A practical method for computing the thermal properties of a Ground Heat Exchanger

The aim of this paper is to show a practical way of estimating the thermal ground properties, namely the ground thermal conductivity, and in particular the thermal diffusivity and the volumetric heat capacity in a reliable manner, for sizing Ground Heat Exchangers (GHEs). A well-known thermal model, proposed by Blackwell in 1954, is applied and is validated both in the heating mode and in the cooling mode, using a GHE as a probe. The value of the thermal conductivity can be easily determined by the model but the procedure also requires knowledge of the ground specific heat capacity and density, which are normally deduced from the (non-accurate) geological data of the site.In addition to the above, the thermal model is also solved analytically –based on the actual parameters used in the experiment–leading to the computation of the ground thermal diffusivity, the volumetric heat capacity and the thermal resistance of the GHE. The possible errors and drawbacks of the whole method are then discussed and finally a complete set of guidelines is provided to the field Engineer for estimating the ground thermal properties from a single test, rendering the use of the geological data of the side unnecessary.     

光学热带法测量固态材料热物性研究

针对接触式瞬态热带法测量导热系数时,加热丝和样品间接触热阻,会影响实验测量结果以及对固体样品形状大小要求较高的现状,根据瞬态热带法原理,本文提出了一种光学瞬态热带法来测量固体材料的导热系数。采用连续激光为加热源,通过透镜将光斑放大并聚焦照射在样品表面,实现样品非接触式测量。构建二维导热模型,采用红外热像仪记录样品表面温升随时间的变化关系,根据导热理论模型求出待测样品的热扩散系数及导热系数。以K9和石英玻璃为样品对本套测量方法进行验证,制备并测量了纯石蜡、0.5%和1%石墨烯-石蜡的固态复合相变材料的导热系数,探讨了影响实验结果的潜在因素。     

The Measurement of Thermal Conductivities of Silica and Carbon Black Powders at Different Pressures by Thermal Conductivity Probe

This investigation was done to study the gas filled powder insulation and thermal conductivity probe for themeasurement of thermal conductivity of powders.The mathematical analysis showed that the heat capacity ofthe probe itself and the thermal resistance between the probe and powder must be considered.The authorsdeveloped a slender probe and measured the effective thermal conductivity of silica and carbon black powdersunder a variety of conditions.     

Reconstruction of thermal conductivity and heat capacity using a tomographic approach

We consider the estimation of the volumetric heat capacity and the thermal conductivity as distributed parameters. The measurement scheme consists of sequentially heating the boundary of the object in different source locations and measuring the induced temperature evolutions in different measurement locations on the boundary. The estimation of the distributions of volumetric heat capacity and thermal conductivity based on these boundary data is an ill-posed inverse boundary value problem. We propose an approach which is based on transient data on the boundary and the modelling of the unknown coefficients as Markov random fields. The intended applications are non-destructive retrieval of defects as well as the estimation of macroscopic characteristics of novel materials. We evaluate the proposed approach by a numerical simulation.     

Experimental determination of the effective thermal capacity function and other thermal properties for various phase change materials using the thermal delay method

The recently presented thermal delay method is an improved version of the well-known T-history method, which is widely used for thermal properties measurement of phase change materials (PCM). The most important difference between the thermal delay and the T-history methods is that the former is based on the use of thermal delay (i.e. temperature difference) between PCM and a reference fluid at any specified time while the latter makes use of their time delay at any specified temperature. Although the thermal delay method has been documented in our previous publication, measurements are performed of the known and indisputable values of ethyl alcohol thermal capacity and the latent heat of the double distilled water (WFI), which confirm the accuracy of the method. Additional comparisons with values provided by PCM producing companies show disagreements lower than 1.7%. The main volume of measurements of the present study includes the following thermal properties of various practically interesting PCM: (a) the temperatures at the ends of the two-phase region; (b) the liquid and solid PCM thermal capacities; (c) the phase change heat; (d) the heat storage capacity during any specified temperature range; and (e) the effective thermal capacity function, which is a very important and useful property for practical applications. The above function is provided for each one of the PCM examined in the form of diagrams, as well as in the form of analytical expressions derived by curve fitting to the processed experimental values. All measurements were repeated 20 times and the results were averaged in order to minimize errors from accidental incidents.     

Simultaneous estimation of spatially distributed thermal conductivity,heat capacity and surface heat transfer coefficient in thermal tomography

In thermal tomography, the thermal properties of a target are estimated as spatially distributed parameters based on non-invasive measurements of surface temperatures. In the measurement setup, the target is sequentially heated at different source locations and the induced temperature evolutions are measured at several measurement locations on the surface. In [V. Kolehmainen, J. Kaipio, H. Orlande, Reconstruction of thermal conductivity and heat capacity using a tomographic approach, Int. J. Heat Mass Transfer 50 (25–26) (2007) 5150–5160], it was demonstrated with simulations that simultaneous estimation of spatially distributed thermal conductivity and volumetric heat capacity from transient boundary data is feasible when the boundary heat flux from the target to the surrounding medium is known all over the target boundary. In this article, we extend the computational methods towards the more practical setup of imaging targets, where the boundary heat flux from the target to the surrounding medium is not known. We model the surface heat transfer coefficient as a spatially distributed parameter on the target boundary and estimate it simultaneously with the spatially distributed thermal conductivity and volumetric heat capacity using the statistical (Bayesian) inversion framework. The feasibility of the approach is evaluated with simulations.     

Measurements of thermal properties of insulation materials by using transient plane source technique

The paper reports on the measuring technique and values of the measured thermal properties of some commonly used insulation materials produced by local manufacturers in Saudi Arabia. Among the thermal properties of insulation materials, the thermal conductivity (k) is regarded to be the most important since it affects directly the resistance to transmission of heat (R-value) that the insulation material must offer. Other thermal properties, like the specific heat capacity (c) and density (ρ), are also important only under transient conditions. A well-suited and accurate method for measuring the thermal conductivity and diffusivity of materials is the transient plane source (TPS) technique, which is also called the hot disk (HD). This new technique is used in the present study to measure the thermal conductivity of some insulation materials at room temperature as well as at different elevated temperature levels expected to be reached in practice when these insulations are used in air-conditioned buildings in hot climates. Besides, thermal conductivity values of the same type of insulation material are measured for samples with different densities; generally, higher density insulations are used in building roofs than in walls. The results show that the thermal conductivity increases with increasing temperature and decreases with increasing density over the temperature and density ranges considered in the present investigation.     

Through-plane thermal conductivity of the microporous layer in a polymer electrolyte membrane fuel cell

Understanding the thermal properties of the microporous layer (MPL) is critical for accurate thermal analysis and improving the performance of proton exchange membrane (PEM) fuel cells operating at high current densities. In this study, the effective through-plane thermal conductivity and contact resistance of the MPL have been investigated. Gas diffusion layer (GDL) samples, coated with 5%-wt. PTFE, with and without an MPL are measured using the guarded steady-state heat flow technique described in the ASTM standard E 1225-04. Thermal contact resistance of the MPL with the iron clamping surface was found to be negligible, owing to the high surface contact area. Effective thermal conductivity and thickness of the MPL remained constant for compression pressures up to 15 bar at 0.30 W/m°K and 55 μm, respectively. The effective thermal conductivity of the GDL substrate containing 5%-wt. PTFE varied from 0.30 to 0.56 W/m°K as compression was increased from 4 to 15 bar. As a result, GDL containing MPL had a lower effective thermal conductivity at high compression than the GDL without MPL. At low compression, differences were negligible. The constant thickness of the MPL suggests that the porosity, as well as heat and mass transport properties, remain independent of the inhomogeneous compression by the bipolar plate. Despite the low effective thermal conductivity of the MPL, thermal performance of the GDL can be improved by exploiting the excellent surface contact resistance of the MPL.     

Estimation of soil and grout thermal properties through a TSPEP (two-step parameter estimation procedure) applied to TRT (thermal response test) data

In this paper, a versatile TSPEP (two-step parameter estimation procedure) based on a three-dimensional numerical model of a geothermal system is presented. The procedure is applied to both simulated and experimental TRT (thermal response test) data in order to restore the grout and soil thermal conductivities and volumetric heat capacities. The TSPEP is essentially a two-step process. The first step uses the parameter estimation procedure, in the early transient regime to restore the grout thermal conductivity and volumetric heat capacity. The values from the first step are used as the input values in the second step, in which the parameter estimation procedure is applied to the late transient regime to restore the soil thermal conductivity and volumetric heat capacity. Further iterations of these two steps can be used to improve the accuracy of the procedure and are discussed in this paper. The time separation used between the estimation of the soil properties and the estimation of the grout properties partially uncouples the two problems and makes the estimation of these four parameters feasible. A criterion to select the time separation is discussed and validated in this paper.     

Thermal Property Measurements of a Large Prismatic Lithium-ion Battery for Electric Vehicles

Because of the high cost of measuring the specific heat capacity and the difficulty in measuring the thermal conductivity of prismatic lithium-ion batteries, two devices with a sandwiched core of the sample-electric heating film-sample were designed and developed to measure the thermal properties of the batteries based on Fourier's thermal equation. Similar to electrical circuit modeling, two equivalent thermal circuits were constructed to model the heat loss of the self-made devices, one thermal-resistance steady circuit for the purpose of measuring the thermal conductivity, the other thermal-resistance-capacitance dynamic circuit for the purpose of measuring the specific heat capacity. Using the analytic method and recursive least squares, the lumped model parameters of these two thermal circuits were extracted to estimate the heat loss and correct the measured values of the self-made devices. Compared to the standard values of the reference samples of the glass and steel plates, the measured values were corrected to improve the measurement accuracies beyond 95% through steady thermal-circuit modeling. Compared to the measured value of the specific heat capacity of the battery sample at 50% state of charge using the calorimeter, the measured value using the self-made device was corrected in order to elevate the measurement accuracy by about 90% through dynamic thermal-circuit modeling. As verified through the experiments, it was reliable, convenient, and low cost for the proposed methodology to measure the thermal properties of prismatic lithium-ion batteries.     

Sequential estimation of borehole resistance and ground thermal properties through thermal response test

Borehole thermal resistance and ground thermal properties (thermal conductivity and heat capacity) are the key parameters to implement the ground source heat pump (GSHP), usually obtained by thermal response test. In this study, a novel sequential parameters estimation method for the above three parameters is proposed, and the sensitivity analysis by using a special correlation method is performed to decide the best estimation sequences. At first, the Spearman partial rank correlation coefficient was used to represent the correlation between the estimated thermal properties and fluid temperature for the line source model (ILS), then the estimation sequence for the three parameters could be determined by the correlation results. Lastly, with the estimation step, Monte Carlo method was adopted to determine the parameters replacing conventional iterative algorithms. In addition, the effect of value bounds and initial inputs as well as random samples was investigated. The results showed that compared to the other estimation steps, the estimation sequence following borehole resistance firstly, then thermal conductivity, heat capacity lastly could get the best precision with 4.5%, 0.4%, 1% respectively. Specially, the estimation precision for ground heat capacity could be promoted by the sequential estimation. Also, the effect of value bounds on estimation precision was nearly eliminated by the proposed method.     

Performance of solid particles flow thermal storage material made of desert sand

It is a safe and low-cost new heat storage method to realize sensible heat storage at medium and high temperature by using flowing inorganic inert solid particle materials. The cost and performance of granular heat storage medium are very important for this kind of heat storage technology. The yellow sand in southeast of Tenggri Desert in Ningxia is studied. By thermal shock and grinding methods, the tests of thermal shock-resistance and wear resistance were carried out, under laboratory conditions, for the unscreened raw sand and the screened sand samples with three grain sizes (40–60 mesh, 60–80 mesh, and 80–100 mesh). The particle size of the raw sand is 150–300 µm (60–100 meshes) accounts for 60% (wt %) or more and meets the requirement of heat storage material. The density, thermal conductivity, and specific heat of raw sand are higher than those of three kinds of screened sand. Thermal shock and grinding affect the particle size distribution, density, specific heat, and thermal conductivity of the particles. The degree of influence varies with the particle size. The volume ratio heat capacity is used to measure the heat storage performance of the particles. Thermal shock results in a better thermal storage performance of the screened sand than the original sand. After comprehensive analysis of the properties of three kinds of screened sand, it is found that the content of 60–80 mesh-screened sand (31.75%) is the highest in the original sand. After thermal shock and grinding, the screened sand not only has good heat storage performance (average volumetric specific heat capacity 3.232 J· K^?3· K^?1), but also has the smallest change of particle size (breaking rate is less than 24, and agglomeration rate is less than 6), and the thermal shock resistance and wear resistance are outstanding. It is suggested that the screened sand with the particle size range of 200-300µm (60–80 mesh), also the particles with the highest content in the original sand, should be selected as the solid particle flowing heat storage medium.     

Borehole temperature evolution during thermal response tests

The measurement of temperature inside a borehole at specified depths during a thermal response test, used to infer the subsurface and the borehole thermal properties for the design of a ground-coupled heat pump system, allows the correlation of the subsurface thermal conductivity with stratigraphy. The temperature signal measured in the borehole during heat injection in a ground heat exchanger made with a single U-pipe, however, depends on the location of the temperature sensor in the borehole, which is difficult to determine in practice. Two-dimensional numerical simulations of the borehole temperature evolution during thermal response tests show that the temperature inside the borehole homogenizes rapidly after heat injection is stopped. Monitoring temperature recovery consequently helps to analyze measurements conducted at depth inside the borehole, since recovery measurements are not significantly influenced by the position of the sensor in the borehole. Numerical simulations also indicate that the borehole thermal resistance is best determined using a combination of recovery and heat injection data.     

Revisiting the block method for evaluating thermal conductivities of clay and granite

Determination of thermal conductivities of porous media using the contact method was revisited and revalidated. Thermal conductivities of granite and clay were determined in the laboratory with and without the use of thermal interface material (TIM) (Arctic Silver®) to reduce contact resistance. KD2 probe was also used with and without TIM to compare results. Thermal conductivity of dry clay sample increased from 0.68 W/mK to 0.85 W/mK while that of granite sample increased from 2.95 W/mK to 3.95 W/mK with TIM. The difference in thermal conductivities with and without TIM was significant at (P > 0.05).     

An optimal guarding scheme for thermal conductivity measurement using a guarded cut-bar technique,part 1 experimental study

In the guarded cut-bar technique, a guard surrounding the measured sample and reference (meter) bars is temperature controlled to carefully regulate heat losses from the sample and reference bars. Guarding is typically carried out by matching the temperature profiles between the guard and the test stack of sample and meter bars. Problems arise in matching the profiles, especially when the thermal conductivities of the meter bars and of the sample differ, as is usually the case. In a previous numerical study, the applied guarding condition (guard temperature profile) was found to be an important factor in measurement accuracy. Different from the linear-matched or isothermal schemes recommended in literature, the optimal guarding condition is dependent on the system geometry and thermal conductivity ratio of sample to meter bar. To validate the numerical results, an experimental study was performed to investigate the resulting error under different guarding conditions using stainless steel 304 as both the sample and meter bars. The optimal guarding condition was further verified on a certified reference material, pyroceram 9606, and 99.95% pure iron whose thermal conductivities are much smaller and much larger, respectively, than that of the stainless steel meter bars. Additionally, measurements are performed using three different inert gases to show the effect of the insulation effective thermal conductivity on measurement error, revealing low conductivity, argon gas, gives the lowest error sensitivity when deviating from the optimal condition. The result of this study provides a general guideline for the specific measurement method and for methods requiring optimal guarding or insulation.     

Prediction of thermal conductivity of ethylene glycol–water solutions by using artificial neural networks

The objective of this study is to develop an artificial neural network (ANN) model to predict the thermal conductivity of ethylene glycol–water solutions based on experimentally measured variables. The thermal conductivity of solutions at different concentrations and various temperatures was measured using the cylindrical cell method that physical properties of the solution are being determined fills the annular space between two concentric cylinders. During the experiment, heat flows in the radial direction outwards through the test liquid filled in the annual gap to cooling water. In the steady state, conduction inside the cell was described by the Fourier equation in cylindrical coordinates, with boundary conditions corresponding to heat transfer between the solution and cooling water. The performance of ANN was evaluated by a regression analysis between the predicted and the experimental values. The ANN predictions yield R² in the range of 0.9999 and MAPE in the range of 0.7984% for the test data set. The regression analysis indicated that the ANN model can successfully be used for the prediction of the thermal conductivity of ethylene glycol–water solutions with a high degree of accuracy.     

Numerical analysis on the thermal behavior of high temperature latent heat thermal energy storage system

High temperature latent heat thermal energy storage technology is a promising option for future cost reduction in parabolic trough or tower power plant. However, low thermal conductivity of phase-change material (PCM) is the major shortage of latent heat thermal energy storage. This paper proposed a new thermal energy storage system (TESS) that metal foam and fins were used to enhance the effective conductivity of PCM. Three-dimensional physical model was established for representative element extracted from TESS. Considering the natural convection in the liquid part of PCM, volume-averaged mass and momentum equations were employed with the Brinkman–Forchheimer extension to Darcy law to simulate the porous resistance. A local thermal equilibrium model was developed to obtain temperature field. The governing equations were solved with finite-volume approach and enthalpy method was employed to account for phase change. The model was firstly validated against low temperature experiments from the literature and then used to predict the charging and discharging behavior of the present TESS. The position of solid/liquid interface was explored and the effects of design parameters, including that of metal foam pore density and porosity, configuration of fin and Rayleigh number, on melting and solidifying rate and energy stored in each time step were revealed and discussed. The results indicate that metal foam and fins can effectively improve the heat transfer performance for thermal storage system and decrease charging and discharging time.     

Simultaneous measurements of thermal conductivity and thermal diffusivity of insulators,fluids and conductors using the transient plane source (TPS) technique

Simultaneous measurements of thermal conductivity and thermal diffusivity of composite red-sand bricks, glycerine and mercury have been made at room temperature by the recently developed transient plane source (TPS) technique. This paper describes, in brief, the theory and the experimental conditions for the simultaneous measurements of thermal conductivity and thermal diffusivity of insulators, fluids and metals. The source of heat is a hot disc made out of bifilar spirals. The disc also serves as a sensor of temperature increase in the sample. The measured values of the thermal conductivity and thermal diffusivity of these samples are in agreement with the values reported earlier using other methods. The advantage of the TPS technique is the simplicity of the equipment, simultaneous information on thermal conductivity and thermal diffusivity, and also the applicability of the technique to insulators, fluids and metals.     

Measurement of in-plane thermal conductivity of carbon paper diffusion media in the temperature range of −20 °C to +120 °C

Carbon paper is commonly used as the gas diffusion layer (GDL) in polymer electrolyte membrane (PEM) fuel cells as it exhibits high chemical and mechanical durability. This diffusion medium is also anisotropic, which directly affects its transport properties and specifically the thermal conductivity. In this study, the in-plane thermal conductivity of the carbon paper GDL was determined using thermal diffusivity measurements for a temperature range from −20 to +120 °C and four Teflon loadings (0, 5, 20 and 50 wt.%). It is important to understand the effect of temperature on the thermal conductivity since PEM fuel cells are designed to operate under various temperatures depending on the application of use. Further, Teflon is used to change the hydrophobic properties of the carbon paper GDL with 20 wt.% as the most widely used percentage. In this study, the Teflon loadings were chosen to gain a comprehensive understanding of the thermal resistance due to Teflon. In this study, a quasi-steady method was used to measure the thermal properties of the carbon paper; hence, the phase transformation in the presence of PTFE was investigated. The thermal conductivity decreases with an increase in temperature for all samples. The addition of as little as 5 wt.% Teflon resulted in high thermal resistance decreasing the overall thermal conductivity of the sample. Further addition of Teflon did not have major effects on the thermal conductivity. For all treated samples, the thermal conductivity lies in the range of 10.1–14.7 W/mK. Finally, empirical relations for the thermal diffusivity and conductivity with temperature were deduced.     

Determination of the thermal conductivities of building and insulating materials by the probe method

A simple and inexpensive electrical circuit based on the transient probe method has been developed for the determination of thermal conductivities of building and insulating materials namely limebrick, gypsum, rockwool and polystrene foam. The solution of the unsteady state heat conduction equation has been approximated by considering certain simplifying assumptions which have been justified by experimental observations. The overall accuracy of the thermal conductivity measurements is estimated to be within ± 3%.