Mathematics
Partial Differential Equations and the Heat Equation Diffusion Model
Quick fact
The heat equation, also known as the diffusion equation, is a linear PDE that describes how heat (or any diffusing quantity) spreads over time. It says that the rate of temperature change at a point is proportional to the curvature of the temperature distribution at that point—so hot spots cool down and cold spots warm up as heat evens out.
Why this is interesting
If you heat one end of a metal rod, how does the temperature change along the rod over time? The answer to this everyday question is a partial differential equation called the heat equation, which models the flow of heat as a smooth, predictable process.