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

# .AixLib.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.ThermalResponseFactors.finiteLineSource

Finite line source solution of Claesson and Javed

## 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 ΔT1-2(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, ks is the soil thermal conductivity and hFLS is the finite line source solution.

The finite line source solution is given by:

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

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