/MAT/LAW18 (THERM)

Block Format Keyword This law describes thermal material.

Format

(1)	(2)	(3)	(4)	(5)	(7)
/MAT/LAW18/`mat_ID` or /MAT/THERM/`mat_ID`
`mat_title`
$ρ_{i}$ $ρ_{i}$		$ρ_{0}$ $ρ_{0}$
$ρ_{0} C_{p}$ $ρ_{0} C_{p}$		`A`		`B`
`fct_ID`_T	`T`₀		`Fscale`_T
`fct_ID`_sph	`fct_ID`_as	`Fscale`_sph		`Fscale`_E	`Fscale`_K

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier (Integer, maximum 10 digits)
`mat_title`	Material title (Character, maximum 100 characters)
$ρ_{i}$ $ρ_{i}$	Initial density (Real)	$[\frac{kg}{m^{3}}]$ $[\frac{kg}{m^{3}}]$
$ρ_{0}$ $ρ_{0}$	Reference density used in E.O.S (equation of state). Default $ρ_{0}$ $ρ_{0}$ = $ρ_{i}$ $ρ_{i}$ (Real)	$[\frac{kg}{m^{3}}]$ $[\frac{kg}{m^{3}}]$
$ρ_{0} C_{p}$ $ρ_{0} C_{p}$	Specific heat (Real)	$[\frac{kg}{s^{3} \cdot m \cdot K}]$ $[\frac{kg}{s^{3} \cdot m \cdot K}]$
`A`	Conductivity coefficient A (Real)	$[\frac{W}{m^{2} K}]$ $[\frac{W}{m^{2} K}]$
`B`	Conductivity coefficient B (Real)
`fct_ID`_T	Function `f(t)` identifier for T. 9 = 0 `T` is computed = n `T`=`T`₀⋅`f`(`t`) (Integer)
`T`₀	Initial temperature Default = 300K (Real)	$[K]$ $[K]$
`Fscale`_T	Time scale factor (Real)
`fct_ID`_sph	Function g(T, E) identifier for temperature versus energy. 7 (Integer)
`fct_ID`_as	Function h(k, T) identifier for conductivity versus temperature. (Integer)
`Fscale`_sph	Temperature scale factor. (Real)	$[K]$ $[K]$
`Fscale`_E	Energy scale factor. (Real)	$[J]$ $[J]$
`Fscale`_K	Conductivity scale factor. (Real)	$[\frac{W}{m^{2} K}]$ $[\frac{W}{m^{2} K}]$

Comments

This material can be used:
- as purely thermal material (only Line 4 is read)
- as boundaries conditions (temperature or flux) (use Line 5)
The $k$ $k$ (thermal conductivity) is computed as:(1)
$k = A + B \cdot T$ $k = A + B \cdot T$
The α (thermal diffusivity) is computed as:(2)
$α = k / ρ_{0} C_{p}$ $α = k / ρ_{0} C_{p}$

Where, $C_{p}$ $C_{p}$ is the heat capacity at constant pressure.
The $k$ $k$ (thermal conductivity) is given by curve $f c t _ I D_{a s} = k (T)$ $f c t _ I D_{a s} = k (T)$ .
The α (thermal diffusivity) is computed with curve fct_ID_sph $α = k / ρ_{0} C_{p}$ $α = k / ρ_{0} C_{p}$ with, $\frac{d E}{d T} = C_{p}$ $\frac{d E}{d T} = C_{p}$ .
Function g(T, E) is similar to the following curve:

Figure 1.
If fct_ID_sph ≠ 0,(3)
$E_{s p e c i f i c} = \frac{\frac{E_{int}}{ρ_{0}}}{F s c a l e_{E}}$ $E_{s p e c i f i c} = \frac{\frac{E_{int}}{ρ_{0}}}{F s c a l e_{E}}$

$T = f_{s p h} (E_{s p e c i f i c}) \cdot F s c a l e_{s p h}$ $T = f_{s p h} (E_{s p e c i f i c}) \cdot F s c a l e_{s p h}$

Where, $f_{s p h}$ $f_{s p h}$ is the function of fct_ID_sph.
If fct_ID_sph = 0,(4)
$T = \frac{E_{int}}{sph}$ $T = \frac{E_{int}}{sph}$

with $S p h = ρ_{0} C_{p} = S p e c i f i c H e a t$ $S p h = ρ_{0} C_{p} = S p e c i f i c H e a t$
If fct_ID_T ≠ 0,(5)
$T = f (T i m e) \cdot T_{0}$ $T = f (T i m e) \cdot T_{0}$

with $T i m e = T i m e \cdot F s c a l e_{T}$ $T i m e = T i m e \cdot F s c a l e_{T}$ ; $E_{int} = T \cdot s p h$ $E_{int} = T \cdot s p h$ .
If fct_ID_as ≠ 0,
(6)
$T = \frac{T}{F s c a l e_{s p h}}$ $T = \frac{T}{F s c a l e_{s p h}}$

$A = f_{a s} (T) \cdot F s c a l e_{E}$ $A = f_{a s} (T) \cdot F s c a l e_{E}$ ; $B = 0$ $B = 0$

Where, $f_{a s}$ $f_{a s}$ is the function of fct_ID_as.