Modeling heat flow in a thermos : an honors thesis (HONRS 499)

The purposes of this thesis are to demonstrate several powerful mathematical techniques such as Fourier Series and the Method of Separation of Variables by exploiting a simple problem and to illustrate an example that should be accessible to most students who are familiar with second and third semester calculus. A mathematical formula (called the heat equation), which describes temperature in a rod, will be derived from general principles. This heat equation will then be used to model a simple physical system, namely a thermos filled with ice-cold lemonade. Finally, the correctness of the mathematical model will be experimentally determined. The experiments conducted will test the correctness of the model both within and beyond the constraints of the simplifying assumptions made to derive the model.