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--- doc:user:elements:boundaries:flux [2026/07/29 19:48] – [RectangularHeatFluxMaterial] papeleux
+++ doc:user:elements:boundaries:flux [2026/07/29 20:13] (current) – [RectangularHeatFluxMaterial] papeleux
@@ Line 39: / Line 39: @@
 ==== UniformHeatFluxMaterial  ====
-The heat flux is directly given by its value given in the Material Parameters $flux = F$
+The heat flux is directly given by its value given in the Material Parameters $flux = Q$
 with :
-  * $F$ : Heat Flux (boundary : W/m² - Source : W/m³).
+  * $Q$ : 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.
@@ Line 53: / Line 53: @@
 ==== RectangularHeatFluxMaterial  ====
-The heat flux is given by its value given in the Material Parameters $flux = F$ if inside a rectangular box (2D or 3D) and $flux = 0$  outside the box.
+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 :
-  * $F$ : Heat Flux (boundary : W/m² - Source : W/m³).
+  * $Q$ : 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.
@@ Line 65: / Line 66: @@
 | ''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) \\
+| ''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  |  -  |
-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 :
-==== UniformHeatFluxMaterial  ====
+<note important> Add Drawing </note>
+$flux = Q \frac{6 \sqrt{3}}{a b c \pi sqrt{\pi}} exp^{(-xpart-ypart-zpart)}$
-The heat flux is directly given by its value given in the Material Parameters $flux = F$
 with :
-  * $F$ : Heat Flux (boundary : W/m² - Source : W/m³)
+  * $Q$ : 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 ($x' < 0$) :
+  * $flux = Q \frac{2ar}{a+ar} \frac{6 \sqrt{3}}{ar b c \pi sqrt{\pi}} exp^{(-xpartR-ypart-zpart)}$
-=== Description ===
+with :
-Thermal heat flux element in 2/3D, first or second order (thermal field of second order), that can be created on "boundary" geometries (//i.e.// curves in 2D and sides in 3D).
+  * $Q$ : Heat Flux (boundary : W/m² - Source : W/m³).
+  * $a$ - $b$ - $c$ : Half diameter of the ellipsoid (related to local axis)
-There are currently 4 different heat flux distributions types that are implemented for this element. These can be selected by using the ''HEATEL_TYPE'' parameter when defining the element properties.
+  * $xpart = 3(\frac{x'}{a})^2$ : distribution parameter in first ellipsoid direction upstream
+  * $xpartR = 3(\frac{x'}{ar})^2$ : distribution parameter in first ellipsoid direction downstream
-== Constant Distribution (=default) ==
+  * $ypart = 3(\frac{y'}{b})^2$ : distribution parameter in second ellipsoid direction
-Heat flux at each Gauss point is equal to ''HEATEL_VALUE'' [W/m$^2$].
+  * $zpart = 3(\frac{z'}{c})^2$ : distribution parameter in third ellipsoid direction
-  prp.put(HEATEL_TYPE, HEATEL_CONSTANT)
+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.
-== Rectangular Distribution ==
-Heat flux at each Gauss point is equal to a uniform distribution of the total heat $Q_{src}$ within a rectangular surface centered on the local heat flux coordinates
-$$
-  q = \frac{Q_{src}}{4a b}~~~\text{if } x'\in [-a,~a],~~ y'\in [-b,~b],
-$$
-where $a$ and $b$ are the half lengths of the rectangle in the $x'$ and $y'$ local coordinate directions respectively.
-  prp.put(HEATEL_TYPE, HEATEL_RECTANGULAR)
-== Ellipsoid Distribution ==
-Heat flux at each Gauss point is equal to an ellipsoid Gaussian distribution function of the total heat $Q_{src}$ centered on the local heat flux coordinates [Goldak //et. al.// 1986]
-$$
-q = \frac{Q_{src} 6\sqrt{3}}{ab \pi^\frac{3}{2}}~ e^{-3\left(\frac{x'}{a}\right)^2}~ e^{-3\left(\frac{y'}{b}\right)^2}
-$$
-where $a$ and $b$ are the semi-axes lengths of the ellipsoid in the $x'$ and $y'$ directions respectively.
-  prp.put(HEATEL_TYPE, HEATEL_ELLIPSOID)
-== Double Ellipsoid Distribution ==
-Modification of the ellipsoid Gaussian distribution function to account for a different distribution at the front  ($x'>=0$) and at the rear ($x'<0$) of the heat flux [Goldak //et. al.// 1986]
-$$
-q_f = f \frac{Q_{src} 6\sqrt{3}}{ab \pi^\frac{3}{2}}~ e^{-3\left(\frac{x'}{a}\right)^2}~ e^{-3\left(\frac{y'}{b}\right)^2}, ~~~~~~~~x'>=0
-$$
-$$
-q_r = (1-f) \frac{Q_{src} 6\sqrt{3}}{a_rb \pi^\frac{3}{2}}~ e^{-3\left(\frac{x'}{a_r}\right)^2}~ e^{-3\left(\frac{y'}{b}\right)^2}, x'<0
-$$
-where $a$ and $a_r$ are the front and rear semi-axes lengths in the $x'$ directions, $b$ is the semi-axis length in the $y'$ direction, and $f=\frac{ba}{a+a_r}$ is the balancing factor.
-  prp.put(HEATEL_TYPE, HEATEL_DOUBLE_ELLIPSOID)
 === 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  |  -  |
-^   Name                                          ^    Metafor Code      ^ Dependency  ^
-| Type of surface distribution                                        |   ''HEATEL_TYPE''    |       -     |
-| Total applied heat $Q_{src}$[W] \\ (heat per area for ''HEATEL_CONSTANT'')                              |  ''HEATEL_VALUE''  |    ''TO/TM''        |
-| Semi-axis Length ($a$)                     |   ''HEATEL_A''   |     -        |
-| Semi-axis Length ($b$)                     |   ''HEATEL_B''   |      -       |
-| Semi-axis Length ($a_r$)                     |   ''HEATEL_AR''   |      -       |
-| Number of integration points                  |   ''NIP''   |      -       |
-| Material Stiffness  \\ (STIFF_ANALYTIC - STIFF_NUMERIC) \\ only if element Stiffness == STIFF_ANALYTIC | ''MATERIALSTIFFMETHOD''  |      -       |
-==== Tm[2]HeatSource[2|3]DElement ====
-=== Description ===
-Thermal heat source element in 2/3D, first or second order (thermal field of second order), that can be created on "volume" geometries (//i.e.// sides in 2D and volumes in 3D).
-There are currently 4 different types of heat source distributions that are implemented for this element. These can be selected by using the ''HEATEL_TYPE'' parameter when defining the element properties.
-== Constant Distribution (=default) ==
-Heat source at each Gauss point is equal to ''HEATEL_VALUE'' [W/m$^3$].
-  prp.put(HEATEL_TYPE, HEATEL_CONSTANT)
-== Rectangular Distribution ==
-Heat source at each Gauss point is equal to a uniform distribution of the total heat $Q_{src}$ within a box volume centered on the local heat flux coordinates
-$$
-  q = \frac{Q_{src}}{8a b c}~~~\text{if } x'\in [-a,~a],~~ y'\in [-b,~b],~~ z'\in [-c,~c],
-$$
-where $a$, $b$ and $c$ are the half lengths of the rectangle in the $x'$, $y'$ and $z'$ local coordinate directions respectively.
-  prp.put(HEATEL_TYPE, HEATEL_RECTANGULAR)
-== Ellipsoid Distribution ==
-Heat source at each Gauss point is equal to an ellipsoid Gaussian distribution function of the total heat $Q_{src}$ centered on the local heat flux coordinates [Goldak //et. al.// 1986]
-$$
-q = \frac{Q_{src} 12\sqrt{3}}{abc \pi^\frac{3}{2}}~ e^{-3\left(\frac{x'}{a}\right)^2}~ e^{-3\left(\frac{y'}{b}\right)^2}~ e^{-3\left(\frac{z'}{c}\right)^2}
-$$
-where $a$, $b$ and $c$ are the semi-axes lengths of the ellipsoid in the $x'$, $y'$ and $z'$ directions respectively.
-  prp.put(HEATEL_TYPE, HEATEL_ELLIPSOID)
-== Double Ellipsoid Distribution ==
-Modification of the ellipsoid Gaussian distribution function to account for a different distribution at the front  ($x'>=0$) and at the rear ($x'<0$) of the heat flux [Goldak //et. al.// 1986]
-$$
-q_f = f \frac{Q_{src} 12\sqrt{3}}{ab \pi^\frac{3}{2}}~ e^{-3\left(\frac{x'}{a}\right)^2}~ e^{-3\left(\frac{y'}{b}\right)^2}~ e^{-3\left(\frac{z'}{c}\right)^2}, ~~~~~~~~x'>=0
-$$
-$$
-q_r = (1-f) \frac{Q_{src} 12\sqrt{3}}{a_rb \pi^\frac{3}{2}}~ e^{-3\left(\frac{x'}{a_r}\right)^2}~ e^{-3\left(\frac{y'}{b}\right)^2}~ e^{-3\left(\frac{z'}{c}\right)^2}, x'<0
-$$
-where $a$ and $a_r$ are the front and rear semi-axes lengths in the $x'$ directions, $b$ and $c$ are the semi-axes lengths in the $y'$ and $z'$ direction, and $f=\frac{ba}{a+a_r}$ is the balancing factor.
-  prp.put(HEATEL_TYPE, HEATEL_DOUBLE_ELLIPSOID)
-=== Parameters ===
-^   Name                                          ^    Metafor Code      ^ Dependency  ^
-| Type of volume distribution                                        |   ''HEATEL_TYPE''    |       -     |
-| Total applied heat $Q_{src}$[W]  \\ (heat per volume $q$[W/m$^3$] for ''HEATEL_CONSTANT'')                              |  ''HEATEL_VALUE''  |    ''TO/TM''        |
-| Semi-axis Length ($a$)                     |   ''HEATEL_A''   |     -        |
-| Semi-axis Length ($b$)                     |   ''HEATEL_B''   |      -       |
-| Semi-axis Length ($c$)                   |   ''HEATEL_C''   |       -      |
-| Semi-axis Length ($a_r$)                     |   ''HEATEL_AR''   |      -       |
-| Number of integration points                  |   ''NIP''   |      -       |
-| Material Stiffness  \\ (STIFF_ANALYTIC - STIFF_NUMERIC) \\ only if element Stiffness == STIFF_ANALYTIC | ''MATERIALSTIFFMETHOD''  |      -       |
-==== Tm[2]ConvectionHeatFlux[2|3]DElement ====
-<note important> **Metafor version >= 3545** </note>
-=== Description ===
-Thermal convection heat flux element in 2/3D, first or second order (thermal field of second order), that can be created on "boundary" geometries (//i.e.// curves in 2D and sides in 3D). These elements are particularly suited to model moving hot gas torches.
-These elements are similar to ''Tm[2]HeatFlux[2|3]DElement'' except that heat flux is computed as a convection boundary
-$$
-q = h(x',y')~(T_s - T_f),
-$$
-with the surface temperature $T_s$ and fluid temperature $T_f$ (''TEMP_FLUIDE''). The convection coefficient $h$ is a space-dependent quantity (in the local coordinates) which writes
-$$
-h(x',y')=A~\mathcal{f}(x',y'),
-$$
-where $A$ is the amplitude of the convection coefficient (''CONV_COEF'') and $\mathcal{f}\in [0,~1]$ is a spatial distribution function which can be selected using the ''HEATEL_TYPE'' parameter.
-== Rectangular Distribution ==
-Convection coefficient is equal to a constant value within a rectangular surface centered in the local coordinates axes and 0 outside the surface
-$$
-h(x',y') =\begin{cases}
- A~~\text{if}~~~ x'\in [-k_x,~k_x] ~~ \text{and} ~~ y'\in [-k_y,~k_y],\\
-~~~\text{else}.
-\end{cases}
-$$
-where $k_x$ and $k_y$ are the half lengths of the rectangle in the $x'$ and $y'$ directions respectively.
-   prp.put(HEATEL_TYPE, CONVHEATEL_RECTANGULAR)
-== Gaussian Distribution ==
-Convection coefficient is distributed with a Gaussian distribution as defined by [Zacherl //et. al.// 2023] centered on the local coordinates
-$$
-h(x',y') = A~e^{(-\left[ \frac{x'}{k_x} \right]^2 -\left[ \frac{y'}{k_y} \right]^2)},
-$$
-where $k_x$ and $k_y$ are concentration coefficients which define the slope of the curve in the $x'$ and $y'$ directions respectively.
-   prp.put(HEATEL_TYPE, CONVHEATEL_GAUSSIAN)
-== Modified Log-Normal  Distribution ==
-Convection coefficient is distributed with a modified log-normal distribution as defined by [Zacherl //et. al.// 2023] centered on the local coordinates
-$$
-h(x',y') = A~e^{(-[\text{ln}\left( \frac{|x'|}{k_x}+1 \right)]^2 -[\text{ln}\left( \frac{|y'|}{k_y}+1 \right)]^2)},
-$$
-where $k_x$ and $k_y$ are concentration coefficients which define the slope of the curve in the $x'$ and $y'$ directions respectively.
-   prp.put(HEATEL_TYPE, CONVHEATEL_LOGNORM)
-== Combined Distribution ==
-Allows to choose between a Gaussian or log-normal distribution in the front ($x' \geq 0$), rear ($x'<0$) and $y'$ directions. Convection coefficient is distributed as
-$$
-h(x',y') =\begin{cases}
- A~\mathcal{f}_{xf}(x',k_x)~\mathcal{f}_{y}(y',k_y) ~~~~~ x' \geq 0\\
- A~\mathcal{f}_{xr}(x',k_{xr})~\mathcal{f}_{y}(y',k_y) ~~~~ x' < 0.
-\end{cases}
-$$
-where distribution function $\mathcal{f}$ is either a Gaussian distribution (''CONVHEATEL_GAUSSIAN'')
-$$
-\mathcal{f_i} = e^{-\left[ \frac{i}{k_i} \right]^2},
-$$
-or a modified log-normal distribution (''CONVHEATEL_LOGNORM'')
-$$
-\mathcal{f_i} = e^{-[\text{ln}\left( \frac{|i|}{k_i}+1 \right)]^2}.
-$$
-Difference between these 2 distribution types is highlighted below for $k_i=1$.
-{{ doc:user:elements:boundaries:heat_GaussLogNorm.png?400 |Distribution Gaussienne v.s. Log-Normale avec k=1}}
-__Example:__ \\
-Modelling of an inclined hot gas torch in Automated Fiber Placement process (AFP).
-Convection heat flux element is modelled using a modified log-normal distribution at the rear and Gaussian distributions at the front and along $y'$.
-    # convection heat source (LogNorm - Gauss - Gauss)
-    prpHeat = ElementProperties(TmConvectionHeatFlux3DElement)
-    prpHeat.put(        HEATEL_TYPE,  CONVHEATEL_COMBINE)
-    prpHeat.put(        TEMP_FLUIDE,          p['T_HGT'])
-    prpHeat.put(          CONV_COEF,          p['HGT_A'])
-    prpHeat.put( CONVHEATEL_TYPE_XF,  CONVHEATEL_LOGNORM) #front
-    prpHeat.put(      CONVHEATEL_KX,         p['HGT_kf'])
-    prpHeat.put( CONVHEATEL_TYPE_XR, CONVHEATEL_GAUSSIAN) #rear
-    prpHeat.put(     CONVHEATEL_KXR,         p['HGT_kr'])
-    prpHeat.put(  CONVHEATEL_TYPE_Y, CONVHEATEL_GAUSSIAN) #y
-    prpHeat.put(      CONVHEATEL_KY,         p['HGT_ky'])
-=== Parameters ===
-^   Name                                          ^    Metafor Code      ^ Dependency  ^
-| Type of surface distribution                                        |   ''HEATEL_TYPE''    |       -     |
-| Distribution along $x'>=0$ \\ (only for ''HEATEL_TYPE'' = ''CONVHEATEL_COMBINE'')                                      |   ''CONVHEATEL_TYPE_XF''    |       -     |
-| Distribution along $x'<0$ \\ (only for ''HEATEL_TYPE'' = ''CONVHEATEL_COMBINE'')                                      |   ''CONVHEATEL_TYPE_XR''    |       -     |
-| Distribution along $y'$ \\ (only for ''HEATEL_TYPE'' = ''CONVHEATEL_COMBINE'')                                      |   ''CONVHEATEL_TYPE_Y''    |       -     |
-| Fluid temperature $T_f$                             |  ''TEMP_FLUIDE''  |    ''TO/TM''        |
-| Amplitude of the convection coefficient $A$                             |  ''CONV_COEF''  |    ''TO/TM''        |
-| Concentration factor ($k_x$)                    |   ''CONVHEATEL_KX''   |     -        |
-| Concentration factor ($k_y$)                     |   ''CONVHEATEL_KY''   |      -       |
-| Concentration factor ($k_{xr}$)                   |   ''CONVHEATEL_KXR''   |       -      |
-| Number of integration points                  |   ''NIP''   |      -       |
-| Material Stiffness  \\ (STIFF_ANALYTIC - STIFF_NUMERIC) \\ only if element Stiffness == STIFF_ANALYTIC | ''MATERIALSTIFFMETHOD''  |      -       |
-===== Interaction =====
-The interaction is defined as:
-  load = HeatInteraction(no)
-  load.push(gObject1)
-  load.push(gObject2)
-  ...
-  load.setAxes(Ox, Oz)
-  load.useRescale(bool)
-  load.addProperty(prp)
-  interactionset.add(load)
-where
-| ''no''       | number of the ''Interaction''  |
-| ''gObject1'', ''gObject2''  | mesh geometric entity where the boundary conditions are applied  |
-| ''prp''      | [[doc:user:elements:general:def_element_properties|Properties]] of [[#Element|boundary condition elements]] to generate |
-| ''Ox'', ''Oz''  | Curve entities that define the local coordinates $x'$ and $z'$ for the heat distribution function (not necessary for ''HEATEL_CONSTANT'')\\ [[doc:user:conditions:displacements]] and/or [[doc:user:conditions:rotations]] can be applied on these curves to obtain a moving heat source |
-| ''useRescale(bool)''  | Rescaling of the heat flux \\ = False (default): do nothing \\ = True: allows the rescaling of all heat source at each beginning of time-step to obtain the exact value of total applied ''HEATEL_VALUE'' \\ :!: not for ''HEATEL_CONSTANT'' and ''Tm[2]ConvectionHeatFlux[2|3]DElement'' |