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Ac 2007-69: Interactive Computer Program for Transient Conductive Heat Transfer Concepts
| Content Provider | Semantic Scholar |
|---|---|
| Author | McMasters, Robert L. |
| Copyright Year | 2007 |
| Abstract | An interactive computer based learning tool for undergraduate students enrolled in Heat Transfer courses has been significantly expanded. A previous version of the program provided graphical depictions of two-dimensional steady state conduction solutions for cases where temperature boundary conditions were prescribed. The present research expands the features of the program to include prescribed heat flux boundary conditions as well as convective boundary conditions. Moreover, the expanded program also handles transient cases so that students can watch temperature changes in a material on a real-time basis. The addition of these boundary conditions also now allows one dimensional problems to be solved by specifying a zero heat flux condition on opposing sides of the body. The solutions for the original version of the program were generated using a code developed for Sandia National Laboratory which was DOS based. The revised program has replaced this computational kernel with a numerical solution which is programmed as part of the native Visual Basic code. This feature allows the program to run more seamlessly, without the need for a black DOS window to appear on the screen. The interface between the student and the kernel program allows visualization of the temperature field generated in the two-dimensional body. The program is used by students on an individual basis as a supplement to their usual textbook, homework and class involvement. Input from the students is prompted via text boxes in a Windows based program. Coincident with the expanded features of the program is a need for considerably more input on the part of the students. The six input items required by the user in the previous program version have been expanded to 17, with a corresponding number of input boxes provided for that purpose. Additionally, there are two “calculate” buttons which start the program running, one for steady state problems and one for transient problems. Students enrolled in the Heat Transfer courses at two separate institutions are given instruction sheets for operating the program, including prescribed temperature values for the boundaries. They are then asked to provide a written response to questions, requiring them to explain where the heat flux is the largest and the smallest in the body. An evaluation of the program by the students is included in the study as a means of determining the effectiveness of the program. Since the learning atmosphere in each of the two schools included in this study is very different, the reaction from the students at each of these schools is of special interest. Introduction A program was previously developed with the intent of giving students a physical feel for conductive heat transfer processes [1]. The program addressed prescribed temperature boundary conditions under steady state conditions in a two-dimensional rectangular object. The user provided input related to the object dimensions, along with the prescribed temperature at each of the four boundaries. The temperature distribution was then displayed using color to depict temperatures on the computer screen. This program was originally based on a code developed through Sandia National Laboratory to find analytical solutions for steady state and transient heat conduction in solids [2]. The code developed for Sandia was intended for use in verification of numerical solutions and was DOS based. The instructional program, which made use of the DOS code, was Microsoft Windows based and essentially served as an interface between the student user and the DOS program. The Windows based program was written in Visual Basic. An input file was required for the DOS program, which was somewhat cryptic. The Windows program provided a more intuitive data entry system and then generated the input file for the DOS program to simplify input for the student user. When the program was activated, a DOS window was automatically introduced onto the screen while the temperature calculations were underway. The exact solution generated by the DOS program was then written to an output file, which was read by the Windows program and displayed in color for the user. This program architecture was chosen because of the inherent speed and accuracy of the analytical solutions. Ironically, a drawback of the DOS program turned out to be a relatively slow calculation rate. The analytical solutions are very fast when only one temperature is needed at one particular time in a transient conduction problem. This is because no previous time steps need to be calculated, as is required in a numerical scheme. Nor are any other temperature values at any other points in the body required to be calculated in order to compute the temperature at just one point. However, when a full temperature grid is required for the display of thermal gradients, the analytical solution offers no advantage over the numerical solution. Indeed, if the analytical solution is not designed for multiple calculations, and terms such as eigenvalues are unnecessarily recalculated for each point in the grid, the computation can become very inefficient. Reference [3] describes a program which is very similar to the one presented in the current research. The added area of study in the present case is the inclusion of a structured set of homework questions given to the students to guide them into utilizing the program to its fullest extent. The questions are designed to make the students study and interpret the results so that they can extract the maximum amount of benefit from the features available in the program. Other initiatives aimed at teaching computational heat transfer are described in references [4] and [5]. The use of spreadsheets is a good teaching tool for getting the students involved in the calculation process. The present research, by contrast, endeavors to give students an intuitive physical feel for the heat transfer processes by looking at the results of calculations, rather than generating the calculations. As part of the work for the program developed under the present research, a numerical solution within the native Visual Basic code was developed to replace the DOS based kernel in the previous version of the program. The numerical scheme was based on a finite difference solution with second order boundary conditions, using the Gauss-Seidel method to solve the equations. The program also now addresses not only steady-state, but transient heat conduction in a rectangular two-dimensional object. The grid contains 100 nodes, arranged 10 by 10, and employs a fully implicit backward-difference method for transient cases. Additionally, the range of boundary conditions was expanded to include prescribed heat flux and convective cases. With the addition of prescribed heat flux boundary conditions, one-dimensional problems can also be dealt with by specifying a heat flux of zero on opposite sides of the object. The differential equation solved by the numerical scheme in the revised program is |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://peer.asee.org/interactive-computer-program-for-transient-conductive-heat-transfer-concepts.pdf |
| Alternate Webpage(s) | http://www.icee.usm.edu/ICEE/conferences/asee2007/papers/69_INTERACTIVE_COMPUTER_PROGRAM_FOR_TRANSIE.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
