modelThermalResistorVertical

Information

1. Purpose of model

Quasi-static vertical thermal resistor for one-dimensional heat conduction between two vertically neighbouring control volumes. The thermal resistance is computed from half the control volume height and the cross-sectional area with a constant thermal conductivity. Same idea as the Modelica Standard Library ThermalConductor, but parametrized by the thermal resistance instead of the conductance, which allows a resistance of zero (no temperature difference) in series connections. This is the variant without dispersion; for hydrodynamic dispersion use ThermalResistorVertical_withDispersion.

2. Level of detail, physical effects considered, and physical insight

L1: Quasi-static 1D heat transport in vertical direction. No thermal storage within the resistor; the temperature drop is given by the calculated thermal resistance.

3. Limits of validity

- No thermal mass inside the resistor (instantaneous conduction).

- Constant thermal conductivity (no temperature dependency, no dispersion).

- The factor 0.5 in the resistance formula assumes the temperature node sits at the centre of the control volume.

4. Interfaces

port_a: lower heat port — heat inlet (Heat, inherited from Element1D)

port_b: upper heat port — heat outlet (Heat, inherited from Element1D)

5. Nomenclature

	R	vertical thermal resistance [K/W]
	lambda	thermal conductivity of the aquifer/aquitard [W/(m·K)]
	A	cross-sectional area of control volume [m²]
	z	height of control volume [m]
	Q_flow	heat flow rate [W] (inherited from Element1D)
	dT	temperature difference across resistor [K] (inherited from Element1D)

6. Governing Equations

Vertical thermal resistance (half-cell formulation):

Heat transport (inherited from Element1D):

7. Remarks for Usage

Used inside ImpermeableLayer to represent vertical heat conduction in the confining layers. A resistance of R = 0 is permitted and yields no temperature difference, which is convenient for series connections. Thermal properties are taken from the Subsurface_Basic (Parameters) record.

8. Validation

Tested in check model "ATES.Validierung.Buoyancy.Val_homogenLayer"

9. References

(no remarks)

10. Version History

Model created by Markus Gillner (markus.gillner@tuhh.de), May 2026

Model revised by Markus Gillner (markus.gillner@tuhh.de), June 2026

- Completed the documentation (10-section template, preferred heading style) and corrected the interface description (heat ports port_a/port_b inherited from Element1D; A is a parameter, not a Real input).

Parameters

Connectors

Components