2D heat equation ∂T/∂t = α∇²T — click to add heat
The heat equation ∂T/∂t = α∇²T describes diffusive thermal transport. The thermal diffusivity α = k/(ρcₚ) combines conductivity k, density ρ, and specific heat cₚ. Higher α means faster heat spreading. In 2D, an initial point source spreads as a Gaussian with σ² = 4αt — click the canvas to place heat sources.