.Buildings.Fluid.Geothermal.Boreholes.BaseClasses.convectionResistance

Information

This model computes the convection resistance in the pipes of a borehole segment with heigth h_Seg.

The correlation of Dittus-Boelter (1930) is used to find the convection heat transfer coefficient as

Nu = 0.023   Re^0.8   Prⁿ,

where Nu is the Nusselt number, Re is the Reynolds number and Pr is the Prandlt number. We selected n=0.35, as the reference uses n=0.4 for heating and n=0.3 for cooling. Dittus-Boelter's correlation is valid for turbulent flow in cylindrical smooth pipe.

References

Dittus P.W. and L.M.K Boelter, (1930). Heat transfer in automobile radiators of the tubular type. Univ Calif Pub Eng, 2(13):443-461. (Reprinted in Int. J. Comm. Heat Mass Transf. 12 (1985), 3:22). DOI:10.1016/0735-1933(85)90003-X.

Interface

function convectionResistance
  input Modelica.Units.SI.Height hSeg "Height of the element";
  input Modelica.Units.SI.Radius rTub "Tube radius";
  input Modelica.Units.SI.ThermalConductivity kMed "Thermal conductivity of the fluid";
  input Modelica.Units.SI.DynamicViscosity mueMed "Dynamic viscosity of the fluid";
  input Modelica.Units.SI.SpecificHeatCapacity cpMed "Specific heat capacity of the fluid";
  input Modelica.Units.SI.MassFlowRate m_flow "Mass flow rate";
  input Modelica.Units.SI.MassFlowRate m_flow_nominal "Nominal mass flow rate";
  output Modelica.Units.SI.ThermalResistance R "Thermal resistance between the fluid and the tube";
end convectionResistance;

Revisions

• 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.