated 850MW. These reactors were ter pumps trip, and turbine trips. Auxiliary feedwater pumps
built by Babcock and Wilcox in 1968–1969 and entered service start up, but can’t deliver water since block valves have been
between 1974–1978. The reactor consisted of 177 fuel assemblies, mistakenly shut after routine maintenance two days earlier
which contained 15  15 array of “fuel rods” 3.5 m long, and 1.1 cm • 4:00:40 AM: Pressure relief valve opens as reactor pressure rises
in diameter. Only 208 of the 225 rods were fuel rods. Sixteen were • 4:00:45 AM: Reactor trips and control rods drop into core to
guide tubes within which the control rods were moved in and out of stop nuclear reaction
the reactor. The fuel rod tubes were made of Zircaloy, a corrosion- • 4:00:50 AM: Pressure relief valve is signaled to close, but
resistant alloy consisting mainly of the metal zirconium. In these doesn’t
long, thin tubes the reactor’s fuel, in the form of small cylinders of • 4:02 AM: Loss of coolant water triggers emergency core-
uranium dioxide, was stacked. cooling system, which is erroneously shut down by operators
soon after
• 4:10 AM: Reactor building sump overflows into contain-
ment building
• 4:15 AM: Saturation temp is reached, meaning boiling can
occur; fuel rods become damaged
• 6:18 AM: Operators close block valve for pressurizer
• 6:57 AM: Radiation level shows marked increase
• 7:30 AM: General emergency is declared
• 5:30 PM: Relief valve is closed, reactor coolant system is
repressurized
A timeline of the reactor core pressure during the accident is
shown in Figure 2. In the aftermath of the accident, 10 MCi of
xenon 133 and 15 Ci of iodine 131 were released into the atmos-
phere, more than 90 percent of TMI-2’s uranium fuel core was
damaged in the accident, between 30 to 50 percent of the core actu-
ally melted (1 Ci  3.7  1010 atomic disintegrations per second).
Figure 3 shows the reactor after the accident.
If the turbine is 30 percent efficient, compute the total thermal
(Source: From Wikipedia, March 31, 2007). power produced by the Three Mile Island Reactor 2. Where do you
think this power goes?

Figure 1. Three Mile Island Nuclear Reactor 2 (From the NRC Fact Sheet on the Three Mile Island Accident, March 2004).

January 2010 Journal of Engineering Education 65

 Figure 2. Reactor Core Pressure during the accident time (From K. Almenas, R. Lee, Nuclear Engineering, Springer-Verlag, 1992, p. 503).

How can a model be used to determine how long it takes for the
reactor core to reach a critical value?

Hydraulics Case Study: Hydro-electric dam failures

At 11:40 am on Saturday, January 7, 1984, the damtender began
reducing water releases from Reclamation’s Bartlett Dam outside of
Phoenix, Arizona. The outlet works was controlled by two 66-inch
water-operated needle valves. Shortly after noon, the Maricopa
County Sheriff’s office received a call from a fisherman downstream
from the dam, saying that he heard a loud “popping” sound from
inside the outlet works gatehouse and then saw water flowing at
high volume from the doorway and windows. John Steffen, Salt
River Project (SRP) Manager, arrived via helicopter at 1:00 pm just
as Glenn Harris arrived from the nearby Horseshoe Dam. Together
they entered the gatehouse from the top of the dam. Mr. Steffen
first closed the upper needle valve, then closed the upstream butterfly
valve for the lower outlet pipe, completely shutting off water
releases. Inspection revealed that the lower needle valve body located
at the end of the penstock had ruptured violently. The top portion
of the body, approximately 1 by 2 meters, had separated, and the
valve operating pedestal on which the operator was probably
standing was destroyed. The gatehouse windows and doors were
blown out, and a walkway inside the door leading to the operating
platform was found in the rubble. The damtender, an 18-year SRP
employee was killed in the accident.

Figure 3. The Three Mile Island reactor 2 after the accident

(Source: From Smithsonian National Museum of American
History, March 31, 2007).

If the coolant temperature was 300 C and the heat transfer

coefficient is 1.77  104 W/m2- C, what would be the reactor fuel
rod surface temperature?
Assume density of the uranium oxide pellet is 10.2  103 kg/m3
and its heat capacity is 360 J/kg- C. Also assume that the convec-
tive heat transfer coefficient initially drops to 1 percent when loss
of coolant occurs. Compute the temperature rise with loss of
coolant.
How is energy balance achieved in a nuclear reactor? How does
the heat transfer occur between the interface of a solid material and
a fluid? Furthermore, the center of the pellets is at a different tem-
perature than the surface. What do you think is going on here?

66 Journal of Engineering Education January 2010

 Shortly after midnight on Wednesday December 6, 1984,
a seven-man maintenance crew was completing work to
automating equipment at Utah Power & Light Company’s
Oneida Station hydroelectric plant, about 32 kilometers
northeast of Preston, Idaho. To put the units back on line, the
144-inch diameter water-operated needle valve was opened.
As the valve opened, it started moving rapidly and then
slammed shut. This event was followed by a 1 by 3 feet erup-
tion of the steel penstock. The water blew out the wall of the
powerplant and swept away the maintenance shop building,
the parking area, four vehicles, and the seven workers. Three
of the workers were able to swim ashore in the sub-zero tem-
perature and darkness, but four were killed in the accident.
Both catastrophic events followed the rapid closure of
needle valves regulating the flow of water from a penstock.
A penstock is a pipeline used to convey water under pres-
sure to the turbines of a hydroelectric plant.
Develop a dynamic system model incorporating a
reservoir and valve resistance for a dam with a reservoir
depth of 188 feet, mean flow rate of 75m3/s, and penstock
length and diameter of 60 m and 4 m, respectively. Do you
anticipate that this model will capture any potentially
destructive pressure increases (or decreases) during
valve closure-induced flow resistance increases?
Now add the fluid inertia of the water in the penstock
to the model. How does this effect the system dynamics
during rapid valve closure? Does this model predict any
potentially destructive pressure increases (or decreases)
during valve closure-induced flow resistance increases?
Now add the fluid capacitance affect of the in-
penstock water bulk modulus to the model. How does
this effect the system dynamics during rapid valve
closure? Does this model predict any potentially
destructive pressure increases (or decreases) during
valve closure-induced flow resistance increases?
What do you think caused the failures? How could
it be related to valve closure events?
How would you keep it from happening again? How
could you use a mathematical model to answer these ques-
tions? What would be the key elements of such a model?
Case study reference: Replacement of Water-
Operated Needle Valve at the U.S. Bureau of Reclama-
tion Facilities, Proceedings of the International Confer-
ence on Hydropower, Atlanta, Georgia, Aug. 5–8, 1997.

January 2010 Journal of Engineering Education 67

 APPENDIX B: PRE-TESTS/POST-TESTS

Thermal TP when the chip is turned on and begins generating heat at a rate
Pre-test: A computer chip is represented in the schematic given by q. If the convective coefficients for chip 1 and chip 2 are
diagram below: such that h2  h1, which arrangement (with or without a heat sink)
does a better job of removing heat from the chip? Please explain
your answer.

Hydraulics
Pre-test: Consider a hydraulic tank in series with a resistive
valve
TP is the temperature of the chip (in degrees C) and
P is its
mass density (in kg/m3), dP is the height of the chip (in m), and AP
is its top surface area (in m2). Assume that only convective heat
transfer occurs through the top surface to the surroundings, which
are at ambient temperature TA. This heat transfer can be described
as follows:
1
qconv = (TP − TA)
R
where qconv is the heat transfer rate (in W) and R represents a thermal
resistance (in units of degrees C/W). Ignore any heat transfer Where:
through any other surfaces. i(t) – inlet flow to tank [m3/s]
Determine an expression for the steady-state chip temperature o(t) – outlet flow from system and tank [m3/s]
TP when the chip is turned on and begins generating heat at a rate Pa – atmospheric pressure [N/m2]
given by qIN. Heat energy can be stored as described by a material’s P(t) – absolute pressure at bottom of tank [N/m2]
heat capacity cP, which is usually given in units of J/kg-degree C. Pg(t) – gage pressure at bottom of tank [N/m2], such that
Develop a differential equation that describes how the chip temper- Pg(t)  P(t) Pa
ature TP responds when the chip is turned on and begins generating R – “flow resistance” of valve
heat at a rate given by qIN.
Post-test: Consider the two computer chips below Determine: input-output differential equation for system where
the input is wi(t), and the output is Pg(t).

Computer chip 1 without a heat sink.

Post-test: Consider a hydraulic tank in series with a resistive valve

Where:
Computer chip 2 with added heat sink. i(t) – inlet flow to tank [m3/s]
o(t) – outlet flow from system and tank [m3/s]
Pa – atmospheric pressure [N/m2]
The mass density of the chip material is represented by
P, cP P1(t) – absolute pressure at bottom of tank [N/m2]
represents the specific heat of the chip material, TP is the tempera- P1,g(t) – gage pressure at bottom of tank [N/m2], such that
ture of the chip, dP is the height of the chip, and AP is its top surface P1,g(t)  P1(t) Pa
area. The heat sink has height dS. Assume that only convective heat P 2 (t) – absolute pressure between resistance and pump
transfer (with convective coefficient h2) occurs to the surroundings, [N/m2]
which are at ambient temperature TA. Conductive heat transfer P2,g(t) – gage pressure between resistance and pump [N/m2],
(with conductive coefficient k) occurs between the chip and the heat such that P2,g(t)  P2(t) Pa
sink. Ignore any heat transfer through the sides and bottom of the P3(t) – absolute pressure between pump and fluid inductance
chip and the sides of the heat sink. [N/m2]
Derive a differential equation for the computer chip with the P3,g(t) – gage pressure between pump and fluid inductance
heat sink that describes the time response of the chip temperature [N/m2], such that P3,g(t)  P3(t) Pa

68 Journal of Engineering Education January 2010

 R – “flow resistance” of valve Determine: equations of motions for the system where the inputs
Ps – supply pressure, such that P3(t)  P2(t)  Ps are Ps and wi(t), and the outputs are P1,g(t) and wo(t). Clearly indicate
I – inductance your process for synthesizing the model. Please explain your answer.

January 2010 Journal of Engineering Education 69