Table of Contents

RACO

Description

Constitutive law for convection and radiation for elements CONRA and CORA3.
Last revision: L. Grisard - sept 1990

The model

Non linear thermal analysis of solids. This constitutive law takes account of heat transfer between the solid and the external world by convection and radiation. The coefficients of convection and radiation may be defined as functions of temperature.

Files

Prepro: LRACO.F
Lagamine: RACO1.F

Subroutines

FileSubroutineDescription
RACO1.F RACO1Main subroutine of the law

Availability

Plane stress state YES
Plane strain state YES
Axisymmetric state YES
3D state YES
Generalized plane state YES

Input file

Parameters defining the type of constitutive law

Line 1 (2I5, 60A1)
ILLaw number
ITYPE 120
COMMENT Any comment (up to 60 characters) that will be reproduced on the output listing

Integer parameters

1 line (I5)
NTEMPNumber of temperatures at which material data are given

Real parameters

1 line repeated NTEMP times (3G10.0)
T Temperature
CONVECConvection coefficient at temperature T (h)
RADIA Radiation coefficient at temperature T (σε with σ=Boltzmann's constant; ε=emissivity)

Remarks about emissivity ε

RADIA = $\sigma\varepsilon$ but sometimes $\varepsilon \rightarrow 1-\varepsilon$

\[\frac{2\varepsilon}{2-\varepsilon}\] $\varepsilon$ no RAYON (ECHRA) elements
\[\frac{1}{\frac{1-\varepsilon}{\varepsilon}+1}=\frac{\varepsilon}{1-\varepsilon+\varepsilon}=\varepsilon\] with RAYON (ECHRA) elements (leak flow)
\[\frac{1}{2\frac{1-\varepsilon}{\varepsilon}+1}=\frac{\varepsilon}{2-2\varepsilon+\varepsilon}=\frac{\varepsilon}{2-\varepsilon}\] Between 2 surfaces: \[\varepsilon_{12}^*=\frac{\varepsilon_1\varepsilon_2}{\varepsilon_1+\varepsilon_2-\varepsilon_1\varepsilon_2}\] \[\text{If }\varepsilon_1=\varepsilon_2=\varepsilon \Rightarrow \varepsilon_{12}^*=\frac{\varepsilon^2}{2\varepsilon-\varepsilon^2}=\frac{\varepsilon}{2-\varepsilon}\] with unique RAYON (ECHRA) element → view factor = 1
\[\frac{1}{2\frac{1-\varepsilon}{2\varepsilon}}=\frac{\varepsilon}{2-\varepsilon}\] $\varepsilon_1=\varepsilon_2$ without RAYON (ECHRA) element
General case: \[q_{pi}=\frac{A_i\varepsilon_i}{1-\varepsilon_i}\sigma(T_i^{*4}-T_p^4)\] \[q_{ij}=\sigma A_i F_{ij}(T_j^{*4}-T_i^{*4})\] With $A_i F_{ij}$ computed by ECHRA
$T^*$ = Fictitious temperature taking into account the computation of radiosity

Stresses

Number of stresses

1

Meaning

SIG(NPI)Heat flow exchanged by convection and radiation

State variables

Number of state variables

3

List of state variables

Q(1)Temperature of the solid at the point under consideration ($= T$)
Q(2)Temperature of the external world ($= T_a$)
Q(3)$=h+\sigma \varepsilon \left(T^3_a+T^2_a*T+T_a*T^2+T^3\right)$