Mathematical optimization of heat conduction algorithms

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For many industrial and scientific applications, it is important to know an object's thermal conductivity, which is essentially a measure resistance to heat flow. in a laboratory or manufacturing setting, the ideal measurement of conductivity is both rapid and non-destructive. One proven method to measure conductivity involves applying a controlled heat source to an object and then measuring how its temperature changes with time. If one has a robust theoretical understanding heat flow in the object, one can infer fundamental thermal properties from the measured time-dependent temperature profile. The purpose of this project is to use modern symbolic computation algorithms to validate current theoretical models for the thermal response of industrially-interesting objects, derive new models for different objects, and to facilitate the comparison of theoretical predictions with experimental results. The research will be undertaken in collaboration with the Fredericton-based company C-Therm, which specializes in non-destructive thermal sensor technology.