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

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 group of line sources of finite length H₁ buried at a distance D₁ from a constant temperature surface (T=0) and the average temperature raise over a group of N₂ lines 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_1->2,H₁,D₁,H₂,D₂,N₂) is the temperature raise over lines in group 2 after a time t of constant heat injection, r_1->2 is the list of distance between all pairs of lines in groups 1 and 2, N_1->2 is the number of distances, 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_Equivalent.

Interface

function finiteLineSource_Equivalent
  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[n_dis] "Radial distance between borehole axes";
  input Integer wDis[n_dis] "Number of occurences of each distance";
  input Modelica.Units.SI.Height len1 "Length of emitting boreholes";
  input Modelica.Units.SI.Height burDep1 "Buried depth of emitting boreholes";
  input Modelica.Units.SI.Height len2 "Length of receiving boreholes";
  input Modelica.Units.SI.Height burDep2 "Buried depth of receiving boreholes";
  input Integer nBor2 "Number of receiving boreholes";
  input Integer n_dis "Number of unique distances";
  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_Equivalent;

Revisions

• June 9, 2022 by Massimo Cimmino:
  First implementation.