functionfiniteLineSource_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 Buildings.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.ThermalResponseFactors.finiteLineSource_erfint. The integral is solved numerically, with the integrand defined in Buildings.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.ThermalResponseFactors.finiteLineSource_Integrand_Equivalent.

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Revisions

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