functionconvectionResistanceCircularPipe

Thermal resistance from the fluid in pipes and the grout zones (Bauer et al. 2011)

Extends from Modelica.Icons.Function (Icon for functions).

Information

This model computes the convection resistance in the pipes of a borehole segment with heigth hSeg using correlations suggested by Bergman et al. (2011).

If the flow is laminar (Re ≤ 2300, with Re being the Reynolds number of the flow), the Nusselt number of the flow is assumed to be constant at 3.66. If the flow is turbulent (Re > 2300), the correlation of Dittus-Boelter is used to find the convection heat transfer coefficient as

Nu = 0.023   Re0.8   Prn,

where Nu is the Nusselt number and Pr is the Prandlt number. A value of n=0.35 is used, as the reference uses n=0.4 for heating and n=0.3 for cooling. To ensure that the function is continuously differentiable, a smooth transition between the laminar and turbulent values is created for the range 2300 < Re < 2400.

References

Bergman, T. L., Incropera, F. P., DeWitt, D. P., & Lavine, A. S. (2011). Fundamentals of heat and mass transfer (7th ed.). New York: John Wiley & Sons.

Inputs

TypeNameDefaultDescription
Modelica.Units.SI.HeighthSegHeight of the element
Modelica.Units.SI.RadiusrTubTube radius
Modelica.Units.SI.LengtheTubTube thickness
Modelica.Units.SI.ThermalConductivitykMedThermal conductivity of the fluid
Modelica.Units.SI.DynamicViscositymuMedDynamic viscosity of the fluid
Modelica.Units.SI.SpecificHeatCapacitycpMedSpecific heat capacity of the fluid
Modelica.Units.SI.MassFlowRatem_flowMass flow rate
Modelica.Units.SI.MassFlowRatem_flow_nominalNominal mass flow rate

Outputs

TypeNameDefaultDescription
Modelica.Units.SI.ThermalResistanceRFluPipConvection resistance (or conduction in fluid if no mass flow)

Revisions

  • June 4, 2023, by Michael Wetter:
    Corrected variability.
    This is for IBPSA, #1762.
  • July 10, 2018, by Alex Laferrière:
    Added laminar flow and smooth laminar-turbulent transition. Revised documentation.
  • February 14, 2014, by Michael Wetter:
    Removed unused input rBor. Revised documentation.
  • January 24, 2014, by Michael Wetter:
    Revised implementation. Changed cpFluid to cpMed to use consistent notation. Added regularization for computation of convective heat transfer coefficient to avoid an event and a non-differentiability.
  • January 23, 2014, by Damien Picard:
    First implementation.