Fourier Number

The Fourier number is dimensionless time: how far a thermal disturbance has diffused compared with the size of the object. It is normally written Fo = αt/L² with the thermal diffusivity α = k/(ρc), but diffusivity has no entry in this calculator's unit picker, so the group is spelled out as kt/(ρcL²) — identical physics, and it has the pleasant side effect of showing where the diffusivity comes from. High-k, low-ρc materials diffuse heat fast: copper's α is 1.1 × 10⁻⁴ m²/s, steel's 1.2 × 10⁻⁵, brick's 5 × 10⁻⁷, and that thousand-fold spread is why a copper pan responds instantly and a masonry wall takes half a day.

Fo ≈ 1 is the rough marker for "the disturbance has crossed the body". Below Fo = 0.2 the one-term approximations in the textbook charts are not valid and you need the full series; above about 1 the transient is essentially over. Worked example: a 100 mm steel plate (L = 0.05 m half-thickness, k = 45, ρ = 7850, c = 480) after 10 minutes has Fo = 45 × 600/(7850 × 480 × 0.0025) = 2.87, thoroughly soaked through. The same plate in firebrick would need most of a day. This is the number behind cooking times, heat-treat soak schedules and the thermal-mass lag that lets a stone building coast through an afternoon.