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

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.

Prepro: LRACO.F
Lagamine: RACO1.F

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

1

3