Heat Flux Material

Heat Flux Materials are sources of heat that can be applied on boundary of a mesh (Tm(2)boundary2D(3D)Element) or on the mesh (Tm(2)boundary2D(3D)Element) according to the physic (or its model) of the heat source.

Excepted to the UniformHeatFluxMaterial, the flux is linked to a spatial distribution functions related to a set of local coordinates {$x'$, $y'$, $z'$}, which are handled by the X, Y and Z Axis defined in the Material. The local Axis are Line Objects that are defined in the CurveSet and referred in the material by their number.

The distribution is following the movement of the Axis (translation/rotation), which is particularly useful for some applications (e.g. additive manufacturing).

Therefore, the first step consist in defining an MaterialProperties, as

mat = materset.define(no, matType )
mat.put(param1, value1)
mat.depend(param1, fct1, Lock1)) #optional

where param1 name of the property associated to the element (for example RAY_EMISSIVITY value1 value of the corresponding property fct1 function which characterises the dependency of the property (optional: no fct if no dependency) Lock1 Lock which defines the dependency variable of the property (compulsory if there is a dependency)

The heat flux is directly given by its value given in the Material Parameters $flux = Q$ with :

• $Q$ : Heat Flux (boundary : W/m² - Source : W/m³).

As the flux can depend on time, solid temperature, but also current position of the integration point, a distribution can be implemented through dependency function.

The heat flux is given by its value given in the Material Parameters $flux = Q / vol$ if inside a rectangular box (2D or 3D) and $flux = 0$ outside the box.

with :

• $Q$ : Heat Flux (boundary : W/m² - Source : W/m³).
• $vol$ : Volume of the box : $vol = c 2a 2b$

As the flux can depend on time, solid temperature, but also current position of the integration point, a distribution can be implemented through dependency function.

The heat flux is given by an ellipsoidal distribution :

$flux = Q \frac{6 \sqrt{3}}{a b c \pi sqrt{\pi}} exp^{(-xpart-ypart-zpart)}$

with :

• $Q$ : Heat Flux (boundary : W/m² - Source : W/m³).
• $a$ - $b$ - $c$ : Half diameter of the ellipsoid (related to local axis)
• $xpart = 3(\frac{x'}{a})^2$ : distribution parameter in first ellipsoid direction
• $ypart = 3(\frac{y'}{b})^2$ : distribution parameter in second ellipsoid direction
• $zpart = 3(\frac{z'}{c})^2$ : distribution parameter in third ellipsoid direction

As the flux can depend on time, solid temperature, but also current position of the integration point, a distribution can be implemented through dependency function.

The heat flux is given by an ellipsoidal distribution wit upstream and downstream different size coefficient (inclined heat source according to first local axis)

upstream ($x' >= 0$) :

• $flux = Q \frac{2a}{a+ar} \frac{6 \sqrt{3}}{a b c \pi sqrt{\pi}} exp^{(-xpart-ypart-zpart)}$

DownStream ($x' < 0$) :

• $flux = Q \frac{2ar}{a+ar} \frac{6 \sqrt{3}}{ar b c \pi sqrt{\pi}} exp^{(-xpartR-ypart-zpart)}$

with :

• $Q$ : Heat Flux (boundary : W/m² - Source : W/m³).
• $a$ - $b$ - $c$ : Half diameter of the ellipsoid (related to local axis)
• $xpart = 3(\frac{x'}{a})^2$ : distribution parameter in first ellipsoid direction upstream
• $xpartR = 3(\frac{x'}{ar})^2$ : distribution parameter in first ellipsoid direction downstream
• $ypart = 3(\frac{y'}{b})^2$ : distribution parameter in second ellipsoid direction
• $zpart = 3(\frac{z'}{c})^2$ : distribution parameter in third ellipsoid direction

As the flux can depend on time, solid temperature, but also current position of the integration point, a distribution can be implemented through dependency function.