An Analytical Solution to Transient Heat Conduction in a Composite Region With a Cylindrical Heat Source

Gu, Yian; O’Neal, D. L.

doi:10.1115/1.2847813

Cited by 58 publications

(15 citation statements)

References 3 publications

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“…Recognizing this difficulty, Gu and O'Neal (1995) developed an analytic solution for the transient heat transfer problem related to a cylindrical heat source in a nonhomogeneous medium. They used this solution later on (1998b) to evaluate grout effects on GHPs.…”

Section: Numerical Modeling Of the Effect Of Debonding On Heat Transfermentioning

confidence: 99%

Properties and Performance of Cement-Based Grouts for Geothermal Heat Pump Applications.

Allan¹

1999

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Section: Numerical Modeling Of the Effect Of Debonding On Heat Transfermentioning

confidence: 99%

Properties and Performance of Cement-Based Grouts for Geothermal Heat Pump Applications.

Allan¹

1999

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“…This is an approximation neglecting the interaction between different boreholes in a borefield. The equivalent borehole filled with grout is schematically shown in Figure 5, where an equivalent diameter approach [21,2,22] is used. In the equivalent diameter approach, the heat transfer from the Utube is approximated by the heat transfer from a single pipe with a hypothetical diameter through which the heat exchanging fluid circulates.…”

Section: Borehole Dynamicsmentioning

confidence: 99%

A convex approach to a class of non-convex building HVAC control problems: Illustration by two case studies

Atam

Helsen

2015

Energy and Buildings

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In this paper, a convexification approach is presented for a class of non-convex optimal/model predictive control problems more specifically applied to building HVAC control problems. The original non-convex problems are convexified using a convex envelope approach. The approach is tested on two case studies: a benchmark building HVAC system control problem from the literature and control of a hybrid ground-coupled heat pump (HybGCHP) system. For the first application, convexified model predictive control was used and results were compared with fuzzy and adaptive control results. For the HybGCHP system, convexified optimal control was applied and the results were compared with dynamic programming based optimal control. In the first case superior performance was observed over the corresponding fuzzy and adaptive control results from the literature. For the HybGCHP system the associated convexified optimal control gave almost global optimal results in terms of responses and cost criteria. The suggested method is especially useful for optimal building HVAC control/design problems which include non-convex bilinear or fractional terms. Since a polynomial expression can be recursively expressed as a system of bilinear equations, the proposed method, in principle, can be applied to all systems where polynomial non-convexities exist.

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“…In such models, the convective-conductive heat flow in the U-tubes is replaced by a constant cylindrical heat source, and the geometry is described by a concentric two-dimensional (radial) composite domain. Gu and O'Neal [4] gave an elaborate literature review on analytical solutions of radial heat conduction in a composite domain. They utilized this technique to simulate transient heat flow due to a constant heat source, resembling U-tubes, surrounded by a backfill (grout) and a soil mass bounded by a far field boundary.…”

Section: Introductionmentioning

confidence: 99%

A spectral model for transient heat flow in a double U-tube geothermal heat pump system

Al‐Khoury

Focaccia²

2016

Renewable Energy

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a b s t r a c tThis paper introduces a semi-analytical model based on the spectral analysis method for the simulation of transient conductive-convective heat flow in an axisymmetric shallow geothermal system consisting of a double U-tube borehole heat exchanger embedded in a soil mass. The proposed model combines the exactness of the analytical methods with an important extent of generality in describing the geometry and boundary conditions of the numerical methods. It calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass using the fast Fourier transform, for the time domain; and the complex Fourier and Fourier-Bessel series, for the spatial domain. Numerical examples illustrating the model capability to reconstruct thermal response test data together with parametric analysis are given. The CPU time for calculating temperature distributions in all involved components, pipe-in, pipe-out, grout, and soil, using 16,384 FFT samples, for the time domain, and 100 Fourier-Bessel series samples, for the spatial domain, was in the order of 3 s in a normal PC. The model can be utilized for forward calculations of heat flow in a double U-tube geothermal heat pump system, and can be included in inverse calculations for parameter identification of shallow geothermal systems.

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An Analytical Solution to Transient Heat Conduction in a Composite Region With a Cylindrical Heat Source

Cited by 58 publications

References 3 publications

Properties and Performance of Cement-Based Grouts for Geothermal Heat Pump Applications.

Properties and Performance of Cement-Based Grouts for Geothermal Heat Pump Applications.

A convex approach to a class of non-convex building HVAC control problems: Illustration by two case studies

A spectral model for transient heat flow in a double U-tube geothermal heat pump system

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