Physics

Heat Equation

The heat equation describes how temperature spreads out over time. Here it plays out in a room: a radiator warms one corner, a cold window chills another, and heat diffuses between them. Drag inside to add your own heat.

Temp at cursor
Thermometer
coldhot

Orange = radiator (hot), blue strip on the right = window (cold), walls sit at room temperature. In Paint heat mode, drag inside to add heat; in Thermometer mode, drag the white ring to probe a point.

What to observe

  1. Drop the thermometer next to the radiator: its temperature shoots up fast, then levels off as the region around it warms and the gradient driving the flow shrinks.
  2. Place it midway between radiator and window. It settles at a steady in-between value: heat flows continuously through it from hot to cold (steady state, not "no flow").
  3. Lower the diffusivity and reset. The same final picture emerges, but the thermometer curve rises far more slowly: diffusivity sets the timescale, not the destination.

Shortcuts: space run/pause · s step · r reset · f fullscreen