====== Heat Flux Material ======

<note important>
This Documentation refers to Metafor version >= 3593.
for more informations on changes see [[https://gitlab.uliege.be/am-dept/MN2L/oo_meta/-/merge_requests/167|MR !167]] for technical informations). 

for a Metafor version < 3593, please refers to this [[flux_pre3593|page]].
</note>

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.


{{ doc:user:elements:boundaries:heat_localcoord.png?400 |Coordonnées locales du la source de chaleur}}

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


===== Material =====


Therefore, the first step consist in defining an ''[[doc:user:elements:general:materials|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) 




==== UniformHeatFluxMaterial  ====

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.

=== Parameters ===
^   Name                                          ^     Description       ^  Dependency ^
| ''HEATFLUX_VALUE'' | Value of the heatFlux |  TM / TO / TX / TY / TZ |



==== RectangularHeatFluxMaterial  ====

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.

=== Parameters ===
^   Name                                          ^     Description       ^  Dependency ^
| ''HEATFLUX_VALUE'' | Value of the heatFlux |  TM / TO / TX / TY / TZ |
| ''HEATFLUX_A'' | dimension of the box in local X' direction  |  -  |
| ''HEATFLUX_B'' | dimension of the box in local Y' direction  |  -  |
| ''HEATFLUX_C'' | dimension of the box in local Z' direction (only for Source Elements. In Boundary elements, c = 1.0) \\ Be Carefull , there are No test if you define C in Boundary element  |  -  |
| ''HEATFLUX_NUM_AX_X'' | number of the Line defining the local X axis  |  -  |
| ''HEATFLUX_NUM_AX_Z'' | number of the Line defining the local Z axis (optional)  |  -  |
| ''HEATFLUX_RESCALE''  | option to enforce the rescaling of the heatFlux  |  -  |

==== EllipsoidHeatFluxMaterial  ====

The heat flux is given by an ellipsoidal distribution : 

<note important> Add Drawing </note>

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

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.

=== Parameters ===
^   Name                                          ^     Description       ^  Dependency ^
| ''HEATFLUX_VALUE'' | Value of the heatFlux |  TM / TO / TX / TY / TZ |
| ''HEATFLUX_A'' | Ellipsoid Half dimension in the local X' direction  |  TM / TX / TY / TZ  |
| ''HEATFLUX_B'' | Ellipsoid Half dimension in the local Y' direction  |  TM / TX / TY / TZ  |
| ''HEATFLUX_C'' | Ellipsoid Half dimension in the local Z' direction (only for Source Elements = 2 in boundary element) \\ Be Carefull , there are No test if you define C in Boundary element  |  TM / TX / TY / TZ  |
| ''HEATFLUX_NUM_AX_X'' | number of the Line defining the local X axis  |  -  |
| ''HEATFLUX_NUM_AX_Z'' | number of the Line defining the local Z axis (optional)  |  -  |
| ''HEATFLUX_RESCALE''  | option to enforce the rescaling of the heatFlux  |  -  |

==== DoubleEllipsoidHeatFluxMaterial  ====

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

<note important> Add Drawing </note>

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.

=== Parameters ===
^   Name                                          ^     Description       ^  Dependency ^
| ''HEATFLUX_VALUE'' | Value of the heatFlux |  TM / TO / TX / TY / TZ |
| ''HEATFLUX_A'' | Ellipsoid Half dimension in the local X' direction UPSTREAM |  TM / TX / TY / TZ  |
| ''HEATFLUX_AR'' | Ellipsoid Half dimension in the local X' direction DOWNSTREAM |  TM / TX / TY / TZ  |
| ''HEATFLUX_B'' | Ellipsoid Half dimension in the local Y' direction  |  TM / TX / TY / TZ  |
| ''HEATFLUX_C'' | Ellipsoid Half dimension in the local Z' direction (only for Source Elements = 2 in boundary element) \\ Be Carefull , there are No test if you define C in Boundary element  |  TM / TX / TY / TZ  |
| ''HEATFLUX_NUM_AX_X'' | number of the Line defining the local X axis  |  -  |
| ''HEATFLUX_NUM_AX_Z'' | number of the Line defining the local Z axis (optional)  |  -  |
| ''HEATFLUX_RESCALE''  | option to enforce the rescaling of the heatFlux  |  -  |