Modeling the Transient Two-Dimensional Temperature Response of Cylindrical Geometry for the Enhancement of Learning Heat Transfer

This thesis considers the topics of heat transfer education, a modern approach to learning, and understanding one-dimensional verses multidimensional problems. The physical problem considered is transient conduction in a short cylinder immersed in an isothermal fluid. Many aspects can be modified, such as the material properties, but the length and radius are of primary concern. The thesis introduces the concepts required to develop a numerical method for solving the temperature gradient within the cylinder. This method is programmed in MATLAB with a graphical user interface allowing for interactive learning by performing iterative tests to discover various concepts; which can have a significant impact on learning. Many published research articles detail the effectiveness of incorporating hands-on computer programs into the heat transfer curriculum. The interaction effects from the inputs are also analyzed using a design of experiments full factorial method to determine which inputs are the most significant concerning the error between the one- and two-dimensional solutions. The main effects are the length and radius by a significant amount followed by the time, material, initial temperature, and convection coefficient. Finally, the program is used to develop a chart which given the geometry, material properties, and Fourier number can tell the user precisely when the one-dimensional assumption for both a slab and infinite cylinder breaks down.