Design Of A Multi Mode Finite Difference Heat Transfer Project

The development of a comprehensive inite-difference project at the end of a heat transfer curriculum is described. The problem requires evaluation of the school’s football ield turf heating system, incorporates all of the major heat transfer modes (convection, conduction, and radiation), and requires students to investigate both steady state and transient versions of the problem, with comparison to analytical solutions when available. The problem is solved using the inite-difference method (FDM) and an ExcelTM spreadsheet with Visual Basic for ApplicationsTM (VBA) programming to facilitate program execution beyond normal spreadsheet capabilities. The project also requires students to conduct a design analysis for environmental and/or system changes, subject to approval by the instructor; suggested topics for this design project are offered. The project is designed so that it is easy for students to understand, and recommendations are offered regarding project design and submission which facilitate grading of student work. While the speciic application described herein is to the school’s football ield, the same approach may be employed in many steady state and transient heat transfer problems—in fact, students have employed the modeling and programming techniques learned in this project to other courses, including their Senior Capstone projects. Results of a student opinion survey, anecdotal data, and performance on the heat transfer portion of the Fundamentals of Engineering examination data are presented. I. Considerations in Designing a FDM Project When designing a problem appropriate for completion in a certain number of class meetings, certain educational and institutional constraints had to be considered. As opposed to the initeelement method (FEM), the inite-difference method (FDM) does not have a steep learning curve, and was therefore ideal to provide students with a tool which would allow analysis of many realistic heat transfer processes. Additionally, it was desired that whatever computational code was employed for implementation of the FDM, it should be readily available and of low cost; Microsoft ExcelTM proved to be ideally suited in this regard, especially since all Microsoft products include the Visual Basic for ApplicationsTM (VBA) programming language. VBA allows more extensive computational capability than possessed in the basic spreadsheet; as juniors, students in the mechanical engineering curriculum at USAFA already receive a block of instruction in VBA object-oriented programming. The project assigned had to include all modes of heat transfer, and needed to involve scenarios which require analysis under both steady state and transient conditions. Being an undergraduate institution, no teaching assistants are assigned at USAFA, so that the instructor must grade all work submitted; ease of grading was, therefore, an important consideration. A ine line had to be walked in ensuring not only the required degree of dificulty, but also allowing that mistakes be easily detected. Figure 1 is a screen shot of the template provided to the students, with all material properties and dimensions depicted. Not only were students required to provide all equations in the blank cells of this template, but they were required to do a certain amount of macro recording and assignment of macros to the control buttons shown. Iteration speed for the steady state problem and time stepping speed in the transient problem were controlled by varying the screen refresh rate using the slide bar shown. To gauge their progress, formula results (rather than formulae) for certain cells were provided to students for comparison with their spreadsheet results. Additionally, two versions of the steady state spreadsheet and two versions of the transient spreadsheet were required turn-in items; each required grids and row and column headings to be displayed. The irst version merely displayed P ge 15358.2