# /MAT/LAW18 (THERM)

Block Format Keyword This law describes thermal material.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW18/mat_ID or /MAT/THERM/mat_ID
mat_title
${\rho }_{i}$ ${\rho }_{0}$
$\rho {\text{ }}_{0}{C}_{p}$ A B
fct_IDT T0 FscaleT
fct_IDsph fct_IDas Fscalesph FscaleE FscaleK

## Definitions

Field Contents SI Unit Example
mat_ID Material identifier

(Integer, maximum 10 digits)

mat_title Material title

(Character, maximum 100 characters)

${\rho }_{i}$ Initial density

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
${\rho }_{0}$ Reference density used in E.O.S (equation of state).

Default ${\rho }_{0}$ = ${\rho }_{i}$ (Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
$\rho {\text{ }}_{0}{C}_{p}$ Specific heat

(Real)

$\left[\frac{\text{kg}}{{\text{s}}^{3}\cdot \text{m}\cdot \text{K}}\right]$
A Conductivity coefficient A

(Real)

$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$
B Conductivity coefficient B

(Real)

fct_IDT Function f(t) identifier for T. 9
= 0
T is computed
= n
T=T0f(t)

(Integer)

T0 Initial temperature

Default = 300K (Real)

$\left[\text{K}\right]$
FscaleT Time scale factor

(Real)

fct_IDsph Function g(T, E) identifier for temperature versus energy. 7

(Integer)

fct_IDas Function h(k, T) identifier for conductivity versus temperature.

(Integer)

Fscalesph Temperature scale factor.

(Real)

$\left[\text{K}\right]$
FscaleE Energy scale factor.

(Real)

$\left[\text{J}\right]$
FscaleK Conductivity scale factor.

(Real)

$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$

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

Where, ${C}_{p}$ is the heat capacity at constant pressure.

4. The $k$ (thermal conductivity) is given by curve $fct\text{​}_\text{​}I{D}_{as}=k\left(T\right)$ .
5. The α (thermal diffusivity) is computed with curve fct_IDsph $\alpha =k/{\rho }_{0}{C}_{p}$ with, $\frac{dE}{dT}={C}_{p}$ .
6. Function g(T, E) is similar to the following curve:
7. If fct_IDsph ≠ 0,(3)
${E}_{specific}=\frac{{E}_{\mathrm{int}}}{{\rho }_{0}}}{Fscal{e}_{E}}$

$T={\mathrm{f}}_{sph}\left({E}_{specific}\right)\cdot Fscal{e}_{sph}$

Where, ${\mathrm{f}}_{sph}$ is the function of fct_IDsph.

8. If fct_IDsph = 0,(4)
$T=\frac{{E}_{\mathrm{int}}}{\mathit{sph}}$

with $Sph={\rho }_{0}{C}_{p}=SpecificHeat$

9. If fct_IDT ≠ 0,(5)
$T=\mathrm{f}\left(Time\right)\cdot {T}_{0}$

with $Time=Time\cdot Fscal{e}_{T}$ ; ${E}_{\mathrm{int}}=T\cdot sph$ .

10. If fct_IDas ≠ 0,
(6)
$T=\frac{T}{Fscal{e}_{sph}}$

$A={\mathrm{f}}_{as}\left(T\right)\cdot Fscal{e}_{E}$ ; $B=0$

Where, ${\mathrm{f}}_{as}$ is the function of fct_IDas.