Heat Transfer Simulation

Heat moves in three ways, and this simulation gives each its own bench. Conduction: a metal bar runs between a hot and a cold bath, and the temperature along it is computed from the heat equation, so you can watch the profile bend towards a straight line. Copper gets there in minutes; oak would take days, because the time scale is the length squared divided by the thermal diffusivity. Take the lagging off and the bar loses heat from its sides, so the steady profile sags into a cosh curve.

Convection: a fluid layer heated from below stays perfectly still until the Rayleigh number — buoyancy against viscosity and thermal diffusion — passes 1708; then convection rolls form and the Nusselt number, the heat carried relative to conduction alone, climbs. Switch gravity off and nothing moves. Radiation: two plates face a hot lamp; the irradiance falls with the square of the distance, and each plate settles where what it absorbs equals what it radiates. Surfaces matter: white paint stays cool, polished metal runs hot.