Is this PDE demo intelligible?

[mcmcclur]

I’ve categorized this post as “Show and tell” but, perhaps, it should be “Show and ask”. Basically, I’ve written some examples that illustrate the conduction of heat in two dimensions and I wonder how broadly accessible they are. This was originally written for students taking a class in Partial Differential Equations but, really, a general understanding based on physical intuition should be more broadly accessible. So, I’ve repackaged it a bit and wonder - is the result intelligible to folks here.

Here’s the notebook:

Illustrations of two-dimensonal heat flow

This is part of a series of notebooks that I’ll publish more broadly soon.

I guess I should include a poll:

• Yes, totally clear
• Not really clear but cool
• Wish I would’ve stayed in bed

[andreasplesch]

Nice illustration of heat flow. A good appetizer. I found myself looking for a short motivation why the equations should describe heat flow. Why use the Laplacian ? Also, perhaps it is worth explaining that the code does not solve equations, it uses precomputed solutions.

[chonghorizons]

The real cool part is if you give extra credit to your students if they run their own simulation and create their own observableHQ.

They should be able to do that just by

1. forking your notebook
2. loading their own JSON data, making sure to match your JSON data’s format.

There might also be an error. In 3D mode, the temperature is offsetting the z-axis.

The bar with a hole is no longer flat.

The pringle starts out more conical: