Heat-Flux Boundary Condition

Unit: [E/(L*T)], [E/(L²*T)]

A heat flux boundary condition applies a predefined heat flux to nodes along a line (2D model) or to nodes enclosing faces of elements (3D). For the calculation of temperature as a simulation result, at these nodes an additional inflow/outflow is considered.

A typical application of this type of boundary condition is the geogenic heat flow at the bottom of a heat transport model.

 

For defining boundary conditions, inflows are considered as negative, outflows as positive. Thus a boundary condition representing the geogenic heat flow into the model has to be set with a negative sign!

   

The meaning of a heat-flux BC depends on whether the convective or divergence form of the transport equation is used. In most practical cases, the usage of this type of boundary condition is to be avoided in combination with the (default) convective form if there is a flow boundary condition on the same nodes. A temperature boundary condition is to be preferred in these cases.

 

3D model

In 3D models, the heat flux boundary condition has the unit [E/(L²*t)], for example defining an inflow of an amount of water per area and time with a certain temperature: [L³/(L²*t)*E/L³].

The boundary condition nodes have to enclose entire faces of elements to define the area in one of the following ways:

 

	For an inflow 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 cuboidal elements) have to be assigned the condition.
	For an inflow at one slice (either on top or bottom of the model or inside) two nodes of an element in one slice and the same two nodes in an adjacent slice have to be assigned the condition.

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

In 2D horizontal confined models, the heat-flux boundary condition has the unit [E/(L*t)], defining an inflow or outflow of heat across a defined line in a certain time. L is derived internally from the length of the line the condition is applied to.

In 2D horizontal unconfined and cross-sectional models, the flux boundary condition has the unit [E/(L₁*L₂*t)], defining an inflow of heat across an area in a certain time. Here, L₁ is taken from the length of the line the condition is applied to, while L₂ corresponds to the saturated thickness in horizontal unconfined models (hydraulic head - bottom elevation in unconfined zones, top elevation - bottom elevation in confined parts of the model). For cross-sectional models, L₂ is assumed at unit length (1 m).

 

The heat flux boundary condition in 2D models has to be set to at least two nodes, defining a length for the inflow or outflow.

 

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.