Thermal Diffusivity: How Fast the Heat Actually Gets Through

Conductivity says how much heat flows once a wall is steady. This lab is about the wait before that. One face of the slab is stepped to 120 C, the far face is held at 20 C, and the solid curve is the temperature through the slab right now — drawn against the dashed straight line that Fourier's law assumes. The clock is the Fourier number, so the same setting is the same picture for every material; only the seconds differ. The six presets are idealised triples that behave like a material, not measurements of one — the still-air-like triple runs about 15 % above the published figure for air, and it says so below.

Thermal conductivity1.000 W/(m K)

Density1995.3 kg/m3

Volumetric heat capacity1.7957 MJ/(m3 K)

Thermal effusivity1340 J/(m2 K sqrt(s))

Fourier number0.100

Time now29.93 min

Time to half way28.34 min

Flux out of the far face29.3 %

Energy stored69.8 %

Steady-state heat flux1000.0 W/m2

The bandThe shaded band between the two curves is the temperature rise the slab has not made yet: at mid-depth it reads 46.3 C against the steady-state 70.0 C.

Thermal diffusivity α = k/(ρc)

0.5569 mm2/s

Time to 99 per cent t = 0.4911 L²/α

2.450 h

Mid-depth now T at x = L/2

46.3 C

Where the slab has got to

Past half way

Thermal conductivity1.000 W/(m K)

Density1995.3 kg/m3

Specific heat capacity900 J/(kg K)

Slab thickness100 mm

Time · Fourier number0.100

The two face temperatures are fixed at 20 C and 120 C: the temperature difference cancels out of every figure here, so a slider for it would change nothing. Thickness does not change the diffusivity either — it changes only the clock, as L squared. The three percentages are each rounded on their own and are not presented as a sum.