5. C modeling

5.1. Characteristics of modeling

Modeling PLAN_DIAG :

5.2. Characteristics of the mesh

20 QUAD8

5.3. note

The latent heat of fusion is provided via enthalpy over an interval of \(0.01°C\).

The mass matrix is diagonalized to limit oscillations.

5.4. Tested values

The observed nodes have the coordinate \(y=0.0\)

Identification temperature	Reference
t = 0.5 s N6 (x = 0.005)	682.43
t = 1.0 s N6 (x = 0.005)	661.33
t = 3.0 s N6 (x = 0.005)	628.20
t = 6.0 s N6 (x = 0.005)	614.25
t = 0.5 s N11 (x = 0.010)	726.05
t = 1.0 s N11 (x = 0.010)	705.75
t = 3.0 s N11 (x = 0.010)	669.63
t = 6.0 s N11 (x = 0.010)	647.49
t = 0.5 s N16 (x = 0.015)	738.11
t = 1.0 s N16 (x = 0.015)	728.70
t = 3.0 s N16 (x = 0.015)	696.06
t = 6.0 s N16 (x = 0.015)	673.22
t = 0.5 s N21 (x = 0.020)	739.86
t = 1.0 s N21 (x = 0.020)	737.22
t = 3.0 s N21 (x = 0.020)	714.94
t = 6.0 s N21 (x = 0.020)	692.06

The finite element calculation requires a discretization in time of \(\Delta t=5.{10}^{-4}s\) at least for the first steps. The originally imposed boundary condition causing the temperature to suddenly change from \(740.°C\) to \(580.°C\). At the level of the first steps of time, some oscillations are observed which then stabilize quite quickly, despite everything the maximum temperature is exceeded, there is no respect for the discreet maximum. This phenomenon is observed during thermal shocks; only a particular numerical treatment at the level of the mass matrix can remedy the latter.