Graphical displays and interactive programs developed at the University of Virginia were used to expose students to complex heat transfer problems in a manner that allowed the student to quickly gain a physical interpretation. Analytical solutions, which often require the use of tabulated results, were presented in traditional lecture style. The Virtual Lab was used to supplement and enhance lecture material, offering an experience unmatched by either lecture material or a physical lab, in that students could vary the conditions and material properties for numerous heat transfer problems and quickly see the effect on the results. This allowed the students to individually develop their deductive skills and provided for added insights into the dynamic nature of the problems. These programs take a large step towards providing the student with real time results. For example, the effect of the velocity profile on the convective heat transfer from a flat plate can be assessed with different velocities and fluids and shown graphically. The computer based modules for the Virtual Lab were often times complemented with a desk-top experiment that was used to gather data for comparison with predicted results. Recognizing that each student learns in a different manner, and that many prefer visual learning aids which is often difficult in the area of heat transfer, these programs offer a variety of tools to enhance the learning process. The programs were positively accepted by the class, as presented here, and some students even pushed the programs past their limits and made suggestions for improvements, which have since been incorporated.

In many engineering disciplines, including the thermal-fluids sciences, the prominent undergraduate and graduate level textbooks continue to stress classical analytic methods for problem solutions, in lieu of a more numerical approach. Authors of these texts, and the faculty using them, argue that the analytical approach, even with its frequent use of exotic special functions, is more "fundamental", thus providing greater insight to the basic physics of a particular problem. According to this view point, the time spent by the student programming a computer to perform a "number-crunching" task should be spent developing the more important physical understanding.

Increasingly it is becoming obvious that a numerical/graphical approach can often provide greater insight, efficiency, and flexibility as an educational tool than can the earlier analytical techniques. The numerical approach can even be used to develop greater fundamental understanding, especially at the entry level of a subject. In many cases a numerical scheme is developed directly from first principles: (a) a conservation statement is proposed for a small representative control volume, (b) the terms representing each process are expressed algebraically, and (c) the algebraic equations are solved using efficient numerical algorithms. Today's desktop computers are so powerful that numerical/graphical simulations of many traditional problems can now be done in seconds in the classroom or the computer laboratory, thus allowing extensive student explorations into the effects of parameter variations. Such varied explorations were not dreamed of even a few years ago. Classical analytic solutions involving complicated mathematical functions generally do not invite this type of exploration, and so a wonderful opportunity is missed to understand and to visualize the physics behind a process.

At the University of Virginia, the sixth-semester mechanical engineering course in heat and mass transfer is normally taught in a three-a-week lecture format with a traditional laboratory, covering topics in both heat transfer and fluid mechanics, given the following semester. We have recently experimented with a new "partial studio" format. The studio model of engineering instruction has been closely associated with the Rensselaer Polytechnic University where lower-level physics and mathematics courses are taught entirely in this mode. Fifty minute lectures there are becoming a thing of the past. They are replaced by "hands-on" two hour sessions in specially constructed rooms equipped with a computer for each pair of students. Light-duty experiments and their analysis and interpretation of results are often part of the exercises. In our modified approach, one of the weekly lecture hours is replaced with a two-hour "studio" session in which students utilize a special classroom equipped with a Pentium computer for each pair of students. Thus, the student pairs can be given "hands on" assignments using specially designed software that highlights the concepts developed in class.

A collection of instructional modules has been developed for use by undergraduates at the University of Virginia. In the studio session, students perform a variety of computer-facilitated design and analysis activities. Some weeks they do "virtual" experiments using computational simulations of heat transfer process--actually taking data from the screen and utilizing it for analysis---all the while making use of modern visualization techniques. Other weekly exercises demonstrate the use of computer-aided solution in the design process, allowing fast and efficient multiple "what-if" calculations. Prior to each studio session a 2-8 page write-up encompassing the background on the physics and numerics, the implementation procedure, and sections on verification, interpretation and display of the results is supplied to the students. These modules emphasize the basic underlying concepts and hence differ greatly from common commercial software packages, which are usually designed for ease of use rather than instructional value. The studio exercises typically require preliminary "pencil and paper" analyses and also provide training in the validation and interpretation of results. Several of the exercises also use a single desk-top experiment for the whole class to generate data for comparison with predicted results.

The seven packaged instructional modules have each been developed using a unique combination of Visual Basic and Fortran programming languages. The extensive number crunching and the generation of all plots is performed in Watcom Fortran 77 (with many Fortran 90 extensions). Windows 16-bit graphics functions are called from the Fortran routines. For each module, the applicable Fortran routines are combined into a single dynamic link library, which is then available for function calls from a tailored Visual Basic executable.

All parameter input is through the VB interface and each module stands on its own, no commercial products requiring licensing or royalties are used. Unlike some more general packages, our especially tailored modules require almost no startup time in class. Some sample data sets are supplied as defaults and the calculation are initiated at the click of a button. Of course to accomplish the tasks required during the sessions, the students must have derived heat balances and computed various non-dimensional numbers as input parameters or to evaluate the process output, much like they would in a traditional laboratory.

Since each of these modules required a great deal of effort for development of the original Fortran algorithm, the Visual Basic interface, and the supporting student-documentation, the topics were selected with great care. In several cases a single module includes nearly all the concepts included in a chapter of a graduate-level text. Many of the modules are sufficiently general that they may be used in a variety of related courses, both graduate and undergraduate, in mathematics, science and engineering. Each of the seven modules will be described briefly below. In each of these modules great flexibility exists so that the students can not only investigate a large range of input parameters, but can also use the software to solve and verify a substantial portion of their assigned homework problems. An expanded description of each may be found in Ribando and O'Leary (1997c).

Extended Surface Heat Transfer (Fins). Traditionally heat transfer analysis of fins involves the analytical solution of governing ordinary differential equations. However, even the analysis of a straight, rectangular fin involves several different solutions depending on the tip boundary condition, and the analysis of annular or triangular fins involves Bessel functions, which the students may not have encountered. The students may learn to evaluate the fin efficiency, but they have no understanding of the temperature distribution along the fin. The new module is based on a finite-volume solution of the governing heat balance equation. The resulting tridiagonal system of equations is readily solved and the student has the whole temperature distribution at their disposal immediately. Using this tool, the student can adjust parameters and immediately gain a good understanding of the impact of various parameters on fin efficiency, effectiveness, and overall performance. For instance, the student can evaluate the effect of using a low thermal conductivity material for a fin, or whether a fin is more effective during free or forced convection, or the "best" length for a fin. Since it does not require the evaluation of different functions for each different geometry, only the appropriate areas for axial conduction and convection to the fluid, this numerical solution is readily carried out for virtually any l-D geometry. In this session a simple benchtop experiment is utilized and experimental data is provided for comparison to analytical results. This experimental data enabled the students to quickly discover that the usual assumption of a uniform convective heat transfer coefficient is not very accurate for free convection flow conditions, and can depend strongly on the shape of the fin.

Two-Dimensional, Steady-State Conduction. This module utilizes the finite difference technique to derive the two-dimensional temperature profile in materials subjected to steady-state conduction (Ribando and O'Leary, 1997a). The students are required to nodalize the conduction region, derive the appropriate heat balance equations for each region of the solution domain (internal points, boundary edges, corners, etc.) and input the resulting numerical coefficients into the program. This approach reinforces the connection between finite different techniques and statements of conservation of energy. The program solves the resulting large system of linear equations and returns a full-color contour plot of the resulting isotherms, all in a few seconds. This visual representation, among other things, enables students to truly understand the implications of different boundary conditions. For instance, an adiabatic boundary condition implies contours of constant temperature are perpendicular at that surface. Several problems for which an analytical solution exists are also set up as examples and included for viewing. These problems are solved numerically and then the analytical solution is evaluated with the number of terms in the infinite series chosen by the student. The results are then plotted for comparison. This comparison of solutions helps demonstrate the limitations of both numerical techniques and analytical solutions.

Transient, 1-D Conduction. Here a finite-volume solution of the transient, one-dimensional heat equation is implemented (Ribando and O'Leary, 1996). The same algorithm applies to slabs, cylinders and spheres. The student inputs the surface Biot number and a stopping criterion (either the overall elapsed time or the criteria that a particular temperature is reached at some specific spatial location). The user may specify the use of an explicit solution, an implicit solution or a weighted average of the two. When an explicit solution is selected, the user can choose conditions that will generate a dramatic display of a numerical instability. In addition to a uniform initial temperature (corresponding to the time-honored Heisler charts), the user may specify an initial temperature distribution corresponding to uniform volumetric heating. Unlike Heisler chart solutions that provide the temperature at a specified location at a specified time, this module enables the student to follow the transient temperature response of the material. The students could witness the dramatic difference in thermal response of an iron sphere versus a granite sphere, for instance, and can use this analysis to estimate the age of the earth from heat transfer measurements. This visualization tool can also help students grasp the abstract concepts of a semi-infinite medium or the lumped capacitance assumption.

External Flows. In this module the boundary layer equations for flow over a flat plate are solved in their primitive form, i.e., without similarity restrictions. The grid grows in the direction normal to the plate along with the boundary layer. The user can input the Reynolds and Prandtl numbers and can specify a fixed temperature or heat flux boundary condition or a combination of the two. A simple mixing length model is used to extend the calculation into the transition and turbulent region. The extent of the velocity boundary layer is plotted and temperatures are shown in the form of color contours. This visual display enables the student to quickly grasp the importance of the Prandtl number on the relative thickness of the velocity and thermal boundary layers, as well as the effect of transition from laminar to turbulent flow. Expressions can be developed for both the local and the overall heat transfer coefficients from data taken directly from the screen.

Internal Flows. This module solves the thermal entry-length problem (velocity profile is fully developed when a change in the wall thermal boundary condition is introduced) for laminar (Ribando and O'Leary, 1994), transition and turbulent flows. Either a fixed wall temperature or fixed wall heat-flux may be specified. The student may take data from the screen for the mixed mean temperature or the surface heat flux as a function of the axial position along the pipe and, using this data, a heat transfer correlation may be developed. The temperature distribution is displayed in the form of color contour plots. Like the external flow module, this simulation allows an infinite number of flow and fluid input parameters, with virtually no setup time.

Heat Exchangers. Two separate modules were developed for instruction on the subject of heat exchangers (Ribando and O'Leary, 1997b). Both modules solve the discretized, coupled heat balance equations for the two fluids and give the same "bottom-line" results as the conventional LMTD and effectiveness-NTU methods. In the module for co-annular and shell-and-tube heat exchangers, where a coupled set of ordinary differential equations applies, the temperature distribution is presented graphically in the form of a simple T vs. X plot. In the module for cross-flow heat exchangers, where a coupled set of partial differential equations applies, the results are depicted as contour plots of temperature distribution for both fluids. With the temperature distributions in both fluids immediately available, the impact of the various parameters becomes quickly apparent and the student can readily assess the quality of a particular heat-exchanger design.

Radiation View Factors. Direct numerical integration is used to compute the viewfactor between two arbitrarily positioned parallelograms (Ribando and O'Leary, 1995). In order to verify the input data, the plates are shown on the screen in a perspective view with hidden surface removal, thus giving student engineers much-needed reinforcement of training in 3-D visualization. In addition to the conventional arrangements covered by viewfactor charts and equations that may be used for program verification (i.e., parallel rectangles and perpendicular rectangles with a common edge), this program computes quite arbitrary arrangements in 3-D space.

Other Modules. In addition to the Fortran/VB modules described above, several exercises have also been utilized in which the students were required to develop a program or spreadsheet model for a particular problem. One such exercise involved an instrumented mockup of a standard residential stud-wall construction. Students developed series and parallel heat flow models of the steady-state conduction problem, most using spreadsheets, and compared their predictions with experimental measurements obtained from the mockup. Another exercise involved application of an empirical correlation for flow over a cylinder to approximate the sensible and latent heat transfer from an Olympic runner under a variety of ambient conditions, including a hot, humid day in Atlanta. In an exercise most appropriate for students at The University, the motivation behind Thomas Jefferson's use of thick stone walls in his home, Monticello, is studied by determining the transient internal air temperature, taking into account the time varying mean solar temperature. The last exercise involved a numerical integration of spectral data to find the total transmissivity of several types of glass to solar and terrestrial radiation. From this exercise the students gained a firm understanding of the greenhouse effect.

The students have responded positively to the partial studio model for teaching heat transfer at University of Virginia. Attendance at the studio sessions is very near 100%, and there is an active learning environment during the sessions. This concept has now been used twice at UVA and feedback from students from the first class exposed to this technique, students who have now had nearly a year to reflect on it, are very encouraging. Some specific examples of feedback from the students include:

"Basically, the studio sessions helped clarify the theory presented in class in several ways. ....They gave us the opportunity to see how the theory and equations acquired in lecture could be applied to real life situations, such as in the Monticello project. Limitations in the theory were also observed by comparing the computer aided predicted heat transfer characteristics with those observed in an actual model. Finally, these studio sessions helped us think about how the principals acquired in the lectures could be applied to new problems."

"The heat transfer studio allowed students the ability to receive a quantitative feel for the concepts that were being discussed in ME 329. One of the challenges facing students learning basic concepts throughout the undergraduate curriculum is visualization of the theoretical concepts presented in class. Many times this is not possible since a lab is not associated with the class either due to time or resource consideration. The computer assisted lab used in ME 329 allowed for this visualization and maintained a direct link to the concepts and theories currently being studied. Also, because the computer models simulated the concepts without undo laboratory setup and equipment, students could concentrate on the concepts being presented. This encouraged experimentation with various models of the system. In addition, because the system was a computer model students could test extremes and odd combinations without dangerous results - something that would not be possible in a real laboratory setting."

"The visualization ability presented through computer based models in ME 329 reinforced the critical concepts of heat transfer and assisted in concept retention through visual feedback. This feedback was critical in establishing the many correlations present between the various components of the system. Since the value of the variables can be changed easily during experimentation, students immediately began to see concept and variable correlations. Therefore, we could immediately begin to connect ideas such as change in Biot number affects the heat transfer rate in this fashion, etc. Without a doubt, this laboratory session provides invaluable insight and greatly assists retention of the concepts presented in ME 329."

"One aspect of the lab I thought was especially interesting was the ability to change parameters and instantly see their effects on the system we were studying."

"The Heat and mass transfer studio session had many advantages over a standard laboratory because of the integration of computer programs. The computer programs not only allowed for quicker calculations, but also gave the students insight into the real-world applications of heat transfer computer programs."

"The examples used in the computer studio sessions were useful in explaining the principles of heat and mass transfer. The students could relate to the examples, which were engineering applications, and learn the fundamentals of heat transfer from performing the studio exercises. ....The heat transfer software designed for the studio gave students a better visual stimulus than the graphics provided in the textbook. The grid provided by the software aided the visualization of the nodal point locations, and the color temperature distribution display eased the visualization of both the heat transfer and the actual temperature distribution."

"The studio sessions, when combined with real-world applications and examples, are beneficial to students. Students are exposed to modern technology that may benefit them when they leave the University, and they are given the opportunity to apply skills acquired from other classes in order to increase their level of understanding in Heat and Mass Transfer."

A large number of studies have been conducted regarding how organized spatial displays increase the learning of associated text. Paivio (1986) devised the dual-coding theory that suggests that information is stored in separate, functionally distinct codes, one representing verbal information and the other representing spatial information. Paivio suggests that connections link the related verbal and nonverbal information. The images created from organized spatial displays provide retrieval cues that facilitate the recollection of related text. Displays are stored and processed as an intact unit; therefore, when the student is asked to read text, they are able to process the text while recalling the active image of the display stored in their memory. This is very helpful for the formation of additional retrieval cues and the recollection of facts. Additionally, information encoded in multiple ways is more easily retrieved from long-term memory than information encoded in just one way. A student can therefore recall information better with the more ways of receiving information, because the student is forced to process the information in a variety of ways.

Animated visual displays are more effective than static visual displays. For example, the modules being discussed in this paper graphically demonstrate the growth of boundary layers or the development of temperature profiles. This constant feedback requires the student to process the information that they just learned and apply it to draw an inference or solve a problem. This is effective in that the student is given the opportunity to determine whether they understand the information based on their ability to apply it. In addition, the modules require the student to pay attention to the information that is being taught, a common problem when teaching information through lectures and textbooks. This and the addition of predetermined expected results are beneficial if selected carefully to support the specific leaming requirements The studio modules provide a successful supplement to lecture material, because the computer exercises confirm the expected results.

The visual aids used in the modules should be simple and concise, and they should include major ideas without overwhelming the student with detail (Ormrod, 1995). While promoting visual imagery, the visual aids can also show students how major ideas relate to and affect one another and provide ways of helping students to organize the information that they receive (Ormrod, 1995).

A partial studio model has been adopted in the undergraduate heat and mass transfer class at University of Virginia. The use of specially designed software to present the fundamentals of heat transfer to students in a visual manner has been generally successful, as measured by student response. The true test will be a test of time. Has the incorporation of visual aids into this curriculum helped to increase the retention rate among the students? Research by others indicates the answer will be yes. A follow-up study to be conducted about 5 years from now will help form the conclusion.

Obviously this partial studio model involves a radical shift away from the usual lecture-and-homework paradigm. Indeed, several of the calculations we have included in our modules would not have been feasible on a PC just a few years ago. In planning our studio sessions and software, however, we were careful to stick to fundamentals, selected many applications having analytical solutions for comparison, and carefully avoided all glitz and gewgaws. In this way we developed an approach that was acceptable both to students and to skeptical colleagues .

Ormrod, J.E., 1995, Educational Psvchologv: Principles and Applications, Prentice Hall, Inc., Columbus, OH.

Paivio, A., 1986, Mental Representations: A Dual Coding Approach, Oxford University Press, NY.

Ribando, R.J., and O'Leary, G.W., 1997a, "UVa2DSS - Steady-State 2-D Conduction," submitted to NSF NEEDS database.

Ribando, R.J., O'Leary, G.W., and Carlson, S.E., 1997b, "A General Numerical Scheme for Heat Exchanger Thermal Analysis and Design," Computer Applications in Engineering Education, in press.

Ribando, R.J., and O'Leary, G.W., 1997c, "Teaching Modules for Heat Transfer," to be presented at the National Heat Transfer Conference, Baltimore, MD, August, 1997.

Ribando, R.J., and O'Leary, G.W., 1996, "UVaONEDT - One-Dimensional Transient Heat Conduction," submitted to NSF NEEDS database.

Ribando, R.J. and Shi, Q., 1995, "Fortran 90 and the Direct Calculation of Radiation Viewfactors," Computer Applications in Engineering Education, Vol. 3, No. 2, pp. 133137.

Ribando, R.J., and O'Leary, G.W., 1994, "Numerical Methods in Engineering Education: An Example Student Project in Convection Heat Transfer," Computer Applications in Engineering Education, Vol. 2., No. 3, pp. 165-174.

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