====== LINADC ======
===== Description =====
Law for linear heat advection diffusion 1D element (only for [[elements:heatx|HEATX]] element)

==== The model ====
This law is used in combination with the finite element [[elements:heatx|HEATX]]. The purpose is the modeling of simplified equations of advection-diffusion of heat in a pipe. A lateral heat flow with the surrounding medium is also taken into account. See GEOTHERWAL reports or more information on the formulation.

==== Files ====
Prepro: LINADC.F \\
===== Availability =====
|Plane stress state| NO |
|Plane strain state| NO |
|Axisymmetric state| NO |
|3D state| YES |
|Generalized plane state| NO |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 108 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (3I5) ^^
|ITYPE|type of lateral of lateral heat exchange (only one case up to now)|
|IBOUND|type of boundary: \\ = 0 → no boundary \\ = 1 → free flow boundary, the fluid runs out of the pipe (necessary at the end of an open pipe) \\ = 2 → loop boundary, the fluid that runs out of the pipe is injected at the beginning of another segment|
|IDEP| fluid velocity v or heat power $Q_P$ \\ = 1 → depends of DMULT and FMULT respectively \\ = 0 → are constant|
{{  :laws:ibound1_ibound2.png?400  |}}

==== Real parameters ====
^ Line 1 (9G10.0) ^^
|RHO |specific mass of the fluid inside the pipe $\left[kg/m^3\right]$|
|COND |conductivity of the fluid inside the pipe $\left[W/m/K\right]$|
|CP |specific heat of the fluid inside the pipe $\left[J/kg/K\right]$|
|v |velocity of the fluid $\left[m/s\right]$|
|TREF |reference temperature for the computation of advection flux $\left[K\right]$|
|h |parameter for the lateral heat flux $\left[W/m^2/K\right]$ \\ convective heat coefficient if (ITYPE == 1) such that $q_l = h (t_{ground} - T_{pipe})$| 
|r |radius of the pipe $\left[m\right]$|
|Qp |heating power if IBOUND=2 $\left[W\right]$|
|RATIO |ratio of the pipe that is modelled $\in \left[0,1\right]$, $=0.5$ for half a mesh $\left[-\right]$| 
===== Stresses =====
==== Number of stresses ====
4
==== Meaning (numerical, not physical) ====
|SIG(1)|conduction heat flux |
|SIG(2)|advection heat flux (depends on the reference temperature) |
|SIG(3)|lateral heat flux  |
|SIG(4)|storage heat flux  |

===== State variables =====
==== Number of state variables ====
1
==== List of state variables ====
|Q(1)| 0 |