Electric Heating Research Articles

Field-Emission Energy Distribution of Carbon Nanotube Film and Single Tube under High Current.

A narrow energy distribution is a prominent characteristic of field-emission cold cathodes. When applied in a vacuum electronic device, the cold cathode is fabricated over a large area and works under a high current and current density. It is interesting to see the energy distribution of the field emitter under such a working situation. In this work, the energy distribution spectra of a single carbon nanotube (CNT) and a CNT film were investigated across a range of currents, spanning from low to high. A consistent result indicated that, at low current emission, the CNT film (area: 0.585 mm2) exhibited a narrow electron energy distribution as small as 0.5 eV, similar to that of a single CNT, while the energy distribution broadened with increased current and voltage, accompanied by a peak position shift. The influencing factors related to the electric field, Joule heating, Coulomb interaction, and emission site over a large area were discussed to elucidate the underlying mechanism. The results provide guidance for the electron source application of nano-materials in cold cathode devices.

RLab Calorimetry: an internet-enabled calorimeter using Arduino for local or remote lab activities

This study presents an internet-connected calorimeter allowing both face-to-face and online laboratory activities. This device aims to create an environment that facilitates enquiry-based teaching strategies. There are three ways to access the device: (i) remotely via the web (WAN—Wide Area Network), locally (ii) through the local network (LAN—Local Area Network), or (iii) as a stand-alone device. It was designed with a client-server structure and utilised the Flask framework in Python. The instrument consists of two isolated containers (calorimeters), allowing for investigative activities that include comparing two liquid samples. The system was built using low-cost components based on the Arduino platform. Unlike virtual laboratories, measurements are performed on real devices. We present the results of direct electrical heating for a short time and record the temperature step of the samples. This straightforward method has proven to be suitable as a learning activity because of its conceptual clarity and effectiveness in teaching and learning. The use of a mechanical stirrer to homogenise the temperature of the liquids is crucial for obtaining high-quality experimental results. The system described in this paper is part of ‘RLab project’, an initiative to develop a platform for remote Experimental Physics Activities in Physics Teaching for public schools in Brazil. This experimental setup can be highly beneficial for implementing an experimental learning methodology, especially in the case of—but not restricted to—distance learning.

Study on heat-treated pyrolytic carbon deposited from methane on directly heated carbon fibres

The study investigated the morphology, microstructure, structure, texture, and mechanical properties of heat-treated at 1600 °C and 2000 °C pyrolytic carbon (PyC) deposited from methane using various methods such as scanning electron microscopy (SEM), X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), selected area electron diffraction (SAED), Raman spectroscopy, and ultrasonic dynamic measurements of Young's modulus. The PyC was synthesised at 1100 °C using a chemical vapour deposition (CVD) method with direct electrical heating of the two types of carbon fibres (CFs). The results showed that the PyC had a low- and medium-texture (LT and MT PyC). Analysis of the graphitization trajectory allowed the determination of structural changes in the material as a function of temperature, including the growth of crystallites and an increase in the crystallinity proportion without the significant rearrangement within PyC. The crystallite size and the number of interstitial defects has increased with temperature that controlled mechanical properties. Therefore, based on the results obtained, the most suitable composites for further research in the context of electrodes for stimulation of nervous tissue were obtained at the temperature of their synthesis, i.e. at 1100 °C.

Application of the AHP-QFD methodology in the sustainability analysis of a trifunctional adsorbent for inorganic micropollutants from contaminated water

An alternative approach to addressing water pollution is through the development of adsorbent materials. Na-jarosite is a promising material capable of removing simultaneously multiple ions from contaminated water. Employing four Quality Functional Deployment (QFD) matrices alongside the hierarchical analysis process (AHP) methodology, this study aimed to select materials, preparation methods, equipment, and processing conditions of Na-jarosite to remove As(V), Pb(II) and F (-) from contaminated water. The analysis of QFD matrices 1 and 2 identified electrical heating as the optimal method for synthesizing Na-jarosite, exhibiting removal capacities of removal capacity of 65.56 mg g−1 for As(V), 94 mg g−1 for Pb(II) and 2.45 mg g−1 for F(-). Rotating disc granulation was chosen for adsorbent formation, demonstrating environmental viability based on E Factor (0.6 kg of waste) and Eco scale (89) indicators. Further analysis of the QFD 3 matrix allowed the selection of essential equipment, including an electrical heating oven, a rotating disc granulator, and an extended tray for synthesis, granulation, and drying processes, respectively. Additionally, the QFD 4 matrix analysis identified drying the adsorbent at temperatures below 100 °C as a critical parameter for effective adsorbent formation. QFD and AHP analyses findings highlight the potential of Na-jarosite as a trifunctional adsorbent material for addressing water pollution challenges.

Discrete element analysis of heat transfer characteristics of concrete pavement under electrical heating for snow melting and deicing

The carbon fiber electrothermal method is an efficient approach for snow melting and deicing of pavements in the cold winter. The heat transfer mechanism needs to be explored for the carbon fiber electrothermal system design, especially how the microstructure affects the thermal behavior of pavement. To do so, a discrete element method (DEM) based heat transfer model considering the pavement microstructure has been established in the current study. The shape and content of coarse-grained aggregates have been represented by using the irregular polygonal aggregate method. The accuracy and feasibility of the proposed model were verified by comparing the numerical results with the measured data. On this basis, the heat transfer characteristics of pavements during snow melting and deicing using the carbon fiber electrothermal method have been investigated. The results show that the ambient temperature and the carbon fiber heating wire (CFHW) temperature are the two primary factors affecting the heating efficiency and the maximum temperature on the pavement surface. The spacing and buried depth of the CFHW also play a crucial role in determining the temperature rise rate and the uniformity of temperature distribution of the road surface layer. Furthermore, the effect of the aggregate content on the overall heating rate is not as significant as that of the specific heat capacity ratio of the aggregate to the mortar, suggesting modifying the thermal conductivity of aggregates to enhance deicing efficiency rather than changing the aggregate contents. The effects of the CFHW design parameters on the temperature distribution of the pavement surface are also investigated. The maximum and minimum temperatures of the pavement layer decrease gradually with the increase of the laying spacing and burial depth of the CFHW, but the temperature difference increases with the increase of the laying spacing of the CFHW and decreases with the increase of the burial depth. The research results can provide a reference for the optimization design of snow melting and deicing of pavements by the CFHW heating method.

Feedback control of an experimental electrically-heated steam methane reformer

Steam methane reforming (SMR) is the most common industrial process to produce hydrogen (H2) from methane and water vapor. The SMR reactions are overall highly endothermic and traditionally, fossil fuels are burned to provide the necessary heat of reaction. However, it was found that electrifying the tubular SMR reactors using renewable electrons instead of conventional heating gives the opportunity of producing H2 with lower carbon emissions, lower reactor volumes, and higher carbon conversion. While current studies in this new technology focus on improving the catalysts or heating sources, a more efficient process control scheme can also significantly contribute to the understanding of potential challenges and opportunities of combining renewables and natural gas in the production of H2 at industrial scales. In order to further develop the electrically-heated SMR process and the associated control strategies, we have constructed an experimental Joule-heated SMR system at UCLA. The system contains a tubular reactor with a washcoated Ni/ZrO2 catalyst, two thermocouples connected to the top and bottom of the reactor, a power supply for providing electrical heating, and an on-line gas chromatograph (GC) for measuring outlet gas concentrations. The synthesis procedure of the catalyst, SMR data collection, and thermal considerations for catalyst degradation are described in this paper and are all accounted for experimentally when using a proportional integral (PI) controller to gradually increase the reactor temperature without harming the catalyst. Advanced control strategies, such as model predictive control (MPC), require a process model that uses measurement feedback to make predictions of the process time-evolution in order to optimize the control actions in real-time. We have previously developed a lumped-parameter modeling strategy for the SMR process. The MPC objective is to control the H2 production rate by manipulating the current flowing through the outer reactor shell. However, to use this model in an MPC, feedback values for all state variables should be provided by the sensors. In our experimental system, the on-line GC only gives discrete measurements with a long sampling period. To this end, the process model is incorporated into an extended Luenberger observer (ELO) that uses the reactor temperature and GC measurements to provide estimates of all the variables needed by the MPC. The ELO-based MPC system is then experimentally implemented on the process and it is demonstrated to be more efficient in terms of speed of the closed-loop response than the PI controller using delayed, measurement feedback by the GC.

Assessing the effectiveness of building retrofits in reducing GHG emissions: A Canadian school case study

This paper investigates the impact of energy retrofits on life cycle greenhouse gas (GHG) emissions across different electricity grid profiles in Montreal, Ottawa, and Halifax, using an existing school building as a case study. Using DesignBuilder for energy simulations and OneClick LCA for GHG emissions estimation, this study evaluates whether the reduction in the operational emission achieved by energy savings from retrofits can outweigh the increased embodied emissions from new envelope materials and equipment. In Montreal and Ottawa, where electricity is mainly generated from renewables and non-fossil fuels, retrofits involving electric heating and envelope improvements could decrease life cycle GHG emissions by up to 75 %. However, if the building initially used electric heating, the retrofits led to an increase in life cycle carbon emissions by 170 % in Montreal and 56 % in Ottawa, respectively, due to the embodied emissions of retrofit materials and equipment. In Halifax, where the electricity grid relies heavily on fossil fuels, all retrofit scenarios showed a positive impact on GHG reductions. Enhancing the building envelope and transitioning from natural gas to electric heating slightly reduced total emissions by 4 %, but retaining natural gas heating decreased the total life cycle GHG emissions by 27 %. This study emphasizes the importance of a comprehensive life cycle assessment in developing policies for achieving carbon neutrality. It demonstrates that the effectiveness of retrofits in reducing GHG emissions significantly depends on the local energy grid, suggesting tailored approaches based on regional energy profiles to optimize emission reductions and energy efficiency.

Оптимизация эксплуатации газобаллонного оборудования технологического транспорта АК «АЛРОСА», использующего компримированный природный газ в качестве моторного топлива в условиях Якутии

The paper justifies the relevance of using compressed natural gas as the motor fuel for utility vehicles in conditions of the high north and the Republic of Yakutia. Natural gas as an alternative energy carrier is stated to have a number of advantages over diesel fuel, however, its use in extremely low temperatures, in particular, in Yakutia, is associated with some challenges. A number of technical solutions are proposed to maintain a constant temperature of compressed natural gas contained in the gas cylinders onboard of the utility vehicles. The paper provides a detailed description of the methods to maintain the required temperature of the compressed natural gas in the gas cylinders using heat from the exhaust gases of the combustion engine, as well as by means of flexible electric strip heaters. One of the possible ways to separate heavy hydrocarbons (C5-C7) that negatively affect the performance characteristics of the combustion engines and the operation efficiency of the gas cylinder equipment is described for production of the compressed natural gas for utility vehicles. Technical requirements are determined for rubber products of the gas cylinder equipment that operate at low ambient temperatures. The article suggests the optimal quality characteristics of the frost-resistant rubbers and sealing materials that are most suitable for application in conditions of Yakutia.

Electrical behavior and water phase transformation in multi‐walled carbon nanotube/polytetrafluoroethylene composite films

AbstractMulti‐walled carbon nanotubes (MWCNTs) with excellent physiochemical properties have been recently applied to energy/power generation and storage systems encompassing polymer electrolyte membrane fuel cells (PEMFCs). However, there is a lack of investigations of the properties of MWCNT composites themselves under the actual operating conditions of systems. In this paper, MWCNTs/polytetrafluoroethylene (PTFE) composites were fabricated as electric and hydrophobic components for energy/power systems. The electrical properties, heating behavior, hydrophobicity, and water evaporation behavior of the composites are characterized within the operating voltage ranges of PEMFC. With 50% MWCNT content, the conductivity and the contact angle were 11.83 S/cm, and the contact angle 128.1°, respectively. The MWCNT/PTFE composite film showed a linear temperature rise with voltages and rapid temperature saturation within 40 s. The rate in the initial heating range was measured at 0.5°C/s for the voltage of 0.5 V. The voltage increase induced an exponential decrease in the height of water droplets on the composite surface. The evaporation rate increased almost 10‐fold, from 0.013 mm/min at 0.0 V to 0.12 mm/min at 1.0 V. The proposed characteristics of the functional composite provide insights into the material requirements for electrochemical devices, including PEMFC.Highlights Multi‐walled carbon nanotube/polytetrafluoroethylene composites can be applied to energy storage and power generation. Key properties of the composites are proposed for polymer electrolyte membrane fuel cell (PEMFC) operating conditions. The composite has a fast heating by high conductivity and temperature uniformity. Water‐vapor transformation under PEMFC operating voltage is quantified.

Literature Review on Conjugated Polymers as Light-Sensitive Materials for Photovoltaic and Light-Emitting Devices in Photonic Biomaterial Applications

Due to their extended p-orbital delocalization, conjugated polymers absorb light in the range of visible–NIR frequencies. We attempt to exploit this property to create materials that compete with inorganic semiconductors in photovoltaic and light-emitting materials. Beyond competing for applications in photonic devices, organic conjugated compounds, polymers, and small molecules have also been extended to biomedical applications like phototherapy and biodetection. Recent research on conjugated polymers has focused on bioapplications based on the absorbed light energy conversions in electric impulses, chemical energy, heat, and light emission. In this review, we describe the working principles of those photonic devices that have been applied and researched in the field of biomaterials.

An exergy-ecology assessment method and its application for basic building heating schemes

ABSTRACT Building heating is the main type of heating consumption in China. At present, there is a lack of attention given to the assessment of ecological cost or impact considering energy depreciation for various heating schemes. In this work, a method of exergy-ecology assessment is proposed to evaluate the energy and ecological characteristics of four basic building heating schemes. The solar-equivalent joule was adopted as the unified quantitative value of ecological impact by converting exergy, material, and cost flows. The exergy-ecology balance was established for each scheme, and a series of indexes were proposed and calculated through two strategies. The results show that the objective exergy efficiency of Scheme 3 heat pump is the highest (53.87%) and that of Scheme 2 electric heater is the lowest (17.58%). Larger difference of energy grade between energy providing side (0.83 for gas fuel and 1 for electricity) and receiving side (0.18 for output water) connects with lower exergy efficiency. Scheme 3 heat pump has the highest eco-exergy efficiency under both assessment strategies (71.89% and 53.86%), followed by Schemes 4 solar collector (61.52% and 36.34%). This method proves that the thermodynamics perfectness of system is positively correlated with ecological sustainability and can be used to assess other energy systems.

Algorithm for control of electric heating of concrete for solving the problem of digital control of quality of monolithic works

Algorithm for control of electric heating of concrete for solving the problem of digital control of quality of monolithic works

Freestanding 3D graphite foam prepared by compressed growth template for superior electro-photo thermal performance

As a promising three-dimensional (3D) graphene architecture, graphene foam has excellent structural, electrical and thermal properties. However, due to the growth template limitation of commercial nickel/copper foam, graphene foam prepared by chemical vapor deposition (CVD) has a fixed 3D framework architecture, which limits its performance and application scenarios. In this paper, independent 3D graphite foam (GF) with different thickness and longitudinal compressibility was prepared by CVD method, and it was confirmed that mechanical compression of nickel foam template before graphite film deposition had a positive effect on the electrothermal, photothermal and mechanical properties of GF. At a low driving voltage of 3 V, the heating temperature of compressed GF with a low density of 8.9 mg/cm3 and a high porosity of 99.59 % can reach nearly 600 °C, which is nearly 250 °C higher than that of uncompressed GF. The excellent electrothermal performance of compressed GF is mainly attributed to the high crystallinity and thicker thickness (150–350 nm) of the graphite layers that make up the 3D framework, thus resulting in higher electrical conductivity. Under 1 and 2 sun illumination, the temperature of compressed GF can reach 83 °C and 109 °C respectively, which is 4–7 °C higher than that of the original GF. Compressed GF has better electrothermal, photothermal and radiant heating properties than traditional graphene/graphite foam and 2D graphene/graphite film. It not only has great application potential in high-efficient and energy-saving high-temperature electric heaters and photothermal converters, but also can be used as conductive supports or fillers with better performance, and has broad application prospects in flexible electronics, household appliances, artificial intelligence, medical care and other fields.

Curing parameters development and long-term performance of ohmic heating cured conductive cementitious composites: A comparative study on fiber fraction

Ohmic heating (OH) curing is a new method for concrete production in cold areas, while the changing regularity for the curing parameters including electric voltage, current, resistivity and curing temperature during the curing process, and the long-term performance evolution law are still unrevealed. In this research, this method was used to fabricate carbon fibers (CFs) reinforced conductive cementitious composites under −20 °C, the early-age curing parameter and the long-term performance evolution law of the specimen were clarified. Higher CFs dosage showed benefits on the electrical conductivity and heating performance of OH pre-cured specimens. To be specific, simulation and experimental results evidenced that the electrical conductivity of fresh mixture was much improved with 0.6 vol% CFs with the electrical resistivity decremental ratio of 74.82 %. Also, the curing temperature was enlarged in the presence of 0.75 vol% CFs with the incremental ratio around 50 %, indicating the much-improved heating efficiency. Strength test results showed that 1-day OH pre-cured specimens possessed the comparable 150-day strength with RT prepared specimens. Moreover, the hydration products and pore structure test results further verified the feasibility of OH curing with high hydration forming ability and denser microstructure at longer duration. In addition, the “RER” was introduced to evaluate the variation law of electrical resistivity in further curing process, and the corresponding prediction equation was derived.

Optimal scheduling of a cogeneration system via Q-learning-based memetic algorithm considering demand-side response

An optimization scheduling method for cogeneration systems based on the Q-learning-based memetic algorithm (QMA) is developed to enhance the system's wind power absorption capacity and economical operation. First, an optimal scheduling model for cogeneration systems is constructed. The model integrates time-of-use electricity pricing and heating comfort into the demand side, fully exploiting the potential of demand-side response (DR) in power generation and heating. An additional heat source (AHS), which consists of an electric boiler and heat storage tank, is used to uncouple heat and power. In addition, a QMA algorithm is designed to find the optimal operating scheme for the cogeneration system. The Q-learning algorithm is introduced to dynamically adjust crossover and mutation parameters during the global evolution stage, improving the algorithm's search capability. The Taguchi method is utilized for algorithm parameter calibration. Finally, the simulation results under various operating scenarios are compared and analyzed, verifying the feasibility and effectiveness of the proposed method. The simulation results show that DR and AHS can improve the system's economic performance and wind power utilization rate. Compared with the IMA, IPSO, MA, and IABC algorithms, the QMA algorithm reduces the average economic cost by approximately 1.18 %, 2.23 %, 5.69 %, and 14.69 %, respectively.

Eco-friendly wearable textiles: Asymmetric structures for EMI shielding, thermal management, and fire safety

This work focuses on developing multifunctional wearable fabrics, specifically targeting the challenge of flammability in this context. An eco-friendly, asymmetrically structured nylon/cotton blend fabric is prepared through the surface modification of phytic acid-induced polyaniline, the application of silver nanowires (AgNWs) and MXene on both sides and encapsulated by polydimethylsiloxane (PDMS). The AgNWs coating suppresses thermal radiation from the human body to achieve radiative heating, while the MXene coating enhances solar heating, ensuring thermal comfort in cold conditions. The treated fabric also exhibits electrical heating for heat compensation in the absence of sunlight, remarkable EMI shielding performance (55.6 dB) is also achieved. Enhanced fire safety is demonstrated as the treated fabric extinguishes when exposed to flame, reducing heat release by 45.9 % relative to the control nylon/cotton blend fabric (CO/NY). Additionally, the treated fabric exhibits significant antibacterial properties against Gram-negative E. coli and Gram-positive S. aureus, along with a notable water contact angle (WCA) of 130.2°. This work provides a promising method for the development of eco-friendly wearable smart fabrics with well-balanced desirable properties.

Superhydrophobic, Highly Conductive, and Trilayered Fabric with Connected Carbon Nanotubes for Energy-Efficient Electrical Heating.

Current electrically heated fabrics provide heat in cold climates, suffer from abundant wasted radiant heat energy to the external environment, and are prone to damage by water. Thus, constructing energy-efficient and superhydrophobic conductive fabrics is in high demand. Therefore, we propose an effective and facile methodology to prepare a superhydrophobic, highly conductive, and trilayered fabric with a connected carbon nanotube (CNT) layer and a titanium dioxide (TiO2) nanoparticle heat-reflecting layer. We construct polyamide/fluorinated polyurethane (PA/FPU) nanofibrous membranes via first electrospinning, then performing blade-coating with the polyurethane (PU) solution with CNTs, and finally fabricating FPU/TiO2 nanoparticles via electrospraying. This strategy causes CNTs to be connected to form a conductive layer and enables TiO2 nanoparticles to be bound together to form a porous, heat-reflecting layer. As a consequence, the as-prepared membranes demonstrate high conductivity with an electrical conductivity of 63 S/m, exhibit rapid electric-heating capacity, and exhibit energy-efficient asymmetrical heating behavior, i.e., the heating temperature of the PA/FPU nanofibrous layer reaches more than 83 °C within 90 s at 24 V, while the heating temperature of the FPU/TiO2 layer only reaches 53 °C, as well as prominent superhydrophobicity with a water contact angle of 156°, indicating promising utility for the next generation of electrical heating textiles.

Multifunctional composite flexible films of hydroxypropyl cellulose and silver nanowires

Flexible wearable devices have aroused attentions since the booming flexible electronic technologies, as well as the requirements for improved comfortableness and real-time monitoring for complex motion state of human body. Developing a flexible integrated wearable device with multi functions provides a promising route for next-generation wearable devices. Meanwhile, transparency and biocompatibility are also considered a lot. Herein, hydroxypropyl cellulose/silver nanowires (HPC/AgNWs) flexible composite films were fabricated with a facile two-step method. The fabricated composite films exhibited sufficient transparency and mechanical strength. More importantly, the HPC/AgNWs composite films afforded good motion sensing performances with current sensitivity as high as 350 %. It can accurately identify different bending angles and frequencies, and remained stable for more than 1000 bending cycles. Apart from being employed as motion sensors, the fabricated HPC/AgNWs could be also used for electrical heating and electromagnetic shielding. The films could be heated to more than 60°C at 3.0 V in 57 seconds, and the electromagnetic shielding efficiency reached more than 99.9 %. This study contributed a feasible strategy for the preparation of multifunctional flexible films which are expected to be further applicated in the field of wearable devices.

LM-Gel Plasticine Based on Binary Cooperative with Kneadable Shaping and Conductivity.

Liquid metal (LM)-based polymers have received growing interest for wearable health monitoring, electronic skins, and soft robotics. However, fabricating multifunctional LM-based polymers, in particular, featuring a convenient shaping ability while offering excellent deformability and conductivity remains a challenge. To overcome this obstacle, here, we propose a strategy to prepare LM-Gel "plasticine" (LGP) with great deformability, which is composed of a PVA (poly(vinyl alcohol)) soft network and an LM conductive phase. LGP can be easily constructed into different shapes such as plasticine and can be applied to different conditions (such as building a 3D circuit, circuit repair, and switch). Meanwhile, LGP has great conductivity (2.3 × 104 S/m) after surface annealing. Besides, LGP has a good electric heating performance, which shows the potential for application in wearable heating devices. Thus, this approach not only provides a way to prepare LM-polymer plasticine but also provides a novel perspective toward extending the applied range of LM-polymer composites.

Thermal performance of a novel traditional Chinese personal heating device (Huotong) combined with PCMs

Chinese traditional individual heating equipment with a history of hundreds of years “Huotong” was widely used in rural areas. The Huotong consisted of a closed wooden barrel-shaped outer wall and an iron basin with combustion layer. However, the traditional Huotong had problems of low energy utilization efficiency and poor thermal comfort. Thus, a novel Huotong combined with phase change materials (PCMs) was proposed. The basic model of novel Huotong was designed and manufactured. The thermal performances of the novel Huotong under two kinds of heat sources of charcoal heating and electric heating were investigated. The results showed that: (1) Under the method of charcoal heating, the heat storage and thermal comfort performance of the novel Huotong were higher than that of the traditional Huotong. Under the three-charcoal mass of 0.15, 0.25 and 0.5 kg, the heat storage performance of the novel Huotong was 1.36, 1.43 and 1.52 times of the traditional Huotong, respectively. The average PMV values of the novel Huotong was 0.92, 1.17 and 1.31, while for the traditional Huotong was 0.87, 1.32 and 1.58, respectively. (2) Under the four electric heating methods, the thermal efficiency of the novel Huotong was 1.63, 1.61, 1.47 and 1.39 times of the traditional Huotong, respectively. The heat storage performance was 1.72, 1.67, 1.47 and 1.28 times than that of the traditional Huotong. The average PMV values of the novel Huotong was 1.25, 1.22, 0.69 and 1.68, while for the traditional Huotong was 1.64, 1.53, 0.87 and 2.03, respectively.