Mathematical optimization of heat conduction algorithms

对于许多工业和科学应用来说，了解物体的导热系数是很重要的，它本质上是对热流阻力的测量。在实验室或制造环境中，电导率的理想测量既快速又无损。一种已被证实的测量电导率的方法是，对物体施加受控热源，然后测量其温度随时间的变化情况。如果一个人对物体的热流有扎实的理论认识，他就可以从测量的随时间变化的温度分布中推断出基本的热性质。本项目的目的是使用现代符号计算算法来验证工业感兴趣物体热响应的现有理论模型，推导不同物体的新模型，并促进理论预测与实验结果的比较。该研究将与总部位于弗雷德里克顿的C-Therm公司合作进行，该公司专门从事非破坏性热传感器技术。

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.