Analytical Heat Transfer Model Research Articles

Thermal Assessment of Repository Footprint Requirement for Advanced Fuel Cycles

Decay heat is an important constraint for repository size and design because it can drive processes that affect performance and compromise critical materials. This paper investigates how compliance with repository thermal limits is affected by three decay heat management strategies: waste package loading, waste package spacing, and surface storage time. In particular, this paper focuses on how repository area, a result of package spacing, is impacted by waste loading and surface storage time. A two-part analytical heat transfer model is presented and executed iteratively to determine the minimum allowable repository area. The analysis considers three generic close-contact repository designs along with the wastes generated from the 40 fuel cycle analysis examples used to generate metric data for the Fuel Cycle Evaluation and Screening study. Detailed results are presented for two fuel cycles: the once-through use of low-enriched uranium fuel in light water reactors and the continuous recycling of U and Pu in sodium fast reactors. Two limits for surface storage time are identified: the time required for disposal to be possible at all and the time at which further surface storage time yields no gains. The impact of waste loading is also diminished with increasing surface storage time. In general, the generic salt repository is most flexible to accept high-heat-generating wastes with less surface storage time than other repository environments. Limited-recycle fuel cycles are shown to pose a disposal challenge because of elevated, sustained decay heat generation in the waste.

Partial crystallization in a Zr-based bulk metallic glass in selective laser melting

Metals and alloys in amorphous state are promising for the use as structural and functional materials due to their superior properties related to the absence of such defects as grain boundaries and dislocations. Obtaining the amorphous state requires quenching from liquid state with a high cooling rate. In conventional technologies, this is the reason for a considerable size limitation hindering application of amorphous alloys. Additive manufacturing (AM) is free of the size limitation. The so-called bulk metallic glass (BMG) alloys have extremely low critical cooling rates and can be used in AM. Recent studies on AM from Zr-based BMGs by selective laser melting (SLM) has proved the possibility of attaining the amorphous state and revealed partial crystallization to be the principal drawback of this process. The present work aims to analyze the conditions for partial crystallization and attempts to control it by optimizing the process parameters. A comprehensive parametric analysis is accomplished in single-track SLM experiments with Zr-based BMG alloy Vit 106. The observed microstructures are related to the temperature fields and thermal cycles estimated by an analytic heat-transfer model in the laser-impact zone. In the cross section of a laser track, a central bright domain is identified as the remelted zone. An annular darker crystallization zone encircles the remelted zone. The model fits the experimentally obtained dependencies of the remelted zone size versus laser power and scanning speed and indicates that 43 ± 2% of the incident laser energy is transferred into the substrate thermal energy. The principal energy losses are reflection of the incident laser radiation and material evaporation. Primary crystalline inclusions existing in the substrate before laser processing dissolve at the laser melting. The mean cooling rate in the remelted zone is up to 4 orders of magnitude greater than the critical cooling rate. Therefore, homogeneous nucleation is not expected. Nevertheless, the theoretically estimated crystallization times are sufficient for a considerable crystal growth in the heat-affected zone where primary crystalline inclusions and nuclei are not completely dissolved.

Analytical interpretation and numerical analysis of multiple energy pile thermal response tests

Thermal response tests (TRT) are an essential in situ test for the sizing of ground source heat pump systems. Its application on energy piles is becoming an established practice, involving key differences in relation to testing boreholes. Recently, group TRTs emerged as an alternative to testing single short energy pile elements. This work assesses the execution and interpretation of those tests through different analytical heat transfer models implemented in a unit-response calculation methodology. To assess the suitability of the method, a comprehensive parametric analysis using a validated numerical model is undertaken, considering different energy pile sizes, thermal properties for both concrete and soil and group pile arrangements. The analytical methodology is validated against experimental and numerical results, and then tested to interpret the numerically simulated TRTs using a curve fitting algorithm. The broad parametric investigation and the evaluation of the capacity of different analytical methods on modelling each scenario provide directions to execute and interpret group TRTs. The soil effective thermal conductivity and energy pile thermal resistance are obtained with less than 5% precision error for most scenarios and less than 10% considering all scenarios. These results can be further improved with specific individual G-functions for the pile elements, that can be implemented on the proposed methodology.

Analiza toplotnih efekata u postupcima frikcionog zavarivanja mešanjem

This paper describes the formation of an analytical model of heat generation and transfer during friction stir welding. By solving differential equations of heat transfer, adapted for friction stir welding, the foundations for the formation of an analytical model were laid. In order to vary the technological parameters of welding that affect the generated heat, certain approximations were performed and the stress state of the material was observed at elevated temperatures. The aim was to simulate heat transfer for thin and thick plates, by obtaining a planar and spatial temperature image for certain welding parameters. The formation of the analytical model was performed in the Python programming language.

Analytical heat transfer model for coaxial heat exchangers based on varied heat flux with borehole depth

In the classical analytical coaxial borehole heat exchanger (CBHE) models, the variations of the specific heat flux exchanged vertically along the depth of CBHE are ignored, which induces considerable prediction errors of the ground temperature. Based on the infinite line source model (ILSM), an improved varied heat flux model for the CBHE is developed using the superposition method, taking the vertical inhomogeneity of the specific heat flux into account. The mathematical expressions of the specific heat flux and the temperatures of the fluids and ground at different working conditions are obtained. The model is validated analytically and numerically. Finally, the influence of the mass flow rate, the outer-to-inner pipe radius ratio, and the thermal influence radius are investigated for optimal design. The results show that the specific heat flux is significantly related to the borehole depth, operation time, and fluid circulation direction. Compared with the finite line source method (FLSM), the relative errors of the ground temperature predicted by the proposed model can be reduced maximumly by 8.9% and 10.3% for heat extraction and injection, respectively. In addition, using higher mass flow rates and larger outer-to-inner pipe radius ratios can eliminate thermal interference to increase thermal efficiency. In general, the improved analytical model can provide an accurate and efficient method for this inhomogeneous problem and a valuable tool for designing and optimizing CBHEs for actual engineering applications.

Analytical modeling of mass transfer dynamics, velocity, heat transfer and enthalpy in a gas-liquid combustible mixture

The article studied the distribution of the droplet and temperature over the volume of the combustion chamber when liquid fuel was injected into it. The study showed that the portable mass in the combustion chambers and temperatures are directly proportional. Compiled systems of dynamic equations describing mass transfer, motion, heat transfer and enthalpy at the beginning inside the chamber phase and during combustion inside the chamber. Mathematically modeled a gasoline-hydrogen-air mixture with the mass transfer method. With this simulation, pressures are determined at the beginning inside the chamber phase and during combustion inside the chamber, taking into account the newly introduced enthalpy coefficient of gas kHg and steam kHp phase media.

An analytical heat transfer model for the mid-deep U-shaped borehole heat exchanger considering groundwater seepage

Ground source heat pump systems consisting of deep boreholes and heat pumps can be used for heating buildings. It is known as an effective way to utilize geothermal resources, however, there is a problem with high development costs. Therefore, it is important to establish a precise heat transfer model to develop a high-efficiency geothermal heat exchanger to reduce the development cost of mid-deep geothermal energy. Most of the existing heat transfer models for deeply buried pipes only consider thermal conductivity and treat the geotechnical soil as a homogeneous medium, or do not consider the stratification and groundwater seepage phenomena, which make the models inaccurate. This study established an analytical heat transfer model considering geotechnical stratification and seepage developed for the U-shaped deep borehole heat exchanger (U-DBHE), and the analytical solution for temperature response is obtained. Using the developed analytical model, we plotted the trends that reveal the relationship between the thermal performance of U-DBHE and various parameters and explored the influence of seepage phenomena on heat extraction performance. The model can also serve as a reference for the development of heat transfer models for buried pipe heat exchangers with groundwater seepage. Given that the proposed analytical model is time-consuming and stable, and can be an efficient tool for U-DBHE design and optimization.

Simulation of thermal behavior evolution in lithium-ion pouch cells using a coupled reaction-thermal-expansion model

Conventional lithium-ion battery thermal simulation methods establish a coupled heat generation/transfer model to calculate the temperature evolution for hard-pack cells. However, the thermal behavior evolution of a pouch cell includes multi-processes such as heat generation, gas production, heat transfer, and pouch expansion. There is currently a lack of computational models for predicting the multi-state parameter evolution in temperature and pressure. In this paper, an efficient and accurate thermal behavior simulation algorithm for lithium-ion pouch cells is developed. A heated/exothermic two-stage hypothesis for the thermal behavior evolution in pouch cells was established under thermal abuse conditions. Analytical models of exothermic reaction, heat transfer and pouch expansion were formulated and integrated into a unified thermal behavior analysis framework. The proposed algorithm simulated the thermal behavior evolution in four commercial lithium-ion pouch cells. The computational and experimental results showed the calculation errors of the cell temperature and gas volume for the four samples were less than 3% and 5%, respectively. In terms of efficiency, the calculation time of the algorithm is within milliseconds. The accuracy and efficiency of the proposed algorithm are verified.

Analytical and numerical modeling and simulation of heat transfer through raffia vinifera bamboo

The permanent search for materials that can improve climatic conditions and thermal comfort in buildings remains a major concern for engineers. The choice of material is motivated by its behavior to the thermal stresses. To predict the distribution of temperature within the material requires mathematical models. In this paper, the heat transfer through raffia vinifera bamboo is modeled using the equation of energy conservation. Raffia vinifera bamboo consists of cork and shell and is treated as two layers material. The thermophysical properties of each layer are constant. The equation is solved analytically by the separation of variables method and numerically by the finite difference method. A numerical simulation with CASTEM software is also performed. A constant temperature is imposed at the external surface of the material while the continuity of the temperature and flux are applied at the cork/shell interface. To test the computational results, the thermophysical properties of the two layers were set equal. The analytical solution in this case of single layer was used as the reference result and the computational methods developed in this work were compared. Results demonstrated that the absolute value of the relative error at the center of material decreases abruptly with time and a maximum value less than 8% occurred for all the developed methods in the paper. Results also indicated that at a given time, the relative error increases slowly to a maximum value less than 8% close the surface. These results showed that the methods presented were correct. The case of two layers with different thermophysical properties was second examined and the raffia vinifera bamboo was viewed as heterogeneous material. The temperature profile at a given time decreases from the surface to the center of the material with a peak occurring at the interface cork/shell. At time t=9750.336s, the temperature at the center increases only by 4.75 °C. Thus, the raffia vinifera bamboo can be used as thermal insulation in buildings.

Numerical simulation and analysis of thermo-hydro-mechanical behaviors of hydraulic fracturing in naturally fractured formation using a THM-XFEM coupling model

Activation and propagation of natural crack during hydraulic fracturing make an essential contribution to the reservoir stimulation. For the sake of figuring out the impact of thermo-poroelastic deformation in multi-field coupling on natural crack activation, a thermo-hydro-mechanical coupled model is developed in this paper. The thermo-poroelastic deformation and non-isothermal fluid flow in fractured media are all taken into account, and the contact problem for natural crack surfaces are solved by the augmented lagrangian multiplier method. Then the extended finite element method is adopted for the discretization of the coupled model. The developed model is verified against the analytical models of fracture propagation, heat transfer and crack loaded in shear. Sensitive analysis is conducted using the numerical model. Numerical results show that the key factors affecting interaction pattern between hydraulic fracture and natural crack are the geomechanical parameters while thermal effect only contribute to natural crack activation. Thermal stress can lead to an increase in fracture aperture but a reduction in fluid pressure in fracture, and the high reservoir temperature and coefficient of thermal expansion will aggravate this. Besides, the non orthogonal intersection angle will cause an asymmetric distribution of fluid pressure and aperture in activated natural crack.

A Study on Comparison of Temperature Distribution between Aluminum and GFRP Mold under Carbon Spar-Cap Manufacturing Process

In this study, temperature distribution as a function of the spar-cap thickness was numerically analyzed using a 20 kW wind carbon blade model. “Realizable k-ε”, which was adopted as a turbulence model for heat transfer analysis, was effective in convection and diffusion calculations. SC/TETRA, a commercial thermal fluid analysis software, was used to calculate the heat flow from the heat panel to the outside boundary of the simulation model. In order to derive the equation for the temperature between the mold surface and the top surface of the spar-cap, the temperature interval of the heat panel was 10 °C, and the range was from 60 °C to 110 °C. As a result, the temperature distribution of the top surface of the spar-cap was insufficient to cure the Carbon Fiber Reinforced Plastic (CFRP) because the heat did not reach from the mold heat panel to the top surface of the carbon spar-cap. To resolve the problem of heat loss, the equation was derived by dividing the temperature boundary conditions between the mold surface and the spar-cap top surface as a function of the thickness of the carbon laminates. The temperature unevenness in the spar-cap curing process was reduced using the improved boundary condition. In addition, the cases where GFRP and aluminum were applied to the upper mold of the heat panel were compared using the same analysis method. An improvement to reduce the temperature non-uniformity of the spar-cap top surface was studied to solve the non-curing issue of the carbon spar-cap under the manufacturing process.

Analytical solution for estimating transient vertical groundwater flux from temperature-depth profiles

Many studies have developed analytical models for describing the subsurface heat transfer to estimate the infiltration rate, that is, the vertical groundwater flux (VGF). These studies assumed that the VGF was constant in time to acquire mathematical tractability. However, the assumption generally violates the natural system and cannot delineate the transient behavior of the VGF. Such an illogical assumption would contribute to unreliable estimation of the VGF from field-observed temperature-depth (TD) profiles. To accurately estimate VGF based on an analytical model, this study develops a new analytical heat-transfer model and a novel inverse approach to estimate the transient VGF. The analytical model is verified by a numerical model based on the finite-element method. We further perform the sensitivity analysis to the analytical model to examine the temperature response to changes in the thermal parameters. It reveals that thermal dispersion has a minor effect on temperature. The results of the numerical experiment show that the present approach can yield the correct transient VGF. Finally, the present approach is applied to estimate the transient VGF for a field case study. The results show that the predicted VGF and the measured VGF are almost consistent, revealing that our method is feasible for the estimation of VGF in the field.

Explosive Spalling Mechanism and Modeling of Concrete Lining Exposed to Fire.

Traditional heat transfer analysis has been adopted to predict the damage in a tunnel under fire without considering the effect of concrete spalling, which leads to underestimation of the fire damage of concrete. However, accounting for the spalling effect of concrete under high temperature in an analytical heat transfer model is difficult because of the complexity of the spalling mechanism. This study aims to establish an analytical model to estimate the influence of concrete spalling on the fire-damage depth prediction. To overcome this challenge, first, a series of fire tests were conducted in a unidirectional heating system. The spalling phenomenon and spalling characteristics were observed. Based on the experimental test results, the moisture content of concrete is one of the key factors of spalling. Obvious layered spalling characteristics of concrete samples without drying could be observed under the unidirectional heat conduction system. The critical temperature of spalling is 600 °C, and the thickness of the spalling layer is 2 cm~2.5 cm. These two parameters are critical spalling conditions. Second, a multilayer model for the heat transfer analysis considering the spalling effect of tunnel lining under fire was proposed. By using Laplace transform and the series solving method for ordinary differential equations, the time-dependent temperature and stress fields of concrete lining during tunnel fire could be obtained, which are the basis of damage evolution. The analytical results agreed with the experimental data. The spalling depth of tunnel lining related to the temperature rise of tunnel fire could be predicted by using the proposed analytical model. The results of this research can be used to provide a better damage evaluation of tunnel lining under fire.

An Analytical Heat Transfer Model in Oil Reservoir during Long-Term Production

Contrary to the assumption of previous researchers, the radial temperature in the petroleum reservoir during production is non-isothermal because several heat transfer mechanisms change the radial temperature in reservoirs. As there have been few studies, especially after long-term production, this work derives steady-state analytic solutions considering the long-term production. It also presents sensitivity analysis with the various production conditions to investigate heat transfer between the producing fluids and surrounding formations during fluids flowing (hereafter, system heat transfer) in a steady-state. For oil production, the system heat transfer induces a cooling effect on the radial temperature in the reservoir, reducing the temperature rise due to the Joule–Thomson (J–T) heating. This cooling effect increases with the larger Peclet number, however, the relative contribution of the cooling effect to the radial temperature change diminishes. The equations explain that the cooling effect is proportional to the temperature increase due to J–T heating. With a larger permeability, a more convective-dominant phase causes more heat transfer actively. Although the cooling effect itself is amplified with the larger permeability, its relative contribution to the temperature change decreases. From the analysis, the cooling effect of system heat transfer is significant in the low-permeability reservoirs with large drawdown. The system heat transfer is confirmed to be an essential factor in measuring the accurate productivity index of unconventional reservoirs.

Recovery of liquefied natural gas cold energy in a clean cogeneration system utilizing concentrated photovoltaics

Natural gas must be liquefied for long distance transport, so a lot of energy is lost during the liquefaction and regasification process. The innovative system proposed in this study recovers the cold exergy of liquefied natural gas (LNG) regasification process and also uses this potential for concentrated photovoltaics (CPV) cooling. The system uses cascades of organic Rankine cycles (ORC) whose boilers' high-temperature sources are supplied by thermal management of the CPV and low-temperature sides are in thermal contact with LNG flow. In the proposed system, the ORC's organic working fluid cools the CPV heat sink directly to reduce exergy destructions. An analytical thermodynamic and heat transfer model is developed which focuses on the heat transfer within the CPV heat sinks. The proposed system is examined in the ambient conditions of the top five LNG importing countries in the world. The results indicate that the proposed approach can deliver up to 24 MW electrical power, which is improved up to 180% in comparison with using the seawater-driven ORCs. The system produces up to 223 kg/s of cooling water in 7 °C, and its exergetic efficiency is up to 31%. From the CPV cooling point of view, the proposed system in 1000 × solar radiation concentration can keep the CPV temperature below 87 °C. Among studied regions, the best annual average of 2nd law efficiency can be achieved in India, about 28.3%. Utilizing the proposed system in a 100 kg/s LNG regasification unit can result in 26–32 MW of annual average power production, depending on the region it is used.

Numerical simulation of falling film sensible heat transfer over round horizontal tubes

Numerical simulations are performed to explore the heat transfer characteristics of falling films over horizontal round tubes with uniform heat flux imposed for a range of Reynolds numbers spanning the droplet, jet, and sheet regimes. Simulations results agree well with available experimental measurements. The study analyzes the local as well as average heat transfer behavior under the different flow modes. The numerical results show that the local Nusselt number (Nu) distribution depends on the flow features in each mode and varies substantially in all directions for the respective mode. In the droplet mode, the Nu value varies significantly as the droplet impinges and the remnant liquid-bridge retracts (peak instantaneous Nu near 6), followed by wave propagation over the tube surface with peak Nu around 0.25. For the jet modes, the local maximum in the heat transfer occurs off-center to the impingement location with magnitudes of peak Nu = 3.1 for the inline jet mode and Nu = 2.7 for the staggered jet mode, while on the rest of the tube surface, it has an inverse relation with the liquid film thickness. Substantial variations in the heat transfer value are also recorded in the middle of the two impinging jets with Nu = 0.95 in the inline jet mode where the neighboring jets do not interact, and Nu = 0.60 in the crest region of the staggered jet mode where the neighboring jets interact with each other. In the sheet mode, the Nu was seen to depend on the thickness of the liquid waves traversing over the tube surface. Lower Nu values were recorded beneath the crest location of the liquid waves, which increases (1.4–11.6% depending on circumferential location) abruptly in magnitude at the advancing fronts of the waves. The temperature distribution in the liquid film in each of the modes was examined to evaluate the mechanism of heat transfer process. This study also compares the local heat transfer coefficient distribution with the analytical heat transfer models derived to predict heat transfer performance over horizontal tube surfaces.

Analytical Model for Heat Transfer in a Discrete Parallel Fracture-Rock Matrix System.

Mass transport and heat transfer in the single fracture situated in the rock matrix have been investigated extensively in the past decades. Extended from the single fracture, the model of parallel fractures in the rock matrix considers the interactions of multiple fractures and the ambient rock matrix. Heat transfer in such discrete fractures is important to understand thermal energy transfer in the fractured porous media. In this study, an analytical solution is developed for transient heat transfer in discrete parallel fractures in the rock matrix. The newly proposed model accounts for thermal convection, conduction, and dispersion in the fractures, transverse thermal conduction in the rock matrix, and the interactions between parallel fractures. The analytical solutions of the spatiotemporal temperature distributions in the fractures and rock matrix are derived in the Laplace domain and verified with the previous study. The results illustrate that: (1) the fracture aperture and spacing are important to the temperature evolutions in the system. Heat transfers faster when discrete parallel fractures are wide and closely spaced; (2) different roles of longitudinal thermal conduction are observed at high and low flow velocities in the fractures; (3) thermal dispersivity in the fractures is important for temperature evolution and should not be ignored; (4) when the fractures are closely spaced, transverse thermal conduction in the rock matrix has minor influence on fracture temperature. It becomes important when the fractures are sparsely distributed; and (5) the sensitivity analysis indicates that the parallel fracture-rock matrix is most sensitive to fracture thermal dispersivity.

Experimental, numerical and analytical modeling of heat transfer of gravity driven dense particle flow in vertical heated plates

The heat transfer coefficient between the gravity driven dense particle flow and vertical heated plates is one of important parameters for the design and optimization of shell-and-plate moving packed bed heat exchangers. This paper gives extensively study on heat transfer between gravity driven dense particle flow and vertical heated plates by combined experimental, numerical, and analytical methods. The wall-to-particle heat transfer coefficients between silicon carbide particles and heated plates are experimentally tested in the designed heat transfer apparatus by varying the mass flow rates of particles with three mean particle diameters (0.207 ∼ 0.364 mm) and different widths of particle flow channel (4 ∼ 10 mm). A numerical calculation model and an analytical model are also established based on plug flow assumption, and compared with the experimental data. The results show that both of the two models exhibit a good agreement with the experimental results when estimating the overall wall-to-particle heat transfer coefficient. However, the numerical calculation model can obtain a more accurate description of the temperature profile than the analytical model attributes to the consideration of the effect of vertical heat diffusion. At last, a new semi-empirical correlation for estimation of overall wall-to-particle heat transfer coefficient was derived based on the analytical solution. Within the test scope of this study, the mean error and maximum error of this new correlation is 3.2% and 9.8%, respectively. The results also show that the reduction of the width of flow channel and the mean particle diameter contributes to the improvement of the wall-to-particle heat transfer coefficient.

Analytical models for heat transfer around a single ground heat exchanger in the presence of both horizontal and vertical groundwater flow considering a convective boundary condition

Ground heat exchanges (GHEs) are widely applied in the ground source heat pump (GSHP) system for exploration of shallow geothermal energy. Heat transfer around a single GHE in the presence of both horizontal and vertical groundwater flow under a convective boundary condition is investigated. To describe the heat transfer process, three typical GHE models including the solid cylindrical heat source (SCS) model, the ring coil heat source (RCS) model and the finite line source (FLS) model are improved by incorporating the effect of horizontal and vertical groundwater flow and considering convection between the air and the ground surface. After introducing a new variable, analytical solutions for the three improved models are established using the Green's function method. Comparison between the analytical solution and a numerical solution of COMSOL is made, and the agreement between the two solutions confirms the derivation and programming process of the analytical solution. Effects of horizontal and vertical groundwater flow on the temperature increment caused by a SCS are investigated using the analytical solution. For situations with high velocities of horizontal groundwater flow, the curve relating the temperature increment and the depth has a depth-independent segment, and the temperature increment for locations near the mid-depth of heat source remains unchanged with the velocity of vertical groundwater flow changing; the variation of average temperature increment of pipe wall with the variation of vertical groundwater velocity is negligible. For situations with low velocities of horizontal groundwater flow (Pex = 10), strong vertical groundwater flow (Pez = 100) makes the aforementioned depth-independent segment disappear, and the temperature increment at a downstream location increases from 0.58 °C to 7.79 °C with the depth increasing from 0 to lc. With Pez increasing from 10 to 100, the average temperature increment of pipe wall decreases from 10.14 °C to 6.92 °C, which reduces the thermal resistance of ground and improves the economic performance of the GSHP system.

A semi-analytical heat transfer model for deep borehole heat exchanger considering groundwater seepage

Groundwater seepage has important effect on the deep borehole heat exchanger (DBHE, having a depth of about 1000–3000 m) performance, but there is lack of efficient analytical or semi-analytical heat transfer model of DBHE considering groundwater seepage. By combing the temperature response functions (G-functions) of moving infinite line source (MILS) model, steady-state MILS model and steady-state moving infinite cylindrical source (MICS) model, a composite G-function is developed to analyze the MICS problem in the DBHE with groundwater seepage. Subsequently a semi-analytical model of DBHE is proposed based on the composite G-function to analyze the DBHE performance with groundwater seepage. The composite G-function and semi-analytical model are verified by comparison with numerical, analytical and experimental results. The composite G-function matches well with the G-function of numerical MICS model for different Péclet numbers (Pe) except during short time, and has higher precision than the G-function of MILS model. The proposed semi-analytical model using the composite G-function matches well with a 3D numerical model for different Darcy velocities at the infinite distance (u∞) and borehole radii (rb), and has higher precision than that using the G-function of MILS model. The proposed semi-analytical model is also applied to a field test of DBHE, and the result shows that the proposed semi-analytical model matches well with experimental data. The results indicate that the proposed semi-analytical model using the composite G-function is efficient to predict the DBHE performance in wide ranges.