Heat Balance Research Articles

Non-central m-point formula in method of lines for solving the Korteweg-de Vries (KdV) equation

AbstractThe present study is committed to devising efficient spatial discretization with two non-central difference formulae incorporated in the method of lines (MOL). The method is then implemented numerically on the renowned dispersive evolution equation, the Korteweg-de Vries (KdV) model while infusing Euler and fourth-order Rung-Kutta (RK4) methods, respectively. The resulting schemes are proven to be numerically stable using Fourier’s stability approach, with the MOL matrix admitting negative real eigenvalues. Moreover, this proposal has been assessed on certain initial-boundary value problems of the KdV model by examining so many factors, like the percentage errors, absolute error differences, the error norms, and the invariants $$I_{k},$$ I k , for $$k=1,2,3,$$ k = 1 , 2 , 3 , among others. In this work, we solve KdV by applying a new approach of MOL to improve the results presented in some published articles. Lastly, the assessment revealed that our proposal was found to be better than those of the exponential finite-difference method (Exponential) and the Heat Balance Integral (HBI) methods, respectively, which serve as competing approaches for validation, in terms of both the accuracy and efficiency. The numerical examples are obtained by using MATLAB.

Инженерная методика определения температурного состояния металла при его нагреве

Currently, the determination of the temperature profile of the furnace required to ensure the specified heating parameters of the metal is carried out using the temperature measurement method or mathematical models. They are most based on solution of the differential equation of non-stationary thermal conductivity. Previously, the thermal diagram method of I.D. Semikin was widely used. It allows us, under given heating conditions, to determine heating duration. In practice, it is important to develop a simple engineering method that would allow the temperature field of the metal to be determined with sufficient accuracy under given heating conditions. The development is based on the thermal diagram method of I.D. Semikina. But at the same time, the final equation describing the heat balance of the metal within the furnace zone is solved relative to the enthalpy of the metal at the exit from the zone. The specified heating conditions (productivity, zone temperature) are used to determine the quantities of the right-hand side of the equation (time heating, average heat flux density). The authors have proposed the method for continuous furnaces of various types (push-type and with a mechanized hearth) that allows us for a given productivity and temperature profile of the furnace to calculate the change in the temperature state of the metal for all heating zones, from the moment of loading to the release of metal. The adequacy of the proposed methodology has been tested for two types of furnaces. For methodical push-type furnaces, the results obtained have been compared to the results of modeling the temperature state of the metal using a numerical method. The discrepancy between the results after passing the inertial heating period does not exceed 1 %. For a walking-beam furnace the calculated value of the metal surface temperature after the furnace has been compared with the results of operational measurements. The discrepancy is less than 2 %. The totality of the results obtained ensures the achievement of the research goal. The proposed method is based on the heat balance equation and allows us to consider it to be correct. It is an engineering method and quite simple to implement. The method is recommended to be used to design furnaces and to calculate the temperature profile of furnaces by engineering departments of metallurgical enterprises.

Woody biomass waste derivatives in decarbonised blast furnace ironmaking process

Modern ironmaking process relies significantly on fossil-related fuels, which ultimately results in the enormous CO2 emitted into the atmosphere. Biomass of plant origin, as a carbon-neutral energy source, has been considered as an alternative to fossil-based reducing agents such as coke. This study aims to investigate the potential of three woody biomass waste derivatives produced from biomass waste pyrolysis and gasification, namely charcoal, bio-oil, and bio-syngas, as the reducing agents in blast furnace. A model based on heat and mass balance and Gibbs free energy minimisation is proposed to simulate an ironmaking process with assistance of these derivatives. The effects of specific composition of biomass waste derivatives on process operation, CO2 emissions, and coke replacement are explored. Also the effects of H2-rich gas produced from biomass waste gasification on the blast furnace operation are estimated. Results indicate that reactions of woody biomass waste derivatives in blast furnace are complex and greatly dependent on composition. When charcoal has a higher carbon content, lower CO2 concentration is found from the top gas. The higher content of hydrogen in bio-oil will inhibit further reduction in CO2 emissions. Bio-syngas with H2/CO ratio of 1.3 proves to have a remarkable potential to reduce CO2 emissions. From the aspects of available biomass waste resources across the world, woody biomass waste derivatives as reducing agents are more suitable for countries with the limited pig iron production. This study provides a reference on the future of moving forward the decarbonised ironmaking by using woody biomass waste derivatives.

Photothermal performance of vitreous products from high-temperature melting of hazardous waste

High-temperature molten vitreous (HTMV), as the primary means of hazardous waste disposal, was produced in large quantities. Exploring its potential in photothermal applications could extend its high-value. Herein, the HTMV was used to explore the photothermal performance potential. It indicates that the HTMV possesses significant photothermal conversion capability, capable of increasing the tested water temperature by 6.65 °C. The HTMV mass and water volume are critical factors affecting the water temperature outcomes. The HTMV exhibits distinct conversion capabilities when applied at different application scenarios on the test object. Application on the bottom primarily focuses on photothermal conversion with high heat production efficiency, while side application additionally demonstrates excellent thermal insulation properties. Based on heat balance and backpropagation neural network predictions, optimal scheme of HTMV on both inside and outside bottom application scenarios of the heated object can achieve a maximum heat input of 660.6 kJ m−2 and 570.1 kJ m−2, respectively, and reduce carbon emissions by 0.062 kg CO2 m−2 and 0.054 kg CO2 m−2. This study not only provides a foundation for the further application of HTMV but also opens a new direction for the development of photothermal conversion materials, which is of great significance in advancing sustainable energy technology.

Multi-objective optimization strategy for multipolar magnesium electrolysis cell based on thermal-electric model

In the operation of industrial multipolar magnesium electrolysis cell, cell voltage and current density are important indicators of the production performance of the cell, while thermal balance is a key factor for normal operation. This paper utilizes the finite element method to establish a three-dimensional full cell thermal-electric model, studying the thermal field distribution and current density distribution in a 165kA multipolar magnesium electrolysis cell. Based on the heat balance of the multipolar cell, the influence of structural parameters on current intensity, average current density at the anode surface and resistance voltage is assessed. Dimensionless analysis yielded optimization criteria, and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed for multi-objective optimization problems. When stringent optimization is executed, significant performance improvements can be achieved in terms of the electrolysis cell's resistance voltage and current density. Moreover, under the optimization criteria, the relative error of the 265kA multipolar magnesium electrolysis cell model is less than 1 %. The results indicate that the workflow combining the finite element method with multi-objective optimization algorithms can be applied to the optimization and scale-up design of high-current multipolar magnesium electrolysis cell.

Biological sex does not independently influence time-dependent changes in core temperature and sweating of children exercising in uncompensable heat stress.

To investigate the influence of biological sex, independent of differences in aerobic fitness and body fatness, on the change in gastro-intestinal temperature (∆Tgi) and whole-body sweat rate (WBSR) of children exercising under uncompensable heat stress. Seventeen boys (mean±SD; 13.7±1.3 years) and 18 girls (13.7±1.4) years) walked for 45 min at a fixed rate of metabolic heat production per kg body mass (8 W·kg-1) in 40°C and 30% relative humidity. Sex and V̇O2peak were entered into a Bayesian hierarchical general additive model (HGAM) for Tgi. Sex, V̇O2peak and the evaporative requirement for heat balance (Ereq) were entered into a Bayesian hierarchical linear regression for WBSR. For 26 (12 M, 14 F) of the 35 children with measured body composition, body fat percentage was entered in a separate HGAM and hierarchical linear regression for Tgi and WBSR respectively. Conditional on sex-specific mean V̇O2peak, ∆Tgi was 1.00°C [90% credible intervals: 0.84, 1.16] for boys and 1.17°C [1.01, 1.33] for girls, with a difference of 0.17°C [-0.39, 0.06]. When sex differences in V̇O2peak were accounted for, the difference in ∆Tgi between boys and girls was 0.01°C [-0.25, 0.22]. The difference in WBSR between boys and girls was 0.03 L·h-1 [-0.02, 0.07], when isolated from differences in Ereq. The difference in ∆Tgi between boys and girls was -0.10°C [-0.38, 0.17] when sex differences in body fat (%) were accounted for. Biological sex did not independently influence the ∆Tgi and WBSR of children exercising under uncompensable heat stress.

Analysis of the impact of plastic utilization technology in a blast furnace on technical and economic indicators and carbon dioxide emissions

Taking into account global trends in reducing the impact of anthropogenic factors on nature, namely the utilization of plastic waste and decarbonization of industrial facilities, the article studies the impact of the use of plastic in a blast furnace, as the most energy-intensive unit in the steel production cycle, on the technical and economic indicators of blast furnace melt and CO2 emissions from the blast furnace based on the heat balance. It was found that the use of plastic in a blast furnace will allow solving the issue of its utilization with the least environmental impact. The quantitative impact of plastic use on furnace performance, coke consumption, and CO2 emissions was determined. The coefficient of coke replacement by different types of plastic when used in a blast furnace was determined.

Development of an Activity Coefficient Model for the Aqueous Amino Acid Solution

AbstractThe enthalpy and solubility of aqueous amino acid solutions are essential thermodynamic properties for the modeling of heat and mass balance, and these properties can be estimated by considering the activity coefficient in thermodynamic calculations. In this study, the parameters of a non‐random two‐liquid model were identified using heat capacity and solubility data together to calculate the acceptable activity coefficient for an aqueous amino acid system. As a result, a highly accurate activity coefficient model of an aqueous amino acid solution was developed, and inaccurate alternative solutions regressed with heat capacity or solubility only can be avoided.

Transformation of internal solitary waves at the edge of ice cover

Abstract. Internal wave-driven mixing is an important factor in the balance of heat and salt fluxes in the polar regions of the ocean. Transformation of internal waves at the edge of the ice cover can enhance the mixing and melting of ice in the Arctic Ocean and Antarctica. In the polar oceans, internal solitary waves (ISWs) are generated by various sources, including tidal currents over bottom topography, the interaction of ice keels with tides, time-varying winds, vortices, and lee waves. In this study, a numerical investigation of the transformation of ISWs propagating from open water in the stratified sea under the edge of the ice cover is carried out to compare the depression ISW transformation and loss of energy on smooth ice surfaces, including those on the ice shelf and glacier outlets, with the processes beneath the ridged underside of the ice. They were carried out using a non-hydrostatic model that is based on the Reynolds-averaged Navier–Stokes equations in the Boussinesq approximation for a continuously stratified fluid. The Smagorinsky turbulence model extended for stratified fluid was used to describe the small-scale turbulent mixing explicitly. Two series of numerical experiments were carried out in an idealized 2D setup. The first series aimed to study the processes of the ISWs of depression transformation under an ice cover of constant submerged ice thickness. Energy loss was estimated based on a budget of depth-integrated pseudoenergy before and after the wave transformation. The transformation of ISWs of depressions is controlled by the blocking parameter β, which is the ratio of the minimum thickness of the upper layer under the ice cover to the incident wave amplitude. The energy loss was relatively small for large positive and large negative values of β. The maximal value of energy loss was about 38 %, and it was reached at β≈0 for ISWs. In the second series of experiments, a number of keels were located on the underside of the constant-thickness ice layer. The ISW transformation under ridged ice also depends on the blocking parameter β. For large keels (β<0), more than 40 % of energy is lost on the first keel, while for relatively small keels (β>0.3), the losses on the first keel are less than 6 %. Energy losses due to all keels depend on the distance between them, which is characterized by the parameter μ, i.e. the ratio of keel depth to the distance between keels. In turn, for a finite length of the ice layer, the distance between keels depends on the keel quantity.

Impact of heat infiltration on the cooling capacity evaluation of an evaporator for household refrigerator-freezers with a non-adiabatic capillary tube

This study experimentally evaluates the cooling capacity of an evaporator in household refrigerator-freezers, typically scaled in hundreds of Watts, and investigates the impact of heat infiltration from the environment. Despite the scarcity of both quantitative and qualitative research in this area, this study provides data from a lab-scaled vapor compression refrigeration system that mimics a real-world side-by-side refrigerator-freezer. Experiments were conducted under conditions reflecting the household refrigerator-freezer, yielding 74 data points under quasi-steady state conditions. Despite careful insulation, heat infiltration from the ambient to the refrigerant flow in the evaporator occurred due to the significant temperature differential, impacting the cooling capacity evaluation fatally with a heat balance error of 26%. However, when considering the effects of heat infiltration, the error in the evaporator heat balance dropped to 6% significantly. The findings highlight the sensitivity of evaporator’s cooling capacity, less than 300 W, to external thermal factors during empirical evaluation. This study underscores the challenges of heat infiltration and the importance of considering such factors when assessing evaporator cooling capacity. The provided comprehensive analyses significantly contribute to the experimental prototyping of evaporators, emphasizing the need to account for external thermal influences during the evaluation process.

Model-based prediction of frost formation inside frozen food packages under temperature fluctuations

Abstract Frozen storage of food products is widely accepted not only in the industry but also by households. Frost formation during long-term storage is recognized as a phenomenon that causes changes in product characteristics and quality losses. However, quantitative prediction and control of frost formation remains a challenge. In this study, a mathematical model was developed to predict frost formation inside frozen food products (i.e., frozen minced meat packed in a polyvinylidene chloride (PVDC) film) under fluctuating temperature conditions in a domestic refrigerator. The proposed model is based on heat transfer and energy balance equations, and the amount of frost formation is estimated from the heat generated by condensation. The heat transfer coefficients were experimentally obtained and applied to the developed model. The interactions between the amplitude and frequency of temperature fluctuations and the corresponding amount of frost formation were visualized using contour plots. Both the amplitude and frequency were found to increase frost formation. For the range of fluctuations tested (temperature amplitudes of 0.5–2.5 K and cooling rates of 0.0125–0.2 K/min when connected to the compressor), the simulation predicted that the amount of frost in the packages varied up to approximately 4.5 times (0.48–2.18 g/month for packages containing 300 g of minced meat) depending on the different temperature fluctuation settings.

Broiler Age Differently Affects Apparent Metabolizable Energy and Net Energy of Expanded Soybean Meal.

Accurately determining the energy values of ingredients is crucial for meeting energy requirements and achieving maximum production performance of animals. This study was conducted to measure the available energy values of three expanded soybean meals (ESBMs) for Arbor Acres male broilers from 14 to 16 day and 28 to 30 day using the difference method. A corn-soybean basal diet was formulated, and test diets were developed with 25% ESBMs as substitutes for energy-yielding ingredients. A completely randomized design was used for determining heat production and energy balance of broilers in 12 open-circuit respiration chambers, with six replicates per group. Prior to measurement, four (14 to 16 day) or two (28 to 30 day) birds per chamber were given a 4-day adaption to diets and chambers. The period lasted for 3 days to determine the apparent metabolizable energy (AME), nitrogen balance, gas exchanges, and heat production. Broilers fed test diets with 25% ESBM exhibited higher nitrogen intake (p < 0.05), nitrogen excreta (p < 0.05), and increased energy deposition as protein irrespective of age (p < 0.05). Furthermore, results showed that AME, nitrogen corrected AME (AMEn), and net energy (NE) values of 3 ESBMs averaged 10.48, 8.93, and 6.88 MJ/kg for broilers from 14 to 16 day, while averaged 11.91, 10.42, and 6.43 MJ/kg for broilers from 28 to 30 day. Broilers from 28 to 30 day showed significantly higher AMEn values but lower NE/AME values of ESBMs compared with those from 14 to 16 day (p < 0.05). Therefore, age-dependent energy values of a single ingredient should be considered in feed formulations to optimize economic returns.

Numerical analysis of the heat transfer of gears under oil dip lubrication

Reliable gearbox operation is based on heat balance. The heat transfer of gears is closely related to the fluid flow of a gearbox. This study focuses on the heat transfer between oil dip-lubricated gears and fluid. A numerical analysis of the mechanisms and influences on the heat transfer coefficient of gears is carried out. The results show that the local interaction between gears and fluid strongly influences the gear heat transfer. The oil wetting and circumferential speed are particularly influential. The fling-off model is capable of predicting the heat transfer coefficient between gears and fluid with reasonable accuracy. The prediction accuracy of analytical models can be improved by incorporating fluid flow properties obtained from numerical calculations.

Attribution Analysis of Discharge Variations in the Inner Mongolia Basin of the Yellow River

Climate change and human activities are the main causes of discharge variation. Therefore, calculating the contribution of climate change and human activities to discharge variation in the Inner Mongolia Basin of the Yellow River can provide a reference basis for alleviating water resources stress in the Inner Mongolia Basin of the Yellow River. Firstly, based on the water balance theory and the Budyko hypothesis-based evapotranspiration formula, this study constructed a coupled water and heat balance equation and calibrated and validated the model using observed annual discharge depth data from the Toudao Guai hydrological station. The results show that the water-heat coupling model has good simulation accuracy at the annual scale, with NSE=0.76, RMSE=10.45, and RRMSE=19.5%, and overall, the simulated discharge results are close to the observed values. Secondly, this study also used the Mann-Kendall test method to determine the abrupt change points of discharge and analyzed the contribution rates of various meteorological factors. The results indicate that precipitation accounts for 88.79% of the discharge variation in the Inner Mongolia segment of the Yellow River basin, followed by land surface changes at 13.6%, while potential evaporation has the smallest contribution to discharge variation.

Spatial variations in leaf trichomes and their coordination with stomata in Quercus variabilis across Eastern Asia

Abstract Leaf trichomes are derived from epidermal cells and serve an important function in regulating leaf heat balance and gas exchange. Variation in leaf functional traits is critical for predicting how plants will react to global climate change. In this study, we aimed to investigate how leaf trichome densities vary along large geographic gradients and how they interact with with stomata in response to environmental change. We investigated the leaf trichome densities of 44 Quercus variabilis populations in Eastern Asia (24° to 51.8° N, 99° to 137° E) and their correlation with climatic factors and stomatal traits. In addition, 15 populations were grown in a common garden to study their adaptive variation and coordination with stomata. The mean value of trichome density in situ conditions was 459.78 trichome mm-2 with a range of 325.79 to 552.38 trichome mm-2. Trichome density increased with latitude and decreased with longitude. Both temperature and precipitation reduced the trichome density. Moreover, trichome density was positively correlated with stomatal density whether in situ or in the common garden, and both increased with drought. Our results suggested that leaf trichomes possess highly adaptive variation and are in close coordination with stomata in response to climate change. Our findings provide new insights toward elucidating the interactions between leaf traits and the adaptive strategies of plants under climate change.

Optimizing Greenhouse Design with Miniature Models and IoT (Internet of Things) Technology-A Real-Time Monitoring Approach.

The market for smart greenhouses has been valued at USD 1.77 billion in 2022 and is expected to grow to 3.39 billion by 2030. In order to make this more efficient, with the help of Internet of Things (IoT) technology, it is desired to eliminate the problem of traditional agriculture, which has poor monitoring and accuracy control of the parameters of a culture. Climate control decisions in a greenhouse are made based on parameter monitoring systems, which can be remotely controlled. Instead of this adjustment of the measured parameters, it would be preferable from the point of view of energy consumption that they should be calculated at optimal values from the design phase of the greenhouse. For this reason, it would be better to perform an energy simulation of the greenhouse first. For the study carried out in this work, a small greenhouse (mini-greenhouse) was built. It was equipped with an IoT sensor system, which measured indoor climate parameters and could send data to the cloud for future recording and processing. A simplified mathematical model of the heat balance was established, and the measured internal parameters of the mini-greenhouse were compared with those obtained from the simulation. After validating the mathematical model of the mini-greenhouse, this paper aimed to find the optimal position for placing a normal-sized greenhouse. For this, several possible locations and orientations of the greenhouse were compared by running the mathematical model, with which the most unfavorable positions could be eliminated. Then, some considerably cheaper "mini-greenhouses" were made and placed in the locations with the desired orientations. Using sensor systems and technologies similar to those presented in this work, the parameters from all mini-greenhouses can be monitored in real time. This real-time monitoring allows for the simultaneous analysis of all greenhouses, without the disadvantages of data collection directly in the field, with all data being recorded in the cloud and other IoT-specific advantages being made use of. In the end, we can choose the optimal solution for the location of a real-size greenhouse.

Ecological flexible protection method of expansive soil slope under rainfall

In this study, a new ecological slope protection method—Anchor Reinforced Vegetation System (ARVS) was applied to the newly excavated expansive soil slope. To explore the effect and mechanism of ARVS protection of newly excavated expansive soil slopes, expansive soil slopes with three different protection methods (bare slopes, grassed slopes, and ARVS slopes) were built. The continuous natural rainfall test and artificial rainfall tests were carried out. The results show that: compared with the bare slope and the grassed slope, ARVS could effectively adjust the moisture and heat balance of newly excavated expansive soil slopes and achieve a satisfactory soil and water conservation performance. Under different rainfall intensities, the runoff and soil loss rates of the ARVS-protected slope were smallest. Under the combined action of vegetation, high-performance turf reinforcement mats (HPTRMs) and anchors, the ARVS provided a superior erosion resistance. The higher the rainfall intensity is, the more significant the anti-erosion effect of the ARVS compared to that of grass protection technology. The ARVS could also effectively limit vertical and horizontal deformation of newly excavated expansive soil slopes. Therefore, the ARVS could effectively reduce the negative influences of the atmospheric environment on newly excavated expansive soil slopes and provide a new solution for shallow protection of newly excavated expansive soil slopes.

A Review on Nano Fluid Production, Mathematical Modelling and Applications

Recently, nano fluids have taken on a significant role in many human endeavours. A fluid called a nanofluid includes nanoparticles, also called nanoparticles. Colloidal suspensions of nanoparticles in a base fluid are what these fluids are made of. The numerous production procedures and mathematical interpretation models for nanofluids are examined in this review study. Marangoni convection’s advantages, which enhance heat transfer and balance temperature distribution, are underlined. The effects of thermophoresis on surface tension as well as surface tension in laminar natural convection are also discussed in this work. The characteristics of carbon nanotubes and their prospective medical uses are covered in the article. The study covers electrochemical double layer capacitors, which offer greater safety, longer cycle stability, and better power densities. The study explores the impact of magnetic fields on entropy formation and natural convection in a hybrid nanofluid enclosure, revealing four distinct models based on thermal conductivity and viscosity correlations. The information review work is relevant. The review information work is relevant to flow tracers, prosthetic heart valves, oil pipelines, chemical industry separation methods, and oil recovery.

Applicability of radiant and convection time series method in coincident design day generation for radiant cooling systems

Previous studies have shown that coincident design day (CDD) can make the calculated design cooling load of an air-conditioning system more rational and accurate. The conversion process of room heat gain to cooling load in radiant cooling systems is different from that in convection cooling systems. The radiant time series method (RTSM) of generating the coincident design day is inapplicable to radiant cooling systems. In this paper, the radiant and convection time series method (RCTSM) is proposed to generate the coincident design day for radiant cooling systems. The relative deviation of design cooling load, computation time for generating coincident design days, and the correct rate are introduced to evaluate the applicability of RCTSM for generating coincident design days. Fifteen room/building characteristic parameters are taken into account to construct 10,000 simulated sample rooms for each city. Compared to the theoretical design cooling load, the relative deviations of design cooling load determined by RCTSM are generally within 7.23 %. RCTSM is suitable to calculate design cooling load and generate coincident design day for radiant cooling systems. The computation time of RCSTM for generating coincident design day is less than one of sixty-third of that of heat balance method. RCTSM can significantly enhance the efficiency in generating coincident design day. The correct rates of the coincident design days generated using RCTSM is higher than those using heat balance method. These results indicate that RCTSM is more suitable to generate the coincident design days for radiant cooling systems than heat balance method.

Exploration on the comprehensive data reconciliation framework for unknown parameter inference in the nuclear power plant system

Nuclear power plants have been considered as a promising future energy source. As for maintenance of the nuclear power plants, it is crucial to acquire complete and accurate measurement, and even make precise inference for the unknown parameters all around the system. In this paper, a new comprehensive data reconciliation framework based on a 310 MW schematic nuclear power plant system is proposed, which is capable for calculation, uncertainty reduction and gross error detection. A new method combined with heat balance calculations is developed based on the classical method, which can make more accurate inferences for the unknown parameters. An interative algorithm is also applied to effectively eliminate the residual of constraints. The proposed framework is evaluated over the simulated datasets, and it proves that the data reconciliation process can effectively capture and reduce the errors in the measurements, as all the sensors with gross errors are detected and have their errors reduced by at least 66.7 %. The results suggest the great potential for this framework to be applied for measurement correction and error diagnostics in those practical nuclear power systems.