thermodynamicsPDEs

The Heat Equation Explained

How temperature diffuses through materials — from cooking pans to CPU cooling and climate models.

7 min read · 2026-06-11

Fourier's heat equation ∂u/∂t = α∇²u says temperature smooths out over time. Hot spots spread; gradients flatten.

The same mathematics appears in Brownian motion, option pricing, and image blurring.

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