### Lecture 14 - First Principles Modeling - PDE Case Study

Lecture 13 demonstrated a first principles model with lumped species and energy balances. For Lecture 14, an example problem in modeling and model-based control is demonstrated with a model that includes both spatial distribution and time dependence. With both space and time, the resulting model is a partial differential equation. This model is discretized in space to produce a set of ordinary differential equations. A heated rod as a simplification of friction stir welding tools is used for this case study.

#### Case Study on Friction Stir Processing

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