1. Reference problem#

1.1. Geometry#

_images/10000CBE0000313200000FD00F25CA2D7CA2FD7F.svg

1.2. Material properties#

These are the characteristics of aluminum indicated by s for the solid phase and by l for the liquid phase. They are assumed to be constant within each phase.

Density

\({\rho }_{S}=2550\mathrm{kg}/{m}^{3}\)

\({\rho }_{1}=2390\mathrm{kg}/{m}^{3}\)

Volume heat

\({c}_{S}=3.{10}^{6}J/{m}^{3}°C\)

\({c}_{1}=2.58{10}^{6}J/{m}^{3}°C\)

Thermal conductivity

\({k}_{S}=210W/m°C\)

\({k}_{1}=95W/m°C\)

Latent heat of fusion

\(L=437.44{10}^{-3}\mathrm{J.kg}\)

Melting temperature

\({T}_{m}=660.°C\)

Volume enthalpy change

\(\Delta H=1.08048{10}^{9}J/{m}^{3}\)

1.3. Boundary conditions and loads#

Temperature imposed at the extremities.

\({T}_{0}=580°C\) in \(x=0\)

\({T}_{i}=740°C\) in \(x=l\)

1.4. Initial conditions#

Uniform initial temperature

\({T}_{\mathrm{init}}={T}_{i}=740°C\)