Heat transfer analysis of pile geothermal heat exchangers with spiral coils

This paper investigates the transient heat conduction around the buried spiral coils which could be applied in the ground-coupled heat pump systems with the pile foundation as a geothermal heat exchanger. A transient ring-coil heat source model is developed, and the explicit analytical solutions for the temperature response are derived by means of the Green’s function theory and the image method. The influences of the coil pitch and locations are evaluated and discussed according to the solutions. In addition, comparisons between the ring-coil and cylindrical source models give that the improved finite ring-coil source model can accurately describe the heat transfer process of the pile geothermal heat exchanger (PGHE). The analytical solutions may provide a desirable and better tool for the PGHE simulation/design.     

Simulation and experimental analysis of optimal buried depth of the vertical U-tube ground heat exchanger for a ground-coupled heat pump system

This paper presents a numerical heat transfer model for vertical U-tube Ground Heat Exchangers (GHE). This model is uniquely able to take into to account different initial soil temperatures and physical properties at different depths. The model has been validated based on an experimental case study and has been used to simulate the thermal performance of GHEs. The simulation results show that for a 100-m vertical GHE, the first 70 m of the vertically buried GHE has a higher heat transfer capability than its last 30-m section. In addition, the validated model is used to investigate the optimal depth of vertical GHEs in five case studies ranging from 60 to 100 m length. Among them, the simulation results demonstrate that the GHE with buried depth of 70 m is able to provide the highest heat exchange rate per unit depth (54.1 and 47.0 W/m under heat rejection/extraction mode). It consequently results in shortest total GHE length of 11,388 m and the minimum cost of 1.82 million Yuan. However, a larger area is needed for boreholes and GHEs installation. Therefore, the optimal buried depth of the vertical U-tube GHEs for the studied case is 70 m on the condition of allocation of an abundant area to set up the boreholes.     

Experiment and simulation of temperature characteristics of intermittently-controlled ground heat exchanges

Because of poor heat transfer coefficients of soil/rock, ground source heat pumps (GSHP) or underground thermal energy storage (UTES) systems always occupy a large area and need many ground heat exchangers. This initial energy investment is so heavy that it cannot be used on a large-scale. Intermittent operation can reduce the extreme temperatures around the ground heat exchangers (GHEs) and keep the temperature in reasonable range. The aim of this study is to implement an experiment and develop a dynamic model of hydronic heating systems of GSHP in order to get a more fair comparison of energy efficiency between continuously controlled and intermittently controlled systems. Factors such as thermal inertia, temperature levels and lag time are also considered to see how they affect the efficiency. It is shown that temperature variation is related to the intermittent period and that intermittence prolongs the heat transfer without reaching at an utmost temperature (operation limitation). An effectively controlled intermittent process can optimize the capacity of heat exchange units so as to achieve better application of the ground energy. Additionally, the intermittent control can decrease the number of GHEs of GSHP and UTES systems and keep better working conditions.     

Natural convection heat transfer from a thermal heat source located in a vertical plate fin

A steady state conjugate conduction–convection investigation is performed on vertical plate fin in which a small heat source is located. Heat from the fin surface is transferred to the surroundings by laminar natural convection. The governing equations for the problem are the heat conduction equation for the fin and the boundary layer equations, which are continuity, momentum and energy equations, for the fluid. A computer program is written by using the finite difference method in order to solve the governing equations which are nonlinear and coupled. The best location of the heat source in the fin for maximum heat transfer rate depends on two parameters which are the conduction–convection parameter and the Prandtl number. The obtained results have shown that for the fin with large conduction–convection parameter, a heat source location for maximum heat transfer rate exists.     

考虑桩土差异的能源桩传热模型及其热响应半径计算

为解决能源桩传热分析中一般将桩土视为相同介质而引起误差的问题,建立一种可考虑桩体与土体之间热物性差异的U型埋管能源桩非稳态传热模型,将其与线热源模型进行对比,验证该模型的准确性。在此基础上,通过级数展开得到近似简化的能源桩热响应半径表达式。最后,对单位桩长换热量、桩体的热扩散系数、桩径以及土体类型进行分析,利用“储热比”评价上述参数对能源桩传热过程的影响。结果表明：该模型较线热源模型可更精准地描述能源桩传热过程,可有效避免传热初期低估桩壁过余温度以及传热稳定期高估桩体温度的问题;在典型的能源桩运行周期内,所提出的热响应半径计算方法误差在0.1 ℃以内,符合工程要求;能源桩传热过程中,土体的储热比随桩体热容、桩土间热扩散系数相对差异的减小而增大;桩壁过余温度及土体储热比均随桩径的增大而减小,随着传热时间的增加,不同桩径对应的桩壁过余温度差逐渐加大,土体储热比差值逐渐减小;相同换热功率作用下能源桩桩壁过余温度的变化率几乎不随传热时间增长而变化;传热90 d后,桩径对能源桩传热过程中能量传递分布影响不大。     

Heat transfer analysis of boreholes in vertical ground heat exchangers

A ground heat exchanger (GHE) is devised for extraction or injection of thermal energy from/into the ground. Bearing strong impact on GHE performance, the borehole thermal resistance is defined by the thermal properties of the construction materials and the arrangement of flow channels of the GHEs. Taking the fluid axial convective heat transfer and thermal “short-circuiting” among U-tube legs into account, a new quasi-three-dimensional model for vertical GHEs is established in this paper, which provides a better understanding of the heat transfer processes in the GHEs. Analytical solutions of the fluid temperature profiles along the borehole depth have been obtained. On this basis analytical expressions of the borehole resistance have been derived for different configurations of single and double U-tube boreholes. Then, different borehole configurations and flow circuit arrangements are assessed in regard to their borehole resistance. Calculations show that the double U-tubes boreholes are superior to those of the single U-tube with reduction in borehole resistance of 30-90%. And double U-tubes in parallel demonstrate better performance than those in series.     

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

The transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21012     

Improved low-order models for heat conduction problems

An explicit simple analytical method is presented for periodic heat conduction transfer in solids by using a perturbation method. Low order models are developed and their accuracy was compared to that of the complete numerical model. It is shown that first and second order models can be used efficiently for relatively low frequencies. An improvement of the method is then proposed by using a convergence acceleration of the series. This allows the use of the method at much higher frequencies.     

Transient heat and mass transfer in soils

Transient heat and mass transfer in soil surrounding a buried heat source are considered. One dimensional (spherical) models are developed to predict the coupled heat and moisture migration phenomena. Numerical solutions of the exact formulation are given. In addition, two types of closed-form solutions are derived employing approximate models. Experimental measurements are presented for two disparate soil types — a well-graded loam (slow hydraulic response) and sand (more rapid hydraulic response). Predicted and measured temperature variations at the heat source surface are compared. In all cases the numerical solution of the exact formulation agrees with the experimental data reasonably well. The closed-form solutions deviate somewhat from the measurements, but are shown to be useful for obtaining approximate predictions in a simple manner.     

Development of a finite element based heat transfer model for conduction mode laser spot welding process using an adaptive volumetric heat source

Numerically computed results of weld pool dimensions in conduction mode laser welding are sensitive to the estimated value of the actual beam energy absorbed by the substrate. In a conduction based heat transfer analysis, the incorporation of the laser beam induced energy as a surface only heat flux fails to realize enhanced heat transfer in weld pool as molten material attains higher temperature and convective transport of heat becomes predominant. An alternate is to include fluid flow analysis considering phenomenological laws of conservation of mass and momentum that greatly increases the complexity in modeling. Uncertainty of material properties such as effective thermal conductivity and viscosity in the weld pool also impedes such extensive fluid flow analysis. A simpler and tractable approach can be to consider a volumetric heat source within weld pool in a conduction based heat transfer analysis. Earlier efforts to accommodate volumetric heat source such as double-ellipsoidal form remained unpopular since the size of the final weld pool shapes is required to be known to begin with the calculation. The present work describes an improved approach where a volumetric heat source is defined adaptively as the size of the weld pool grows in size within the framework of a conduction based heat transfer analysis. The numerically computed results of weld pool dimensions following this approach have shown fair agreement with the corresponding measured values for laser spot weld samples.     

A modified genetic algorithm for solving the inverse heat transfer problem of estimating plan heat source

This work considers a new approach for solving the inverse heat conduction problem of estimating unknown plan heat source. It is shown that the physical heat transfer problem can be formulated as an optimization problem with differential equation constraints. A modified genetic algorithm is developed for solving the resulting optimization problem. The proposed algorithm provides a global optimum instead of a local optimum of the inverse heat transfer problem with highly-improved convergence performance. Some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.     

Experimental study of several types of ground heat exchanger using a steel pile foundation

An experimental study of several types of ground heat exchangers (GHEs) installed in a steel pile foundation, including double-tube, U-tube, and multi-tube GHEs, was carried out at Saga University. Water flows through the heat exchangers and exchanges heat to or from the ground. The performance of GHEs was investigated under actual operation in the cooling mode with flow rates of 2, 4, and 8 l/min. Temperatures of the ground and GHE tube wall were measured to find the temperature distributions according to the depth of the ground and depth of the GHE tube wall. The temperatures of the inlet and outlet of circulated water were also measured to calculate the heat exchange rate. The double-tube had the highest heat exchange rate, followed by the multi-tube and U-tube GHEs. For example, the average heat exchange rate of GHEs over 24 h of continuous operation with a flow rate of 4 l/min was 49.6 W/m for the double-tube, 34.8 W/m for the multi-tube, and 30.4 W/m for the U-tube. An increasing flow rate increased the heat exchange rate of the GHEs. The heat exchange rates increased significantly for flow rate increases from 2 to 4 l/min, but only slightly changed from 4 to 8 l/min.     

A fast algorithm for the hourly simulations of ground-source heat pumps using arbitrary response factors

Hourly energy simulations are an important part of the design and analysis of ground-source heat pump systems. In order to evaluate the fluid temperature in the borehole of a geothermal heat pump system, most of the current models express the heat transfer rate as a sum of step changes in heat transfer rate. The borehole temperature is then computed as a superposition of the different contributions of each time step. The main difference between the different models lies in the way the step response is computed. Since all these methods are based on a convolution scheme, long time simulations are very time consuming. Many load aggregation algorithms have been proposed in order to reduce this computational time. In a previous paper we proposed a new algorithm to evaluate the overall response which was much faster than the classical aggregation schemes. However this new algorithm was based on the cylindrical source step response for a single borehole. In this paper, we present a generalization of this scheme for any kind of step response making it a very powerful tool for hourly simulations.     

An improved thermal response test for U-tube ground heat exchanger based on optical fiber thermometers

As part of a new thermal response test (TRT) and to determine ground thermal conductivities, vertical temperature profiles were obtained using retrievable optical fiber sensors inserted into the U-tubes of two ground heat exchangers (GHEs) installed at Maebaru City (Fukuoka, Kyushu) and Kushiro City (Hokkaido), Japan. Measured profiles and outlet temperatures from TRTs were history-matched with the cylindrical source function. Nonlinear regression was used to estimate the vertical distribution of ground thermal conductivities. The computed distribution is consistent with measured data indicating both the reliability of the optical fiber thermometer and TRT interpretation. It is expected that TRTs and optical fiber thermometers will prove to be increasingly useful for optimizing the depth of the GHEs installed in heterogeneous formations, and consequently will minimize installation costs of geothermal heat pump systems.     

heat in history Isaac Newton and Heat Transfer

Abstract

An attempt is made to provide historical perspectives on the influences of Newton's law of cooling (1701) on the development of heat transfer theory. Newton's cooling law provides the first heat transfer formulation and is the formal basis of convective heat transfer. The cooling law was incorporated by Fourier (1822) as the convective boundary condition (Biot number) in his mathematical theory of heat conduction. The decisive step in the application of the concept of heat transfer coefficient occurred with the publication of the “basic law of heat transfer” by Nusselt in 1915. Newton's law is valid only for forced convection with constant physical properties. The close relationships for various heat transfer theories are pointed out. Heat transfer phenomena can also be classified based on the relationship between surface heat flux and temperature difference as a driving force.     

Axial heat conduction in a moving semi-infinite fluid

This paper considers the steady state conduction of heat from a wall to a fluid moving at a uniform velocity. The wall is heated by a step change in temperature. Although this appears to be a classical heat conduction problem, its application to various convective heat transfer problems is new. The mathematical procedure leads to the computation of the temperature field and the heat transfer coefficient. In the presence of a step change in the wall temperature, it is shown that the Stanton number is a function of the Peclet number alone. The acquired analytical results show that, near the thermal entrance location, heat conduction dominates and the local heat flux becomes independent of velocity. This phenomenon applies to classical convection problems in various-shaped ducts.     

Experimental study of heat transfer of buried finned pipe for ground source heat pump applications

Ground heat exchangers have vital importance for ground source heat pump applications. Various configurations tried to improve heat transfer in the soil. A new kind of aluminium finned pipe buried in the soil for this aim. In order to compare effectiveness of the Al finned pipe over the traditional PPRC pipe an experimental study carried out. The experimental GSHP system was installed at Y?ld?z Technical University Davupasa Campus on 800 m² surface area with no special surface cover. Temperature data were collected using thermocouples buried in soil horizontally and vertically at various distances from the pipe center and at the inlet and the outlet of the ground heat exchanger. Experimental results were compared with results from analytical study. To compare effectiveness of the Al finned pipe and PPRC pipe a new parameter defined as transferred amount of heat per unit mass of working fluid per unit time for this aim. It is found that Al finned pipe has higher heat transfer values than the traditional PPRC pipe.     

基于线热源理论的垂直U型埋管换热器传热模型的研究

基于经典常热流线热源理论,通过引入叠加原理、阶跃负荷及孔洞热阻思想将其发展为能够适用于变热流埋管换热与地源热泵系统模拟的变热流线热源模型,并与改进的经实验与理论验证的圆柱源理论模型进行了比较与分析。结果表明:所发展的变热流线热源模型能够有效地模拟地下埋管的换热过程,可作为地下垂直U埋管换热过程的计算模型,为地源热泵地下埋管换热器的设计计算及地源热泵系统的模拟提供了一种新的简单而又实用的计算方法。     

Conjugate heat transfer characterization in cooling channels

Cooling technology of gas turbine blades,primarily ensured via internal forced convection,is aimed towards withdrawing thermal energy from the airfoil.To promote heat exchange,the walls of internal cooling passages are lined with repeated geometrical flow disturbance elements and surface non-uniformities.Raising the heat transfer at the expense of increased pressure loss;the goal is to obtain the highest possible cooling effectiveness at the lowest possible pressure drop penalty.The cooling channel heat transfer problem involves convection in the fluid domain and conduction in the solid.This coupled behavior is known as conjugate heat transfer.This experimental study models the effects of conduction coupling on convective heat transfer by applying iso-heat-flux boundary condition at the external side of a scaled serpentine passage.Investigations involve local temperature measurements performed by Infrared Thermography over flat and ribbed slab configurations.Nusselt number distributions along the wetted surface are obtained by means of heat flux distributions,computed from an energy balance within the metal domain.For the flat plate experiments,the effect of conjugate boundary condition on heat transfer is estimated to be in the order of 3%.In the ribbed channel case,the normalized Nusselt number distributions are compared with the basic flow features.Contrasting the findings with other conjugate and convective iso-heat-flux literature,a high degree of overall correlation is evident.     

Development of suitability maps for ground-coupled heat pump systems using groundwater and heat transport models

The thermophysical properties of subsurface materials (soils, sediments and rocks) and groundwater flow strongly affect the heat exchange rates of ground heat exchangers (GHEs). These rates can be maximized and the installation costs of the ground-coupled heat pump (GCHP) systems reduced by developing suitability maps based on local geological and hydrological information. Such maps were generated for the Chikushi Plain (western Japan) using field-survey data and a numerical modeling study. First, a field-wide groundwater model was developed for the area and the results matched against measured groundwater levels and vertical temperature profiles. Single GHE models were then constructed to simulate the heat exchange performance at different locations in the plain. Finally, suitability maps for GCHP systems were prepared using the results from the single GHE models. Variations in the heat exchange rates of over 40% revealed by the map were ascribed to differences in the GHE locations, confirming how important it is to use appropriate thermophysical data when designing GCHP systems.