modelThermalResistorVertical_withDispersion

model of thermal resistor can consider dispersion

Diagram of ThermalResistorVertical_withDispersion

Extends from Modelica.Thermal.HeatTransfer.Interfaces.Element1D (Partial heat transfer element with two HeatPort connectors that does not store energy).

Information

1. Purpose of model

Quasi-static vertical thermal resistor for heat conduction between two vertically neighbouring aquifer control volumes. Optionally adds hydrodynamic dispersion to the effective thermal conductivity based on the local vertical Darcy velocity.

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. Thermal resistance is computed from half the control volume height and the cross-sectional area. Dispersion increases effective conductivity proportionally to the magnitude of the vertical Darcy flux.

3. Limits of validity

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

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

4. Interfaces

Interface diagram: port_a (heat in, bottom), port_b (heat out, top), q_v (Darcy velocity signal, left)

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

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

q_v: vertical Darcy velocity input for dispersion calculation (Signal)

5. Nomenclature

	R	vertical thermal resistance [K/W]
$\lambda_\mathrm{eff}$	lambda_overall	effective thermal conductivity incl. dispersion [W/(m·K)]
$\lambda_\mathrm{disp}$	lambda_disp	dispersion contribution to thermal conductivity [W/(m·K)]
	q_v	vertical Darcy velocity [m/s]
$z_\mathrm{cv}$	z	height of control volume [m]
	A	cross-sectional area of control volume [m²]
	disp_length	vertical dispersivity length [m]
	C_f	volumetric heat capacity of fluid [J/(m³·K)]
$\dot{Q}$	Q_flow	heat flow rate [W] (inherited from Element1D)
$\Delta T$	dT	temperature difference across resistor [K] (inherited from Element1D)

6. Governing Equations

Effective thermal conductivity with optional dispersion:

lambda_disp = d_L * |q_v| * C_f

Vertical thermal resistance (half-cell formulation):

R_v = 0.5*z / (lambda_eff * A)

Heat transport (inherited from Element1D):

dT = R * Q_flow

7. Remarks for Usage

Connect q_v to the q_trans output of the corresponding ControlVolumeL4 cell. Set dispersion = false (default) to use pure conduction.

8. Validation

(no remarks)

9. References

(no remarks)

10. Version History

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

Parameters

Type	Name	Default	Description
SI.ThermalConductivity	lambda		Heat Conductivity of the aquifer
SI.Area	A
SI.Length	z		heights of all control volumes in aquifer
SI.Length	disp_length	0.7	vertical dispersion length
Real	C	nC_f + (1 - n)C_s	volumetric heat capacity of stone and fluid
Real	C_f	4.3*10^6	volumetric heat capacity of fluid
Real	C_s	1.81*10^6	volumetric heat capacity of stone
Real	n	0.25	porosity of underground
Boolean	dispersion	false	whether dispersion is considered or not

Connectors

Type	Name	Default	Description
HeatPort_a	port_a (from Element1D)
HeatPort_b	port_b (from Element1D)
Modelica.Blocks.Interfaces.RealInput	q_v

Components

Type	Name	Description
SI.HeatFlowRate	Q_flow (from Element1D)	Heat flow rate from port_a -> port_b
SI.TemperatureDifference	dT (from Element1D)	port_a.T - port_b.T
SI.ThermalResistance	R	Thermal resistance of material
SI.ThermalConductivity	lambda_overall	overall effective thermal conductivity
SI.ThermalConductivity	lambda_disp	dispersion depending part of thermal conductivity