The Phase Change Material node is used to solve the heat equation after specifying the properties of a phase change material according to the
apparent heat capacity formulation.
Instead of adding a latent heat L in the energy balance equation exactly when the material reaches its phase change temperature
Tpc, it is assumed that the transformation occurs in a temperature interval between
Tpc − ΔT ⁄ 2 and
Tpc + ΔT ⁄ 2. In this interval, the material phase is modeled by a smoothed function,
θ, representing the fraction of phase before transition, which is equal to 1 before
Tpc − ΔT ⁄ 2 and to 0 after
Tpc + ΔT ⁄ 2. The density,
ρ, and the specific enthalpy,
H, are expressed by:
where the indices ph1 and
ph2 indicate a material in phase 1 or in phase 2, respectively. Differentiating with respect to temperature, this equality provides the following formula for the specific heat capacity:
Here, θ1 and
θ2 are equal to
θ and
1−θ, respectively. The mass fraction,
αm, is defined from
ρph1,
ρph2 and
θ according to:
It is equal to −1 ⁄ 2 before transformation and
1 ⁄ 2 after transformation. The specific heat capacity is the sum of an equivalent heat capacity
Ceq:
Finally, the apparent heat capacity, Cp, used in the heat equation, is given by:
