I threw twelve different blocks of cheese in the microwave last weekend. Here is video of five of them, 1-cm, 2-cm, 3-cm, 4-cm, and 5-cm cubes:
My goal is to use those data to predict how long it'll take this guy to fully melt:
For fun, I also threw in two blocks with the same surface area and two blocks with the same volume, just to test out my two prevailing hypotheses, neither of which played out.
Here are the numbers in a Google spreadsheet. You could help me out by coming up with a model that fits the data well and (especially) explaining why your model makes sense in the world of microwaving cheese. I'll post my own model as a spoiler in the comments. I have no idea why it works, though.