Internal Temperature Profiles Research Articles

An Electro-Thermal Model for LFP Cells: Calibration Procedure and Validation

Lithium batteries for energy storage systems are a prominent solution for both stationary and mobile applications. Electro-thermal modelling of the cell is a useful tool for monitoring voltage and temperature in order to predict battery behaviour especially in cases of critical operative conditions. This paper provides a modelling approach focusing on the calibration of parameters of an electro-thermal model for large prismatic LFP lithium cells. The designed model is tuned by means of experimental tests that identify a set of parameters that are function of a cell’s state-of-charge and temperature. The model outputs are voltage, cell surface, and internal temperature profiles, which are validated against experimental data referring to realistic working conditions, even providing an intense level of thermal stress. The model accuracy is marked by a voltage mean average error lower than 1% and a mean cell surface temperature deviation lower than 1 K.

Thermoregulatory morphodynamics of honeybee swarm clusters.

During reproductive swarming, honeybee clusters of more than 10,000 individuals that hang from structures in the environment (e.g. tree branches) are exposed to diurnal variations in ambient temperature for up to a week. Swarm clusters collectively modulate their morphology in response to these variations (i.e. expanding/contracting in response to heating/cooling) to maintain their internal temperature within a tolerable range and to avoid exhausting their honey stores prematurely. To understand the spatiotemporal aspects of thermoregulatory morphing, we measured the change in size, shape and internal temperature profiles of swarm clusters in response to dynamic temperature ramp perturbations. Swarm clusters showed a two-fold variation in their volume/density when heated from 15°C to 30°C. However, they did not reach an equilibrium size or shape when held at 30°C for 5 h, long after the core temperature of the cluster had stabilized. Furthermore, the changes in cluster shape and size were hysteretic, contracting in response to cooling faster than expanding in response to heating. Although the base contact diameter of the cluster increased continuously when the swarm was heated, the change in length of the swarm (base to tip) over time was non-monotonic. Consequently, the aspect ratio of the swarm fluctuated continuously even when held at a constant temperature. Taken together, our results quantify the hysteretic and anisotropic morphological responses of swarm clusters to ambient temperature variations while suggesting that both mechanical constraints and heat transfer govern their thermoregulatory morphodynamics.

A Large-Eddy Simulation study on the effect of fuel configuration and pan distance towards chemical species for under-ventilated compartment fire scenario

A set of numerical analyses was conducted to investigate the effect of fuel location of dual burners in an under-ventilated ISO9705 compartment room. Moreover, the influences of the burner separation displacement on the fire development, the evolution of thermal layers, the distribution of toxic gas species were comprehensively studied. The simulations were conducted using a novel in-house large eddy simulation (LES) based fire field model comprised of subgrid-scale (SGS) turbulence, detailed chemical kinetics of combustion, soot and radiation models. The first part of the simulation focused on 3 different fuel distributions: single centre burner (SCB), single rear burner (SRB) and two distributed burner (TDB). Alternative configurations were considered for dual burners with 4 different distances between the dual burners, to study the influence towards air flow at the doorway, internal temperature profile and major chemical species (i.e. CO/CO2) distributions. The numerical outcome states that fuel distribution has a minor effect on heat release rate and the total CO2 amount but noticeable differences in CO's generation and distribution. Overall, the temperature and gas field predictions were almost identical for all dual burner cases, while significant differences were observed at the rear section of the compartment, especially temperature, CO/CO2vol fraction and soot concentration.

Identification of Coating Thickness in Cement Rotary Kiln

The cement industry is one of the major industries in every country. This industry is the driving force behind the development of a nation. The heart of this industry is the rotary kiln. One of the significant concerns about a rotary kiln is forming a cover of molten materials on the kiln's inner wall called coating. The low thickness of this coating cause burns to the wall refractory bricks and heavy damage to the kiln, while its high thickness reduces the production volume and quality of products. Currently, the kilns are checked by experienced technicians for empirical coating estimation. This paper aims to identify the thickness of the coating for the automatic control purpose of the kiln. The identification problem of coating thickness is based on thermal resistances in different layers of the kiln and heat transfer equations between these layers. For this purpose, the linear and nonlinear identification methods such as Ordinary Least Squares (OLS), Recursive Least Squares (RLS), global search method, and genetic algorithm are used. The coating can be identified in the proposed identification approach by having the kiln's ambient and internal solid temperature profiles. The raw data for the identification process has been extracted by Finite Element Analysis (FEA) for a given solid temperature profile along with the kiln and different kiln coating thicknesses. The modeling and simulations carried out in this paper show that the identification methods were able to determine the amount of coating with acceptable errors depending on the method.

An Anatomical Thermal 3D Model in Preclinical Research: Combining CT and Thermal Images.

Even though animal trials are a controversial topic, they provide knowledge about diseases and the course of infections in a medical context. To refine the detection of abnormalities that can cause pain and stress to the animal as early as possible, new processes must be developed. Due to its noninvasive nature, thermal imaging is increasingly used for severity assessment in animal-based research. Within a multimodal approach, thermal images combined with anatomical information could be used to simulate the inner temperature profile, thereby allowing the detection of deep-seated infections. This paper presents the generation of anatomical thermal 3D models, forming the underlying multimodal model in this simulation. These models combine anatomical 3D information based on computed tomography (CT) data with a registered thermal shell measured with infrared thermography. The process of generating these models consists of data acquisition (both thermal images and CT), camera calibration, image processing methods, and structure from motion (SfM), among others. Anatomical thermal 3D models were successfully generated using three anesthetized mice. Due to the image processing improvement, the process was also realized for areas with few features, which increases the transferability of the process. The result of this multimodal registration in 3D space can be viewed and analyzed within a visualization tool. Individual CT slices can be analyzed axially, sagittally, and coronally with the corresponding superficial skin temperature distribution. This is an important and successfully implemented milestone on the way to simulating the internal temperature profile. Using this temperature profile, deep-seated infections and inflammation can be detected in order to reduce animal suffering.

Physicochemical characteristics, microbiological safety and sensory acceptability of coconut dregs during fermentation using Rhizopus oligosporus

The aims of this study were to determine the changes in physicochemical characteristics, microbiological safety and sensory acceptability of coconut dregs during fermentation using Rhizopus oligosporus. Fermentation of coconut dregs was done using Rhizopus oligosporus as a starter culture for three days (fresh coconut dregs was used as control). The control sample is fresh dregs without any process while other samples will through fermentation. The physicochemical analyses included internal temperature, pH, total soluble solids (TSS), water activity (aw), colour, proximate analysis and texture profile. Microbiological analyses included total plate count (TPC), Escherichia coli, Salmonella spp., Pseudomonas aeruginosa, Bacillus cereus, Staphylococcus aureus and LAB. Sensory acceptability was also carried out. The results showed that internal temperatures and TSS were increased and the pH decreased throughout the fermentation. The aw showed no changes. The colour of fermented coconut dregs had a higher percentage in lightness compared to yellowness and redness which showed that the colour of fermented dregs still maintains the white colour. A gradual increased in hardness, springiness, cohesiveness, chewiness and resilience was observed. Moisture content, crude fat and protein increased while ash and crude fibre decreased but no changes in carbohydrate throughout the fermentation. The results for microbial count showed the reducing number of S. aureus and B. cereus while increasing number of TPC and LAB. Interestingly, E. coli, Salmonella spp. and P. aeruginosa was not detected in fermented and non-fermented coconut dregs. The non-fermented coconut dregs were preferred more by the panellists as it obtained the highest score in term of colour, odour, texture and overall acceptability on sensory attributes evaluation.

I–Love–Q relations for realistic white dwarfs

ABSTRACT The space-borne gravitational wave interferometer, Laser Interferometer Space Antenna, is expected to detect signals from numerous binary white dwarfs. At small orbital separation, rapid rotation and large tidal bulges may allow for the stellar internal structure to be probed through such observations. Finite-size effects are encoded in quantities like the moment of inertia (I), tidal Love number (Love), and quadrupole moment (Q). The universal relations among them (I–Love–Q relations) can be used to reduce the number of parameters in the gravitational-wave templates. We here study I–Love–Q relations for more realistic white dwarf models than used in previous studies. In particular, we extend previous works by including (i) differential rotation and (ii) internal temperature profiles taken from detailed stellar evolution calculations. We use the publicly available stellar evolution code mesa to generate cooling models of both low- and high-mass white dwarfs. We show that differential rotation causes the I–Q relation (and similarly the Love–Q relation) to deviate from that of constant rotation. We also find that the introduction of finite temperatures causes the white dwarf to move along the zero-temperature mass sequence of I–Q values, moving towards values that suggest a lower mass. We further find that after only a few Myr, high-mass white dwarfs are well described by the zero-temperature model, suggesting that the relations with zero temperature may be good enough in most practical cases. Low-mass, He-core white dwarfs with thick hydrogen envelopes may undergo long periods of H burning which sustain the stellar temperature and allow deviations from the I–Love–Q relations for longer times.

Performance-based design of RC columns using an equivalent standard fire

The extreme variability of natural compartment fires poses a significant challenge in the process of performance-based fire design. To reduce this variability, the severity of a natural fire can be related to that of a standard fire, known as a time equivalent (te). In this paper, the applicability of a time equivalent, previously derived based on the average internal temperature profile (AITP) that develops within reinforced concrete (RC) beams exposed to fire from three sides, is examined for RC columns exposed to fire from four sides. A parametric study is presented to examine the suitability of the existing AITP te in representing the internal temperatures of RC columns. The accuracy of the AITP te in approximating column performance, is judged based on the moment-curvature, axial load-axial strain, and bending moment-axial force relationships during fire exposure. Comparison with existing methods is provided to further demonstrate the superior suitability of the AITP te in representing natural fire severity for RC columns.

Experimental investigation of compartment fires with circular opening: From the aspects of internal temperature and facade flame

This paper experimentally investigated the internal temperature and the facade flame for compartment fires involving circular openings. A series of experiments were carried out by using a reduced-scale model which composed of a cube compartment with various circular openings and a vertical fireproofing board (used as building facade). A porous burner with propane fuel was set inside the compartment as fire source. The internal temperature profile was measured by vertical thermocouple arrays at the inner and outer corners, and the facade flame was captured by a CCD camera from a side view. This paper revealed that: (1) With the same area, maximum heat release rate inside the compartment with circular opening is larger than that with square opening. (2) For relatively larger circular openings, facade flames tend to ceiling jet flame extension. With the increasing of heat release rate, facade flame induced by ceiling jet flame extension will convert to spill fire plume. (3) A dimensionless number R, which represents the ratio of total heat release rate to internal maximum heat release rate, is proposed to distinguish spill fire plume and ceiling jet flame extension when facade flames appear at exterior. (4) A non-dimensional correlation is developed to characterize the facade flame heights for both ceiling jet flame extension and spill fire plume. These findings and results can provide fundamental knowledge for understanding compartment fire with a circular opening.

A method for reconstructing two-dimensional surface and internal temperature distributions in structures by ultrasonic measurements

A new method for simultaneously reconstructing surface and internal transient temperature distributions in structures is presented by ultrasonic measurements. The principle of ultrasonic thermometry is based on temperature dependence of the velocity of ultrasonic wave (acoustic velocity) propagating through heated structures. Considering the bending effect of ultrasonic propagation path in non-uniform temperature field, an approach for predicting two-dimensional ultrasonic propagation path is developed using the Fermat theory. Combining the advantages of the ultrasonic pulse-echo measurements and an inverse analysis of thermo-acoustic coupling problem, a reconstruction algorithm is proposed to estimate two-dimensional surface and internal temperature fields. The presented approach is discussed in some detail and a number of examples are given as verification to demonstrate the feasibility and reliability of this method. The surface and internal temperature profiles determined by ultrasound agree well with the exact values. In addition, the influences of bending effect of wave propagation, measurement error of ultrasonic wave propagation time, number and position of measurement points on the reconstruction of temperature fields are analyzed in detail. It shows that the presented method is a promising means for high-accurately and nondestructively determining surface and internal transient temperature distributions in heated structures.

Peltier Heats of LiFePO4 electrodes from a Thermoelectric Cell

Temperature is known to affect ageing and performance of lithium ion batteries [1]. We need to improve the understanding of the heat sources in the electrode compartments in order to accurately model internal temperature profiles. Reports of reversible heat effects local to electrode surfaces in lithium-ion batteries are therefore important, but are scarce in literature [2]. The reversible heat production at a battery electrode interface is investigated in this experimental work, measuring the Peltier heat of the electrode LiFePO4 electrode. The Peltier heat at an electrode can be found by measuring the change in electric potential across the cell with two identical electrodes when a temperature difference is applied [3]. We present the Seebeck coefficient and Peltier heat of a symmetric pouch cell consisting of two commercial LiFePO4 electrodes and a 1M LiPF6 and Ethylene Carbonate (EC) /Diethyl Carbonate (DEC) (50:50 w%) electrolyte-soaked separator. The electrodes have been thermostatted to the wanted temperatures T and T+ ΔT, respectively. Al (s,T) | LiFePO4 (s,T) | EC, DEC, LiPF6 | LiFePO4 (s,T + ΔT) | Al (s,T+ ΔT) We show that the thermoelectric effect is time-dependent due to a build up of concentration gradients within the cell, and the establishment of not only one, but two Soret equilibria. The initial Seebeck coefficient gives the Peltier heat of one electrode for a homogeneous electrolyte in a battery [4]. We derive equations that will describe the approach of the cell to steady state, and use this to estimate the initial value. The consequences of the Peltier heat of LiFePO4 for battery discharging and charging will be discussed. Acknowledgment The authors are grateful to the Research Council of Norway through its Centres of Excellence funding scheme, project number 262644, PoreLab. We acknowledge ENERSENSE for financial support. The group of authors also acknowledge the Research Council of Norway (RCN) project no. 228739, for funding through the project "Life and Safety for Li-ion batteries in Maritime conditions (SafeLiLife)".

The partial ionization zone of heavy elements in F-stars: a study on how it correlates with rotation

ABSTRACT We study the relation between the internal structures of 10 benchmark main-sequence F-stars and their rotational properties. Stellar rotation of main-sequence F-type stars can be characterized by two distinct rotational regimes. Early-type F-stars are usually rapid rotators with periods typically below 10 d, whereas later-type F-stars have longer rotation periods. Specifically, and since the two rotational regimes are tightly connected to the effective temperatures of the stars, we investigate in detail the characteristics of the partial ionization zones in the outer convective envelopes of these stars, which in turn, depend on the internal temperature profiles. Our study shows that the two rotational regimes might be distinguished by the relative locations of the partial ionization region of heavy elements and the base of the convective zone. Since in all these stars is expected a dynamo-driven magnetic field where the shear layer between convective and radiative zones (tachocline) plays an important role, this result suggests that the magnetic field may be related to the combined properties of convection and ionization.

Online Temperature Estimation Based on a Coupled Diffusion-Electro-Thermal Model for Lithium-Ion Batteries

The performance of Lithium-ion batteries is strongly influenced by the temperature. Therefore, an accurate estimation of the cells’ temperature becomes a critical issue for a battery thermal management system to reduce its energy consumption and improve the overall performance of the whole battery system. In this paper, a coupled diffusion-electro-thermal model is established to acheive the real-time estimation of the temperature distribution of large prismatic lithium-ion batteries. The presented model consists of two parts: a diffusion-elctro model to calculate the heat generation rate of the cell and a multi-node thermal model to estimate and predict the battery’s internal temperature profile. The two sub-models are parameterized by pulse and constant discharge experiments under different ambient temperatures. Both simulation and experimental results reveal that while the irreversible heat of the cell is governed by its cycling current and overpotential, the reversible heat is dependent on the pseudo surface lithium-ion concentration, which indicates that the thermal behavior of the lithium-ion battery is directly coupled with the diffusion of lithium-ions in the solid phase. The performance of the full model is validated by dynamic driving cycles under liquid cooling conditions and the results show that the model can capture the cell’s temperature distribution during cycling with an acceptable computational cost.

Thermo-Electrochemical in-Situ Instrumentation for Smart Energy Storage

Lithium-ion rechargeable cells are widely used as instant power delivery devices. High energy and power densities along with capacity retention over tens of thousands of cycles are highly beneficial compared to alternative technologies. However, recent failure incidents and constant health and safety concerns are slowing down the adoption of this technology and limiting the performance through cautious approach. In order to alleviate these issues, a better understanding of the performance and safety limits and the cells’ internal thermodynamic responses is required. Both the in-situ thermal and electrochemical mechanisms need to be carefully characterised to unlock the full performance without jeopardising safety. This work focuses on an altogether new in-situ instrumentation methods coupling the use of a quasi-reference electrodes, optical sensing technology and miniature thermistors for supplemental internal and external temperature profiles. This methodology allows for new level of analysis, providing insight into in operando in-situ parameters of a range of cell shapes and formats. Higher reliability, shorter charging times and early fault detection can be achieved with the use of smart instrumented Li-ion cells, enabling significant advances in the battery technology. Figure 1

An Iterative Methodology for Model Complexity Reduction in Residential Building Simulation

The present paper introduces an iterative methodology to progressively reduce building simulation model complexity with the aim of identifying potential trade-offs between computational requirements (i.e., model complexity) and energy estimation accuracy. Different levels of model complexity are analysed, from commercial building energy simulation tools to low order calibrated thermal networks models. Experimental data from a residential building in Germany were collected and used to validate two detailed white-box models and a simplified white-box model. The validation process was performed in terms of internal temperature profiles and building thermal energy demand predictions. Synthetic profiles were generated from the validated models and used for calibrating high order models. A reduction (trimming) procedure was applied to reduce the model complexity using an energy performance criterion prior to model trimming. The proposed methodology has the advantage of keeping the physical structure of the original RC model, thus enabling the use of the trimmed lumped parameter building model for other applications. The analysis showed that it is possible to reduce the model complexity by half, while keeping the accuracy above 90% for the targeted building.

Equivalent standard fire duration to evaluate internal temperatures in natural fire exposed RC beams

With the recent shift towards performance-based fire design, practical methods to account for natural fire loading when designing concrete structures are needed. Available design methods and analysis approaches are based on standard fire curves. To apply these methods, a natural fire event can be converted to a standard fire with a specific duration (time equivalent). However, existing time equivalents often ignore the influence of internal temperature gradients on the section behaviour, which is unacceptable for concrete structures.This paper introduces a time equivalent method suitable for reinforced concrete (RC) beams exposed to natural fire. The method is based on the actual temperature gradient within a concrete section. To simplify analysis of RC beams exposed to fire, an average internal temperature profile (AITP) can be utilized, which records the average temperature variation along the height of a section. Two equations are provided such that a standard fire duration can be determined to accurately or conservatively represent the AITP of a beam section exposed to natural fire. Characteristics of the natural fire, as well as the influence of section dimensions are accounted for. The developed AITP time equivalent method is found to be superior to the existing methods and accurate in approximating the moment-curvature response for RC beam sections.

In-situ study of plastic layers during coking of six Australian coking coals using a lab-scale coke oven

An in-situ study on the formation mechanism of plsatic layer was carried out by using a 4 kg laboratory-scale coke oven under controlled heating conditions. The coke oven rig enabled in-situ measurements of internal gas pressure (IGP) and temperature profiles in five locations in the coal charge and allowed sampling of semi-coke which consisted of the coke/semi-cokes, the plastic layers and loose coal. Six Australian coking coals with varying properties were used in the coking experiments. The semi-coke samples were scanned by micro-CT at the Imaging and Medical Beamline at Australian Synchrotron to study the physical structure transitions inside the thermoplastic regions and investigate the fissure patterns at the coke/semi-coke sides. The thicknesses of the plastic layers in different locations inside the coal charge were estimated from the measured temperature profiles and the initial softening temperatures and the solidification temperatures measured from the Gieseler fluidity tests. The results showed that the thicknesses of the plastic layers increased from the heating wall to the center of the coal charge. The IGP curves measured in different locations were used to obtain the maximum IGP values and the IGP termination temperatures across the coal charge. The difference in the extents of fissuring appeared to influence the maximum IGPs measured at the center of the oven. The higher extent of fissurin appeared to facilitate the release of volatile matterfrom the thermoplsatic region through the semi-coke sides, thus leading to lower maximum IGPs at the center. It was found that the extents of the fissuring and the maximum IGPs at the center were sensitive to the coal properties such as the petrographic properties, Gieseler maximum fluidity and volatile matter content.

Thermal performance of waste materials as aggregate replacement in asphalt pavement

The high surface temperature of the conventional asphalt pavement due to high solar energy absorption could contribute to the Urban Heat Island (UHI) phenomenon. Concurrent with this phenomenon, rapid urbanization and industrial development have led to a large quantity of waste products available for disposal or recycling. Therefore, this study investigates the thermal performance of selected waste materials that could potentially be used as aggregate in asphalt pavement to combat the problem of increased pavement surface temperature. A number of waste materials were selected for the thermal performance measurement and compared to granite as conventional aggregate. The cylindrical and slab samples of AC14 dense graded asphalt were prepared for the different selected aggregate types. The samples were then measured for solar reflectance using Spectroradiometer. In addition, the surface and internal temperature profiles of the samples were monitored using infrared camera and thermocouples, respectively, in exposed environments. Based on the results, it is possible to use some of the waste materials as an aggregate replacement in order to reduce the UHI impact.

Non-contact measurement of the temperature profile of PET preforms

This paper describes a system for the measurement of the internal and external temperature profiles of PET preforms used in the Injection Stretch Blow Moulding (ISBM) process. Many works in literature highlighted the importance of these quantities to improve the production quality of PET bottles, but none addressed the development of a measuring system suitable for this scope. A measuring system based on two thermopiles for the identification of the internal temperature profile and a thermal camera for the measurement of the external one has been designed. The adopted sensors were individually calibrated and the uncertainty budget, accounting for both instrumental uncertainties and the effect of multiple reflections, was derived. A prototype of the measuring system was tested on an industrial ISBM machine. The dependence of the preforms temperature profile on the settings of the ISBM machine was investigated. Results evidenced that the minimum variations of the machine settings induced temperature differences significantly larger than the measurement uncertainty, thus proving the effectiveness of the proposed system.

(Invited) Thermal Gradients and Thermal Conductivity in PEM Fuel Cells, Compared to Li-ion Batteries and Super Capacitors

The PEM fuel cell has been developed into a very effective energy converter. That is, the development efforts on PEM fuel cell has been mainly focussed in terms of output power density, rather than in terms of energy efficiency; the operational cell voltage remains constant and the current density increases. In turns the heat flux, released from the reaction increases too [1]. This heat flux leads to increased temperature gradients inside the PEMFC, and in particular across the gas diffusion layer (GDL), the microporous layer (MPL) and the catalyst layers (CL). Over the past decade, several studies of the thermal conductivity of PEMFC components have been undertaken in order to provide models with more accurate thermal conductivity data as a function of: compression, PTFE loading, ageing, water content, direction (in- vs. through-plane), material types, and material integration. As many of these now seem to be well understood, there are still room for more fundamental mechanistic studies, which are highlighted in this presentation. With a modern fuel cell operation at a cell voltage of +0.7V, one can easily see temperature differences between the polarisation plates and the membrane of more than 10oC, depending upon the state of water and material selection. [2] A summary of PEMFC material thermal conductivity and gradients is also described in this presentation. Heat transfer in the components in a PEM fuel cell and the corresponding temperature gradients is dominated by heat flux through the passive components (GDL and MPL), leading to linear gradients. In other electrochemical energy storage devices such as supercapacitors (SC) and lithium ion batteries (LiB), it is the active materials (electrodes and separators) that dominate the temperature gradients, which in turn becomes more parabolic (2nd order). From an engineering point of view, it is interesting to compare thermal gradients and internal temperature differences of a PEMFC to these other devices, because; the thermal conductivity of the heat generating materials are similar for the three, the operation voltage is higher in a LiB and SC than in a PEMFC, the electrode thicknesses are larger in a LiB and SC than in a PEMFC; there are less opportunities for cooling in side a LiB and SC than in a PEMFC, and remarkably; relevant current density of a PEMFC, SC, and LiB are 30,000, 200, and 50 A m-2, respectively. [1,3,4] A brief comparison of PEMFC, SC, and LiB thermal conductivity and gradients are discussed in this presentation. [1] O. S. Burheim, J. G. Pharoah, A review of the curious case of heat transport in polymer electrolyte fuel cells and the need for more characterisation, Current Opinion in Electrochemistry, (2017). [2] O. S. Burheim, "Review: PEMFC Materials' Thermal Conductivity and Influence on Internal Temperature Profiles, ECS Transactions, 80 (2017) 509-525. [3] F. Richter, S. Kjelstrup, P. J. S. Vie, O. S. Burheim, "Thermal conductivity and internal temperature profiles of Li-ion secondary batteries", Journal of Power Sources 359 (2017) 592-600. [4] H. H. Hauge, V. Presser, O. Burheim, "In-situ and ex-situ measurements of thermal conductivity of supercapacitors", Energy, 78 (2014), 373-383