AME Seminar: Kevin Cole
Thursday, October 20th, 2022 - 4:00 p.m.
Dr. Kevin Cole
Professor Emeritus
Mechanical and Material Engineering
University of Nebraska
"Something Old and Something New: Green’s Functions and Thermal Modeling"
AME Lecture Hall, Room S202 | Zoom link
Abstract: Although they were developed in the nineteenth century, Green’s functions continue to be an important tool for solving engineering problems in the twenty-first century. Solutions constructed from Green’s function are of present interest as benchmarks for checking fully-numeric solutions, as rapidly-computable direct solvers for inverse problems, and as building blocks for semi-analytical methods. Two current applications of Green’s functions will be discussed in this seminar.
The Exact Analytical Conduction Toolbox, or EXACT, is an internet database which contains over 170 solutions of the diffusion equation, organized and classified by a numbering system. Each solution in EXACT is bundled with tables, plots, algorithms, and verified computer codes, to make them more useful to engineers and scientists. The method of Green’s functions, from which many of the solutions in the EXACT database were developed, will be briefly described. Recent work on thermal modeling based on discrete Green’s functions and graph theory will be presented. This new semi-analytical method is verified by comparison with an EXACT case that is transient and fully three dimensional. In a 50-layer thermal simulation of an additive manufacturing process, the new method is many times faster than commercial finite-element software at comparable precision. The new method is also validated by comparison with experimental thermal data from an Inconel part built with an instrumented laser powder bed fusion machine.
Bio: Dr. Cole has degrees from Iowa State University, the University of Minnesota, and Michigan State University, and he is a registered professional engineer. He is a professor emeritus, having retired from teaching to focus on research and software commercialization. Dr. Cole has experience in thermal sensor technology, diffusion theory, inverse problems, thermal-property measurements, and numerical modeling. He has developed two archival web sites based on his research. He has current funding from the National Science Foundation and the Department of Energy. The second edition of the book he co-authored, “Heat Conduction Using Green’s Functions” was published in 2011.