Mathematical Model Of Heating Research Articles

Thermal decomposition and combustion of interior design materials

Research findings on the patterns of thermal decomposition and combustion are reported for widely used interior design materials. The experiments were conducted using a hardware and software system including a thermogravimetric analyzer (to record the characteristics of thermal decomposition), a gas analyzer (with H2, CH4, H2S, SO2, CO and CO2 sensors) and a high-speed camera (to record the characteristics of ignition and combustion). The temperature of the oxidizing medium ranged from 500 to 900°C to investigate the conditions of thermal decomposition initiation and sustained combustion. It was established that the highest concentrations of toxic emissions were typical of the combustion of polypropylene at a maximum temperature of the oxidizing medium (900°C). Wood showed the shortest ignition delay time and the longest duration of combustion. The experimental data were used for a physical problem statement and mathematical model of heat and mass transfer to explore the thermal decomposition and combustion of interior design materials in different rooms. A comparison of the experimental findings with the mathematical modeling results validates the developed model. The growth rates of carbon monoxide and carbon dioxide concentrations were determined for construction (wooden) and interior design (polymer) materials. The maximum concentrations of CO and CO2, and the minimum times taken to reach their threshold values corresponded to wood and polyvinyl chloride panels. This research provides a deeper insight into the thermal decomposition of a wide range of fuels and the formation of gaseous pyrolysis products of these fuels. The results obtained can be used to evaluate the toxicity of construction and interior design materials during compartment fires as well as to estimate the safe egress time and risks involved in the process. They can also serve as a database for the development and testing of mathematical models describing fire outbreaks and propagation in confined spaces.

Numerical parametric analysis of the decomposition and propagation of combustion products in a confined environment in the early stages of a fire

Numerical research findings are presented on the patterns of spread of thermal decomposition products of wood-based materials in confined spaces isolated from the external environment. Based on the experimental data, a physical problem statement was formulated and a mathematical model of heat and mass transfer was developed for rooms with the most typical sources of fire hazard. The experimental and numerical research findings were obtained for the conditions corresponding to compartments isolated from the external environment (e.g., rooms at dedicated facilities, like ships, small and medium-sized rooms) and to underventilated rooms. The performed experiments and calculations revealed satisfactory agreement in the findings and demonstrated the validity of the proposed model of heat and mass transfer. Wood was used as the main material in fires. A comparative analysis was also carried out for paper of different quality. The modeling was performed for the most frequent causes of fires: careless handling of fire, unsafe operation of heating equipment and electrical short circuits. The rates of growth of thermal decomposition product concentrations were determined for different distances from the material. The impact of a number of factors on the characteristics under study was determined. These are the fire and room sizes, fire cause, supply and exhaust ventilation. The data were extrapolated to the conditions corresponding to business, warehouse and residential premises.

Mathematical Model of Heat and Mass Transfer of Coal in a Stack

A mathematical model of coal’s self-heating in the stack is presented, where the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order concerning temperature t of coal’s self-heating and volume fraction C of oxygen in the cavities of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and initiation of self-ignition are observed in a relatively small layer adjacent to the surface of the stack and called the zone of oxygen influence. In this mathematical model authors have taken into account the influence on the process of coal’s self-heating of parameter Ф – specific heat release power, which in addition characterises the preservation of coal during storage. There were also used such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack cavity, temperature coefficient of exponential growth of heat release power when compiling the differential equations. For numerical implementation of this mathematical model, there were introduced dimensionless variables and criteria, which allowed to apply the grid method. Analysis of the final results allowed to obtain: changes in stack temperature profiles in time; changes in stack oxygen concentration profiles in time; influence on stack temperature profile of specific heat release power; influence on stack temperature profile of the parameter characterising exponential growth of heat release intensity with increasing temperature. It has been found that the greatest influence on the dynamics of self-heating of coal in the stack has the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and the effective thermal diffusivity of coal. The results obtained suggest that self-heating in the stack is due, on the one hand, to intensive penetration of air oxygen and, on the other hand, to impaired heat dissipation. Self-heating and the transition of self-heating into ignition is associated with the occurrence of turbulent diffusion in the stack, arising from increased heat blowing, the effect of which can be enhanced when directed perpendicular to the surface of the stack.

Modeling of heat conduction processes in porous absorber of open type of solar tower stations

An analysis of existing methods for calculating heat and mass transfer processes in porous absorbers of receivers of tower solar power plants is carried out. It is shown that the resulting thermophysical properties of the material are influenced not only by the porosity but also by the location of the pores in the material volume. The criterion of the dislocation vector is proposed as a mathematical indicator of various porous structures. The shortcomings of the existing dependences of the effective thermal conductivity of a material on the type of porosity are shown. The most reliable dependences for determining the thermophysical parameters of a porous medium are also determined and independent factors are proposed on which the mathematical model of heat and mass transfer in open-type solar receivers should be based.The current state of research on the effective thermal conductivity of the porous structure of solar receivers is described in detail. A new formula for calculating the effective thermal conductivity of a porous structure with regard to the dislocation vector and a method for calculating the processes of heat transfer in open solar receivers based on the proposed formula are proposed. The proposed equation has been tested. It is determined that for simple channel structures it is sufficient to use the existing equations to calculate the thermal conductivity coefficient, while for more complex porous structures, such as the StepRec absorber, it is better to use the proposed equation.Among the strengths of this study is a new calculation formula that allows us to build an analytical model of heat transfer in a porous medium. The use of the analytical model can significantly reduce the complexity of modern calculations of heat transfer processes in a porous absorber and will help improve the quality of optimization models of solar receivers.

Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples in the literature do not provide third-order accuracy in two stages. The scheme was explicit and correct to the third order. The stability region and consistency analysis of the scheme for linear ODE are provided in this paper. Moreover, a mathematical model of heat and mass transfer for the non-Newtonian Casson nanofluid flow is given under the effects of the induced magnetic field, which was explored quantitatively using the method of Levenberg–Marquardt back propagation artificial neural networks. The governing equations were reduced to ODEs using suitable similarity transformations and later solved by the proposed scheme with a third-order accuracy. Additionally, a neural network approach for input and output/predicted values is given. In addition, inputs for velocity, temperature, and concentration profiles were mapped to the outputs using a neural network. The results are displayed in different types of graphs. Absolute error, regression studies, mean square error, and error histogram analyses are presented to validate the suggested neural networks’ performance. The neural network technique is currently used on three of these four targets. Two hundred points were utilized, with 140 samples used for training, 30 samples used for validation, and 30 samples used for testing. These findings demonstrate the efficacy of artificial neural networks in forecasting and optimizing complex systems.

Study on Water Intake Characteristics and Influencing Parameters of Drinking Water Emergency Extraction Vehicle

In this paper, by analyzing the heat and mass transfer characteristics of the dehumidification runner microelement channel of a drinking water emergency extraction vehicle, a mathematical model of heat and mass transfer in the water intake process is established, and the influence of the runner parameters (adsorbent thickness, regeneration angle, rotation speed) and air parameters (treatment air temperature/humidity, regenerated air temperature/humidity) on the water intake characteristics is mainly studied. Water extraction experiments are carried out in arid desert areas and humid island environments. The test results showed that compared with the calculated data, the deviations in the temperature and humidity of the treated air outlet were 3.03% and 4.14%, respectively, and the deviation value of the water intake was 8.23% when the moisture content of the inlet air was 2 g/kg.

An unconditionally stable third order scheme for mixed convection flow between parallel plates with oscillatory boundary conditions

AbstractThis work proposes an unconditionally stable third‐order multistep technique for time‐dependent partial differential equations. Its unconditional stability is proved by employing von Neumann stability analysis, and constructed Matlab code is another solid proof of the existence of the such scheme. The scheme is constructed on three consecutive time levels, and a compact fourth‐order scheme is considered for spatial discretization. The convergence conditions are found when applied to the system of parabolic equations. The scheme is tested on two examples of flow between parallel plates. The mathematical model of heat and mass transfer of flow between parallel plates under the effects of viscous dissipation, thermal radiations, and chemical reaction is given and solved by the proposed scheme. The impact of some parameters, including radiation and reaction rate parameters, on velocity, temperature, and concentration profiles is also illustrated by graphs. The proposed scheme is also compared with the existing scheme, providing faster convergence than an existing one. The fundamental benefit of the proposed scheme is that it can give a compact fourth‐order solution to parabolic equations.

Numerical investigation on thermal performance of thermoelectric-cooler integrated cold plate of thermal control liquid loop in spacecraft

The traditional single-phase fluid loop (SFL) and traditioanl thermal control algorithm can barely control the temperature rapidly. Thermoelectric cooler (TEC) has been proved to be a good thermal controller because of its high reliability, liquid-free characteristics, and fast response. This paper proposes a TEC-based precooling module that resides in front of the cold plate (CP), and consists of a TEC-CP system, manifesting a high compatibility between the novel precooling module and traditional SFL. The TEC-CP system was designed, and a mathematical model of heat and mass transfer was developed to numerically investigate the effects of the geometric parameters, TEC operating conditions, and liquid cooling states of the precooling module upon payload thermal performance. Through analysis, an optimal TEC-based precooling module with optimal geometric dimensions was attained, where the coolant temperature was decreased by 13.04 K, resulting in a 28.98% reduction compared to that without the precooling module. Transient results also demonstrate that the temperature response time can be within 3 min, indicating a fast response system for temperature control. Results outlined in this paper provide structural and data references for future designs of scientific rack-level thermal control loops in space stations.

Mathematical model of heat and humidified air treatment in the injector camera

The article describes a mathematical model for the heat-moisture treatment of air in the nozzle chamber. The dynamics of unsteady processes of heat and mass transfer between the working substances in the apparatus and the transfer characteristics, balance equations of exchanging media are considered. A physical and mathematical description of heat and mass transfer processes in a thicker working medium and the relationship between the heat and mass fluxes through a surface unit and the mass-average temperature and potential are presented. The expression and their dependencies are presented for determining the final parameters of air in the irrigation chamber.

Сравнительный анализ схем тепломассообменных аппаратов косвенно-испарительного охлаждения воздуха

In this paper, a comparative analysis of schemes of heat and mass transfer devices of indirect evaporation type is carried out. These devices are a family of plane-parallel channels, in one of which the evaporation of water film takes place. Mathematical modeling of heat and mass transfer devices is based on solving a system of differential equations that represent the heat balance equations for each of the channels. Numerical studies are carried out in a wide range of input parameters: temperature from 15 to 50 °С, relative air humidity from 20 to 100 %, and Reynolds number 50…1500. The calculations are carried out at atmospheric.

Determining patterns of the influence of low temperatures of the external environment on head protection for a mountain rescuer

The basic principles of the need to develop a methodology for determining the level of protection of the rescuer's head during search and rescue operations in mountainous areas under conditions of low temperatures have been substantiated in this paper. The shortcomings of the existing system for ensuring the safe mode of search and rescue operations of rescuers in mountainous areas at low temperatures have been identified. Based on the statistical analysis of search and rescue operations, it was established that the greatest number of them occurs in the fall-winter period. It was determined that on the territory of the Carpathian Mountains the largest number of search and rescue operations is carried out in Zakarpattia, Ivano-Frankivsk, and Lviv oblasts. An analysis of working conditions was carried out. The results of studies into the effectiveness of thermal insulation of protective clothing of a mountain rescuer were analyzed. Mathematical modeling of heat and mass transfer in the body of a mountain rescuer was carried out using MATLAB software. Modeling of changes in temperature processes in the volume of the rescue head model was carried out under the influence of environmental temperatures: –10 °C, –20 °C, –30 °C, and a metabolic rate of 600 W/m2. Modeling was carried out on a 4-layer segment of the head. It was established that the effect of low temperatures on the face, head and, accordingly, the hypothalamus through the frontal part of the rescuer's skull leads to disability already at minute 17 in the absence of head protection equipment. The use of a model for predicting a decrease in body temperature as a result of exposure to the external environment and the level of protection by the rescuer's individual means will determine the time of risky decrease in brain temperature (up to +32 °C) and prevent a negative impact on the health of the rescuer

Mathematical Modeling of Heating and Strain Aging of Steel during High-Speed Wire Drawing

In this article, a mathematical model of the wire’s average temperature change in the process of multiple drawing on high-speed straight-line drawing machines has been developed. The calculation results showed that the average temperature of the wire during a drawing at a speed of up to 45 m/s on straight-line drawing machines could reach 400 °C. Deformation heating of the wire during drawing does not exceed 60 °C, and heating due to sliding friction can reach 300 °C, depending on the friction coefficient, which ranges from 0.05 to 0.15. The average strain rates under the conditions of the modern high-speed drawing process reach 7000 s−1. Over the course of the research, it was found that there are no conditions for the occurrence of dynamic deformation aging due to impurity atoms of carbon, nitrogen and oxygen. At the same time, at the temperature and speed parameters of the high-speed wire drawing, conditions are created for the onset of the dynamic strain aging of steel in the presence of hydrogen atoms. Therefore, during heat treatment and pickling, it is necessary to exclude the hydrogenation of steel. It has been established that in order to exclude static strain aging of steel during drawing, it is necessary to prevent heating the wire above 180–200 °C.

Mathematical Modeling of Heat and Mass Transfer during Moisture–Heat Treatment of Castor Beans to Improve the Quality of Vegetable Oil

An important process in the technology of plant oil production by mechanical pressing is the wet–heat treatment of crushed oilseeds, in which the oilseed (compressed seed) is exposed to saturated vapor and a conductive heat supply. Optimal mode selection of wet–heat treatment based on a detailed study of the physical processes taking place in the compressed seed increases oil release, improves its quality indicators, and decreases energy consumption. Mathematical modeling is an advanced method for studying the dynamics of humidification and frying in the compressed seed. The article introduces a mathematical model and a numerical method for calculating heat-and-mass transformation and phase conversion in the process of the humidification and frying of compressed seeds of the castor plant in a continuous multi-stage heating kettle. This study provides equations for calculating the intensity of phase transformation on the inner and outer surfaces of the wet layer. Data verification indicates the adequacy of the mathematical model, effectiveness of the numerical method, and possibility of their use in optimizing the modes of wet–heat treatment for compressed seed raw material.

Numerical Analysis Nucleation and Growth Conditions of Single-Crystallinity Control during Laser Surface Modification of Ni-Based Single-Crystal Superalloy Part I: Thermal and Chemical Determinants

Nucleation and growth conditions of single-crystallinity control are convincingly elaborated by multi-scale mathematical modeling of heat and mass transport to totally abate undesirable weld defects, e.g. disoriented crystal and hot cracking inside molten pool of nonequilibrium crystallization, in order to illustrate the usefulness of predictive capability through theory and experiment procedures. Crystal growth is complicated by crystallinity-dependent thermal and chemical driving forces in front of dendrite tip during viable laser surface modification of Ni-based single-crystal superalloy. These two thermal metallurgical determinants play crucial role in crack-insusceptible columnar crystal growth, which is favorably oriented throughout weld depth. There is particular challenge in complete elimination of disoriented crystal, i.e. stray grain formation, for acceptable surface quality. Conservative (001)/[100] crystalline orientation is desired to diminish Al concentration and supersaturation, and morphologically satisfy epitaxial growth kinetics to successfully lessen central cracking with satisfactory variability of laser power and welding speed. Comparatively, (001)/[110] crystalline orientation is disadvantageous to asymmetrically augment Al concentration and supersaturation and aggressively increase interface instability, microstructure heterogeneity and hot cracking vulnerability along disoriented crystal boundaries. Disoriented crystal is increasingly withstood if the Al concentration and supersaturation in front of dendrite tip are low enough and crack-unsusceptible part is relatively large enough in case of attractive (001)/[100] crystalline orientation with optimal range of heat input to ameliorate microstructure homogeneity. Crystalline orientation region varies with diverse welding configurations, and epitaxy across solid/liquid interface is also sensitive to heat input of laser processing, which necessitate high efficient welding conditions optimization. Considerable effort is made to distinguish diffusion-driven crystal growth between a series of combinations of multiple welding conditions, such as critical welding configuration and heat input. Metallographically, the morphologies of crystal growth and hot cracking are experimentally observed to consistently support kinetics calculation result and well explain correlation between solidification behavior and crystal growth.

Optimization of multilayer clothing assemblies for thermal comfort in cold climate

This paper presents a theoretical study on the optimization of key material parameters of multilayer clothing assemblies for thermal comfort in cold climate. A mathematical model of heat and moisture transfer through a multilayer clothing assembly is established. The existence and uniqueness of the solution of the model are verified by using the fixed point theorem. The model predicts the optimum thicknesses and porosities of the two internal layers of the clothing assembly, with which the thermal comfort index will fall within the required intervals with the greatest probability. This study is significant for the optimum design of multilayer clothing assembly for thermal comfort.

Solar chimney power plant combined with membrane distillation (SCPPMD), Part II: techno-economic characteristics

In this paper, the techno-economic characteristics of the solar chimney power plant combined with membrane distillation (SCPPMD) under typical operating conditions are further evaluated, based on the mathematical model of heat and mass transfer and performance analysis established in Part I and the economic evaluation model based on cash flow calculations. The sensitivity of some economic parameters and the effect of operating parameters and air gap spacing on system economy are discussed. The results show that the net present value is always positive during the service period. The total net income and total net present value are 16.79 and 2.72 million yuan respectively. The system economy is sensitive to inflation rate, loan interest rate, water price and electricity price, but not to operation and maintenance costs and personal income tax rates. The decrease of inlet seawater temperature and the increase of seawater thickness both lead to an increase in total water yield and a decrease in power generation. The increase in water yield compensates for the economic loss caused by the reduction in power generation, so the system profitability is improved. The reduction of air gap spacing causes a significant increase in total water yield and power generation. But too small an air gap has high requirements for membrane components in large-size system, inconvenient for construction, operation and maintenance.

ENERGY ANALYSIS OF THE PERFORMANCE OF A SOLAR ADSORPTION REFRIGERATOR

This paper presents a contribution to the study of the process of cold production by adsorption from solar energy. This study mainly includes a modeling, simulation and sizing study of an adsorption solar refrigerator using the zeolite-water couple. For this purpose, a mathematical model of heat and mass transfers in each component of the adsorption solar refrigerator was developed. The results show that the performance of the adsorption solar refrigerator depends on several parameters. For example, with a maximum solar radiation of 990W/m2, the maximum temperatures of the absorber plate, zeolite and condenser are 396 K (123°C), 395 K (122°C) and 320 K (47°C), respectively. The evaporator temperature can drop to a minimum temperature of 276 K (3°C). Furthermore, the simulation showed that the climatic conditions also have a great influence on the operation of the solar refrigerator. Thus, the amounts of cold produced, the average solar flux densities and the COPs during March and December are 6.391 MJ and 4.642 MJ, 590 W/m2 and 514 W/m2 and 0.25 and 0.21, respectively, relative to the values of the climate parameters. Similarly, with a daily average solar flux density of 436 W/m2 and 480 W/m2 respectively for the months of August and October, the COPs are 0.11 and 0.15 respectively, with a total amount of cold produced of 2.12 and 3.1 MJ respectively.

Solution of a mathematical model for the concentration of a hexane solution of technical paraffin to obtain its food modification

For pectin-containing film structures, which are used for the production of biodegradable packaging materials and are hydrophilic in nature, their paraffinization, i.e., applying a thin layer of molten food paraffin to the surface of the film for subsequent protection of packaged food products from moisture and sunlight, will reduce the influence of external factors, primarily moisture, To rationalize the convective preconcentration of a hexane solution, it is necessary to select such regime parameters that will allow not only the removal of hexane with toxic components dissolved in it from the object of study in a relatively simple apparatus, but also significantly reduce the time for the process within temperature restrictions. The latter condition, in view of the complexity of the empirical determination of the temperature distribution in a thin layer of the object of concentration, is advisable to implement by solving the system of equations for the transfer of thermal energy and mass in partial derivatives, however, we can restrict ourselves to one equation for the transfer of thermal energy, using empirical kinetic dependences that describe the removal of n-hexane from the composition. The aim of the study was to adapt paraffin to a hexane solution and solve the model of heat and mass transfer during its concentration in order to exclude the possibility of reducing its temperature below the value of possible preliminary crystallization. The model was implemented numerically by the finite difference method. As a result of the solution, the intensity of the temperature front advancement along the height of the film of the hexanoparaffin composition was found with varying the proportion of paraffin in the process of its concentration with convective supply of thermal energy to it, i.e., it was adapted to the resulting solution and a mathematical model of heat and mass transfer was solved during its concentration to eliminate the likelihood of a decrease in its temperature below the value of possible pre-crystallization. The data obtained do not conflict with the known results of other researchers and can be successfully used for operational calculation and design of the designated processes and units.

Mathematical modeling of heat and mass transfer in the process of drying seeds of agricultural crops in vacuum conditions

Purpose. To analyze the effect of vacuum on the process of drying seeds of agricultural crops using mathematical modeling. Methods. Methods of differential calculus were used, in particular first-order differential equations, as well as differential geometry. The analysis of the mathematical model was carried out using graphs that were built by computer programs for solving differential equations. Results. On the basis of balance equations of heat and humidity flows of the seed drying process in the drying chamber, a system of differential equations was compiled and solved. Analytical dependencies describing the kinetics of drying and heating crop seeds when using vacuum in the drying chamber are obtained. On the example of soybean seeds, graphic dependencies of the kinetics of drying and heating at different pressures and the initial absolute humidity of the air in the drying chamber are constructed. These graphic dependences show that an increase in the vacuum in the drying chamber leads to an increase in the rate of seed drying, and a decrease in the initial absolute air humidity also increases the drying rate and decreases the equilibrium humidity. Analysis of the graphical dependencies of seed heating kinetics shows that drying in a vacuum reduces some of the thermal energy used directly to heat the seeds and reduces their heating temperature. Conclusions. To describe the process of heat and mass transfer in the process of drying seeds of agricultural crops under vacuum conditions, a mathematical model has been developed using a system of differential equations. The solution of which, on the example of soybean seeds, shows that when using a vacuum in the process of drying seeds, the exposure time and the proportion of thermal energy used directly to heat the seeds are reduced. Reducing the initial absolute humidity of the air inside the drying chamber also reduces the exposure time and equilibrium humidity. Therefore, drying in a vacuum reduces the negative impact of the heater on the seeds. Keywords: seeds, seed moisture, seed temperature, vacuum, absolute humidity, drying kinetics, drying chamber, equilibrium humidity.

Mathematical modelling of thermal microexplosion in a catalyst granule with point sources of heat release

A mathematical model of heat and mass transfer in a spherical catalyst granule is proposed. Exothermic synthesis reactions are carried out on point active centres located inside a porous ceramic granule. From the surface of the granule the heat of catalytic reactions is removed into liquid synthesis products. The rate of a chemical reaction is modelled by a modified Arrhenius law. In contrast to the homogeneous model of a catalytic granule methods for calculating heat transfer processes in a system of point, active centres do not develop. An iterative procedure is suggested to calculate the unknown temperature and concentration of the reagent at the active centre. It is shown that the temperature of the active centres is significantly higher than in the volume of the granule. The results of modelling a thermal explosion with increasing granule size and reactor temperature are presented.