Abstract
A solution to the three-dimensional finite line-source (FLS) model for borehole heat exchangers (BHEs) is identical to Hantush’s M function, commonly used in groundwater pumping modeling. A modified Hantush function E appears in the steady-state solution to the moving finite line-source (MFLS) model for borehole heat exchangers (BHEs) with groundwater flow that takes into account heat conduction and advection by Péclet number. An exact series representation is obtained for this two-parametric function E, and from it two-types of approximate expressions for the E are derived. One is suitable for small values of a parameter Pe and the other for its large values. High accuracy of the approximate formulae is verified by comparison with the exact values provided by modified Hantush’s function E in those validity domains.These analytical expressions can be used for designing complex borehole configurations and may be useful in steady-state analysis of partially penetrated wells (PPWs) in a leaky aquifer.
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