.BuildingSystems.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.ThermalResponseFactors.finiteLineSource

Information

This function evaluates the finite line source solution. This solution gives the relation between the constant heat transfer rate (per unit length) injected by a line source of finite length H₁ buried at a distance D₁ from a constant temperature surface (T=0) and the average temperature raise over a line of finite length H₂ buried at a distance D₂ from the constant temperature surface. The finite line source solution is defined by:

where ΔT_1-2(t,r,H₁,D₁,H₂,D₂) is the temperature raise after a time t of constant heat injection and at a distance r from the line heat source, Q' is the heat injection rate per unit length, k_s is the soil thermal conductivity and h_FLS is the finite line source solution.

The finite line source solution is given by:

where α_s is the ground thermal diffusivity and erfint is the integral of the error function, defined in BuildingSystems.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.ThermalResponseFactors.finiteLineSource_erfint. The integral is solved numerically, with the integrand defined in BuildingSystems.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.ThermalResponseFactors.finiteLineSource_Integrand.

Interface

function finiteLineSource
  extends Modelica.Icons.Function;
  input Modelica.Units.SI.Time t "Time";
  input Modelica.Units.SI.ThermalDiffusivity aSoi "Ground thermal diffusivity";
  input Modelica.Units.SI.Distance dis "Radial distance between borehole axes";
  input Modelica.Units.SI.Height len1 "Length of emitting borehole";
  input Modelica.Units.SI.Height burDep1 "Buried depth of emitting borehole";
  input Modelica.Units.SI.Height len2 "Length of receiving borehole";
  input Modelica.Units.SI.Height burDep2 "Buried depth of receiving borehole";
  input Boolean includeRealSource = true "True if contribution of real source is included";
  input Boolean includeMirrorSource = true "True if contribution of mirror source is included";
  output Real h_21 "Thermal response factor of borehole 1 on borehole 2";
end finiteLineSource;

Revisions

• March 17, 2019, by Massimo Cimmino:
  Modified the upper bound of integration to avoid underestimating the value of the integral. This is for IBPSA, issue 1107.
• March 22, 2018 by Massimo Cimmino:
  First implementation.