Latent heat

Methods

Latent heat (of crystallisation) can be implemented as a source term (usually numerically not very stable):

GeoParams.MaterialParameters.LatentHeat.ConstantLatentHeat Type

ConstantLatentHeat(Q_L=400kJ/kg)

Set a constant latent heat:

$$Q_L=cst$$

where $Q_L$ is the latent heat [$J/kg$].

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Alternatively, you can implement it by modifying the heat capacity, which is often numerically better.

GeoParams.MaterialParameters.HeatCapacity.Latent_HeatCapacity Type

Latent_HeatCapacity(Cp=ConstantHeatCapacity(), Q_L=400kJ/kg)

This takes the effects of latent heat into account by modifying the heat capacity in the temperature equation:

$$\rho C_p^{\text{new}}\frac{\partial T}{\partial t}=\frac{\partial }{\partial x_i}\left(k\frac{\partial T}{\partial x_i}\right)+H_s$$

with

$$C_p^{\text{new}}=C_p+\frac{\partial \varphi }{\partial T}{Q}_L$$

where $Q_L$ is the latent heat [$J/kg$], and $\frac{\partial \varphi }{\partial T}$ is the derivative of the melt fraction with respect to temperature

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