The ability to study the interior of an object without destroying it is an important industrial tool. One method of recent interest is thermal imaging . The idea is to use heat energy as a kind of ''x-ray'', to form an image of the interior of an object without causing damage to the object. More precisely, one applies a controlled source of heat energy to the exterior boundary of the object, then monitors the temperature of the object's boundary over time. This measured boundary temperature is influenced by the internal structure of the object. For example, an internal crack or void may block the flow of heat energy, and the heat is forced to flow around the defect. The goal is to determine the internal structure---e.g., locate cracks---from this exterior temperature data.

Author Bio

I am a graduating senior at the University of Akron, with a double major in mathematics and applied mathematics. My research partner, Hilary Spring, and I completed this paper as part of a Research Experience for Undergraduates at the Rose-Hulman Institute of Technology under the supervision of Dr. Kurt Bryan. We presented the work at the Undergraduate Poster Session during the Joint Mathematics Meeting in San Antonio and won a prize for the work.

Hilary Spring is a senior at Mount Holyoke College in South Hadley, Massachusetts. She will graduate with an AB in Mathematics and Philosophy in May 2006. The work in this paper was completed during the summer of 2005 at the Rose Hulman Institute of Technology under the guidance of Kurt Bryan, and made possible by an NSF-REU grant 0352940.