1. Reference problem

1.1. Geometry

1.2. Material properties

The material has the following thermal characteristics:

Thermal conductivity: \({k}_{s}=6\mathrm{kJ}/h/m/°K\)

enthalpy volume change: \(\Delta H=2.4105\mathrm{kJ}/{m}^{3}\),

and the following characteristics relating to moisturizing behavior:

Heat by hydration level: \({Q}_{0}=1.4904105\mathrm{kJ}/{m}^{3}\)

Arrhenius constant: \(\mathrm{Ar}=4000/°K\).

Note:

The Arrhenius constant is always expressed in degrees Kelvin. Temperatures are expressed in \(°C\).

Affinity as a function of hydration:

Degree of hydration \(h\)	Affinity \(A(h)(1/h)\)
0	6510
0.008	6360
0.016	2485
0.019	2460
0.038	9520
0.047	21800
0.08	37600
0.138	51600
0.232	51400
0.351	28200
0.44	16100
0.5	11700
0.63	5570
0.73	4240
0.81	1780
0.88	302
0.97	50
1.00	0

1.3. Boundary conditions and loads

A zero heat flux is imposed on all faces of the solid. Charging is only initiated by a heat source dependent on hydration \(\Delta Q={Q}_{0}\Delta h\).

1.4. Initial conditions

The initial temperature is \(20.9°C\)

1.5. Discretization in time

The explicit integration of hydration requires fine temporal discretization until the end of the hydration phenomenon:

From \(t=0\) to \(t=\mathrm{20h}\), \(\Delta t=\mathrm{7,5}\mathrm{min}\) is 160 steps.

From \(t=\mathrm{20h}\) to \(t=\mathrm{60h}\), \(\Delta t=1h\) is 40 steps.