Coffee Cooling Race: Heat-Transfer Model of Cup Materials (2D)

The 3D original lets you pick from four preset cooling-rate buttons labelled by cup type — the numbers behind "Thermos" or "Metal can" are hand-picked constants with no visible derivation. This 2D companion builds the cooling constant instead of assuming it: a wall's thickness and thermal conductivity combine with an ambient convective coefficient (set by the still-air / breeze / fan buttons) into an overall transfer coefficient U = 1/(d/λ + 1/h), which combines with the liquid's mass, specific heat and exposed surface area into Newton's cooling constant k = UA/(mc_p). Ceramic and steel share that conduction-plus-convection model but differ in λ and wall thickness, so blowing a fan on them visibly speeds both up — while the vacuum thermos is modelled on a different, physically correct basis: its evacuated double wall suppresses conduction and convection almost entirely, so its curve is capped by a small, near-fixed radiative-limited U that barely reacts to the airflow slider at all. Racing all three from the same starting temperature makes that qualitative difference — not just a different number — directly visible.