Mammoth snow lab - 2D cross-section

Heat conduction with phase change

The enthalpy per volume H combines sensible and latent heat: H = ρ c_s T for T < 0 (ice), 0 ≤ H ≤ ρ L at T = 0 (a mushy mix of ice and water, liquid fraction f = H / ρ L) and H = ρ L + ρ c_l T when fully liquid, with L = 334 kJ/kg. Heat flows by Fourier's law, ∂H/∂t = ∇ · (k ∇T). Because the front never needs to be tracked explicitly, melting and refreezing are handled by the same update; the snow stays at exactly 0 °C while its latent heat is being paid.

Snow properties and the carcass

The thermal conductivity of snow grows with density, k = 2.22 (ρ/1000)^1.88 W/m/K (Yen, 1981), so fresh snow insulates far better than old firn. The carcass is one lumped body of heat capacity C = ρ_b c_b π a² (3.5 MJ/m³/K) at a uniform temperature that exchanges heat with the neighbouring snow cells and may add a decay heat q (W/m³). The top boundary is convective, q = h (T_air - T) with a day-night air temperature T_air(t) = T_mean + A sin(2π t / 1 day) + the half-cell conduction resistance; the bottom is frozen ground at a fixed temperature, the sides are mirror planes.

For the check, the one-phase Stefan problem (solid at the melting point, wall at T_w) has the exact Neumann front s = 2 λ √(αt) with λ e^λ² erf λ = St / √π and St = c T_w / L.

Honest simplifications: liquid water does not percolate or drain (real meltwater runs down and refreezes, which is the real "migration"), liquid and ice share one conductivity, there is no radiation or wind or snowfall, the carcass is a single lumped temperature body in a 2D slice with no fat layer or insulation, and the cells are 8 cm wide so the front is smeared over about one cell.

• Run Warm carcass in cold snow and watch the carcass temperature fall as its heat melts a pocket of snow.
• Switch to Spring thaw: the day-night cycle melts and refreezes the surface layer while the carcass slowly adds heat from below.
• Raise the snow density: the pocket grows faster because denser snow conducts better but also needs more latent heat per volume.
• Add decay heat and compare the melted area after the same time.