functionconvectionResistanceCircularPipe

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

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

Outputs

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

Revisions

  • 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.