Heat-Transfer Boundary Condition
Unit: [Θ]
A heat transfer boundary condition applies a predefined reference temperature combined with a conductance parameter (transfer rate).
Transfer boundary conditions are applied in cases where a reference temperature is linked to the temperature of groundwater via a separating heat-conductive medium.
The inflow/outflow of heat is calculated from the relevant area, the transfer rate, and the difference between reference and groundwater temperature:
Qheat = AΦ(Tref-T)
where
Qheat: inflow or outflow to/from the model
A: relevant area
Φ: transfer rate
T ref: reference temperature
T: current temperature in groundwater
The transfer rate is the heat transmission coefficient describing the properties of the material between the reference temperature and the temperature in groundwater or the properties of a boundary layer. The heat transmission coefficient for a single material is defined by
Φ = λ/d
where
λ: heat conductivity
d: thickness
When setting the boundary condition, the reference temperature is defined as the value for the boundary condition. The transfer rate is set separately as a material property.
3D model
The boundary condition nodes have to enclose entire faces of elements to define the area in one of the following ways:
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For an inflow of energy at one slice (either on top or bottom of the model or inside) all the nodes of an element in one slice (three nodes when using prismatic elements, four for cuboid elements) have to be assigned the condition. |
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For an inflow of energy at a vertical element face two nodes of an element in one slice and the same two nodes in an adjacent slice have to be assigned the condition. |
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The area for the inflow or outflow calculation includes the area of all the element faces the boundary condition has been assigned to. If the condition is inside the model, there are always two neighboring elements for each face therefore the area of the face is taken twice. At outer boundaries or on top/bottom of the model, the area of the face is only taken once. |
2D model
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The heat-transfer boundary condition in 2D models hast to be set to at least two nodes, defining a length for the inflow or outflow. |
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The length for the inflow or outflow calculation includes the length of all the element edges the boundary condition has been assigned to. If the condition is inside the model, there are always two neighboring elements for each edge. Therefore the length of the edge is taken twice. At outer boundaries, the length of the line is only taken once. |