Development And Implementation Of Interactive/Visual Software For Steady State And Transient Heat Conduction Problems

This paper describes a versatile, user-friendly, and easy to understand computer program that has been developed to teach the numerical solution of steady state and transient heat conduction. The program has been class room tested for many semesters and it was very well received by the students. Introduction The school of Mechanical and Aerospace Engineering at Oklahoma State University offers MAE 3233, “Heat Transfer”, as a required course for the Mechanical Engineering degree and an elective course for the Aerospace Engineering degree. Student use of software to analyze 1-D and 2-D steady state and transient heat conduction problems has been an important part of this course since 1994. Use of software has been particularly important in appreciating the power of numerical methods in solving engineering heat transfer problems. The software described in this paper is based on the finite difference method and can handle three types of boundary conditions (constant temperature, specified heat flux, and convection) and two types of numerical schemes (implicit and explicit). The user has access to a built in material properties library for selection of realistic material properties. The program provides tabular output, graphical output, and shaded and animated temperature plots for steady and transient cases. The primary goal of this project was to develop MS Windows based software that is effective for teaching; easy to use, maintain and update; and freely available to all. Motivation for the Project Before starting this project, the authors were aware of many existing software options for computer based heat transfer analysis. Unfortunately, all of them had major drawbacks for our purposes. There are professional level programs that can perform highly detailed heat transfer and fluid flow analysis, and most are available at a substantial educational discount. These programs have three major drawbacks: they are not designed to teach numerical heat transfer analysis; the time required to learn to use these programs is substantial; and the cost to individual students is still fairly high. Many heat transfer textbooks (see for example References 1 and 2) now include software aimed at teaching the concepts of numerical heat transfer analysis, but these are only available to students who purchase the textbook. Our preferred textbook did not offer such software at the time we undertook this project. In general, we prefer to choose the textbook on the basis of the content of the book itself. Any software provided by the book is an added bonus. This paper is in no way intended as a criticism of the software available with current Heat Transfer textbooks. “Proceedings of the 2006 American Society for Engineering Education Annual Conference and Exposition Copyright ©2006, American Society for Engineering Education” We offer our software as a freely available alternative that may be adopted by anyone who finds it useful. There is software available designed to teach numerical heat transfer analysis, that is available at low or no cost to faculty and students, including software written in 1994 by the first author. Unfortunately, those programs use old DOS based programming techniques and user interface styles. Student reaction to our own “dated” software was uniformly negative. Our goal was to develop modern; teaching oriented software for numerical analysis of heat transfer. Our intent was to make this software freely available to our own students, and to offer it freely to other heat transfer instructors and their students. This software development project contributed in a synergistic way to three different educational missions. It provided a high quality MS level creative component project for the MS student who developed the software. The software is now being used by undergraduates in MAE 3233. The software was written in a modular and expandable way so that it can be used for future research work by MS students. Numerical Solution of Steady State and Transient Heat Transfer Problems The fundamental partial differential equation for analysis of heat transfer include Laplace’s equation and Poisson’s equation which can be applied to steady state heat transfer, and the general heat balance equation which incorporates transient effects. These equations are derived and presented in nearly all heat transfer textbooks, including References 1-3. Analytical solutions to those equations are available for a few simple but important geometries and boundary conditions. For most non-simple geometries or boundary conditions, where analytical solutions are not available, numerical solution techniques are used. The most common numerical techniques include finite elements, finite differences, and finite volume techniques. The finite difference method appears to be the method used most often by people working in the area of heat transfer and fluid flow, and is presented in most undergraduate textbooks on heat transfer including References 1-3. The finite difference method is usually featured prominently in most numerical methods textbooks, including Reference 4. The finite difference method and its application to heat transfer problems will not be described in detail in this paper because it is so readily available in other references. Instead, a small sampling of the geometries and equations will be shown to give a rough idea of the technique. The essence of the finite difference method consists of replacing the pertinent differential equation and boundary conditions with a set of algebraic equations that provide an approximate solution. Also, the continuous geometric and temporal domains are approximated with a set of discrete points in time and space. Figure 1 shows a two-dimensional sub-region of space, and a single point in time, approximated by a set of uniformly spaced points called “nodes”. The uniform organization and spacing of the nodes forms what is commonly called the “grid”. Because the spacing is uniform, the nodes may be identified by a pair of integers (m,n) denoting location of the node within the grid. The differential equations are approximated by algebraic equations expressing heat flow relationships between neighboring nodes within the grid. “Proceedings of the 2006 American Society for Engineering Education Annual Conference and Exposition Copyright ©2006, American Society for Engineering Education”