ARCTIC SYSTEMSHEAT TRANSFER · METHODS & VERIFICATION

Arctic Systems / Heat Transfer

TECHNICAL DOCUMENTATION / PHYSICS

One energy balance.
Two thermal regimes.

Heat conduction in a stationary medium, with local equilibrium freezing and thawing represented through volumetric enthalpy.

Conservation and Fourier conduction

∂H(T)/∂t + ∇·q = Q
q = −k(T) ∇T

H is volumetric enthalpy [J/m³], q is heat flux [W/m²], Q is a volumetric source [W/m³], and k is scalar thermal conductivity [W/(m·K)]. Temperature differences use kelvin; temperature fields are displayed in degrees Celsius.

Latent heat belongs in the energy

H(T) − H(T₀) = ∫T₀T Csens(τ) dτ + Lv[f(T) − f(T₀)]
Capp(T) = dH/dT = Csens(T) + Lv df/dT

Here f is the fraction of the freezable water that is liquid, and Lv is the latent energy per bulk volume. The implemented model uses Lv = ρwL(θtotal − θresidual), with water-equivalent volumetric contents. Sensible heat capacity and conductivity interpolate between their frozen and thawed values.

The time step uses the change of H, rather than approximating it by one heat-capacity value multiplied by a temperature jump. Capp also enters the nonlinear derivative.

From this balance to discrete equations →