Mathematical Model Of Heat Transfer Research Articles

MATHEMATICAL MODELING AND EXPERIMENTAL INVESTIGATION OF THE PROCESS OF NON-STATIONARY HEAT TRANSFER IN A BLOCK FOAM GLASS SAMPLE AT THE ANNEALING STAGE

The specifics of the technology for the production of block foam glass are presented, the results of experimental studies of the properties of the material are presented, a method for improving production based on mathematical modeling of heat transfer processes is proposed. It is shown that the processes of high-temperature processing of foam glass make a key contribution to the formation of a high-quality porous structure, therefore, this area of ​​research needs the development of adequate methods for calculating the main macrophysical parameters based on the theory of heat transfer. A technique for checking the adequacy of the mathematical model of heat transfer is presented using the example of spontaneous cooling of a foam glass block. The entire procedure for checking the adequacy of the mathematical model was carried out in three stages. At the first stage, the degree of validation of the model is assessed, functional dependencies with the results of an experimental study based on the Pearson determination coefficient. The main stage includes the evaluation of the confidence intervals of the experimental data and the discussion of the convergence of the results of the analytical calculation with the results of the experimental data. The final stage, at which a comprehensive assessment of the adequacy of the mathematical model is given, includes both the results of the preparatory and the main stages. The results of the study showed that it can be concluded that the calculated data have sufficient convergence with the experimental data and indicate the adequacy of the developed mathematical model of heat transfer.

Waste Heat Recovery from Converter Gas by a Filled Bulb Regenerator: Heat Transfer Characteristics

The iron and steel industry is a high-energy consumption and high-pollution industry. Energy recovery in its process is of great significance. Converter gas is an important by-product in the process of iron and steel production. It is difficult to take effective measures to recover waste heat from converter gas due to its flammability. In this paper, a new technology is proposed based on waste heat recovery by a filled bulb regenerator. The mathematical model of heat transfer and flow in the compound regenerator for converter gas containing dust is established. The effects of the diameter and concentration of dust to heat transfer and flow are discussed. The results show that the temperature of converter gas declined to 132 °C, and recovery efficiency was above 90% using this technology system. Resistance loss increased by 25% due to the dust; with the increase in the diameter and initial concentration of dust, the heat transfer rate in the regenerator was reinforced. At the entrance of the regenerator, dust’s effects are more obvious, and the efficiency of heat transfer is increased by 4.5–8.5%. The results can provide a theoretical basis for a new converter gas waste heat recovery method.

Unconditionally Stable Numerical Scheme for Heat Transfer of Mixed Convective Darcy–Forchheimer Flow of Micropolar Fluid Over Oscillatory Moving Sheet

AbstractThis contribution proposes a third-order numerical scheme for solving time-dependent partial differential equations (PDEs). This third-order scheme is further modified, and the new scheme is obtained with second-order accuracy in time and is unconditionally stable. The unconditional stability of the new scheme is proved by employing von Neumann stability analysis. For spatial discretization, a compact fourth-order accurate scheme is adopted. Moreover, a mathematical model for heat transfer of Darcy–Forchheimer flow of micropolar fluid is modified with an oscillatory sheet, nonlinear mixed convection, thermal radiation, and viscous dissipation. Later on, the dimensionless model is solved by the proposed second-order scheme. The results show that velocity and angular velocity have dual behaviors by incrementing coupling parameters. The proposed second-order accurate in-time scheme is compared with an existing Crank–Nicolson scheme and backward in-time and central in space (BTCS) scheme. The proposed scheme is shown to have faster convergence than the existing Crank–Nicolson scheme with the same order of accuracy in time and space. Also, the proposed scheme produces better order of convergence than an existing Crank–Nicolson scheme.

Mathematical Model and Numerical Method of Calculating the Dynamics of High-Temperature Drying of Milled Peat for the Production of Fuel Briquettes

Milled peat must be dried for the production of peat fuel briquettes. The current trend in the creation of drying technologies is the intensification of the dehydration process while obtaining a high-quality final product. An increase in the temperature of the drying agent, above 300 °C, significantly accelerates the reaching of the final moisture content of the peat. In the final stage, it is also accompanied by partial thermal decomposition of the solid phase. Its first stage, which is the decomposition of hemicellulose, contributes to a decrease in weight and an increase in the caloric content of the dry residue. The development of high-temperature drying modes consists of determining the temperature and velocity of the drying agent, wherein the duration of the material reaching the equilibrium moisture content will be minimal and the temperature of the material will not rise above the second-stage decomposition temperature of cellulose. This problem can be solved by the mathematical modeling of the dynamics of peat particles drying in the flow. The article presents a mathematical model of heat and mass transfer, phase transitions, and shrinkage during the dehydration of milled peat particles. The equations of the mathematical model were built based on the differential equation of mass transfer in open deformable systems, which, in the absence of deformations, turns into the known equation of state. A numerical method for implementing a mathematical model has been developed. The adequacy of the mathematical model is confirmed by comparing the results of numerical modeling with known experimental data.

Study on refined mathematical model of solar chimney power plant integrated with seawater desalination and the influence of dewing

In order to more accurately evaluate the operation and output characteristics of the solar chimney power plant integrated seawater desalination, a refined mathematical model for unsteady heat and mass transfer was built under consideration of the convection heat transfer mechanism of the collector, dewing phenomenon, and the disturbance to the hot airflow caused by the oblique-toothed flow channel boundary. The influence of nighttime dewing and humid environments on system performance was discussed. The results show that it is feasible and more appropriate to use the forced convection heat transfer coefficient of bellows to consider the influence of the oblique-toothed flow channel boundary; the refined mathematical model is also more accurate and reliable. Due to the effect of seawater heat storage, dewing has little effect on system performance, and the integrated system has a better anti-dewing negative impact characteristic. However, when the ambient humidity reached a higher level, dewing had a greater negative impact on freshwater production. The critical value of relative humidity for dewing to occur is 51 %. When the relative humidity increases from 45 % to 60 %, the daily utilization efficiency of solar energy decreases from 27.4 % to 22.5 %.

Mathematical Modeling of Heat Transfer in a Room with a Gas Infrared Emitter, an Air Exchange System, and a Local Fence of the Working Area

Mathematical Modeling of Heat Transfer in a Room with a Gas Infrared Emitter, an Air Exchange System, and a Local Fence of the Working Area

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.

Mathematical Modeling of Heat Transfer in Composite Materials under Fire Conditions

Mathematical Modeling of Heat Transfer in Composite Materials under Fire Conditions

Mathematical Modeling, Prediction and Research on Heat and Moisture Transfer of a Kind of Textile Materials

The structure, layers, and mix of a particular type of textile material affects how warm and permeable to moisture a piece of clothing is. The microclimate region between the human body and clothes also has an impact on it. Designing warm clothing and choosing materials can be guided by the inverse problem of the heat and moisture transfer model and its parameter determination in winter clothing. This paper investigates the mathematical modeling of heat and moisture transfer of a class of textile materials based on PSO (abbreviation: PSO). Under the two categories of temperature and humidity combinations mentioned above, the three materials exhibit extreme values and are one of a kind. The disturbance function of polypropylene fiber material at 5% is 10, the disturbance function of polyester material at 5% is 8, and the disturbance function of wool material at 5% is 18 when the fabric thickness reaches 0.012. PSO was used in this experiment to calculate the thickness inversion results for fabrics made of polypropylene, polyester, and wool. The results are consistent with those in the figure. In order to solve the inverse problem of functional design, it is necessary to mathematically study the transfer of heat and moisture through textile materials.

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.

Determination of the Heat Transfer Coefficient in Mathematical Models of Heat and Mass Transfer

Determination of the Heat Transfer Coefficient in Mathematical Models of Heat and Mass Transfer

Research on energy-saving coupling correlation of new energy buildings based on carbon emission effect

In order to improve the promotion effect of new energy on building energy conservation, this paper combines intelligent analysis of green building energy conservation, and conducts a coupling correlation study of new energy building energy conservation based on carbon emission effect. Moreover, based on the basic laws of thermodynamics, this paper solves the first-order ordinary differential equations for the unsteady temperature field variables of the differential equation in the rectangular coordinate system under different boundary conditions, and finally obtains the mathematical expression of the unsteady temperature field of the three-dimensional envelope structure. In addition, this paper establishes a mathematical model of the unsteady heat transfer of the building envelope under the influence of the dynamic thermal disturbance of the building envelope. From the clustering results, it can be seen that the energy-saving coupling correlation of new energy buildings based on carbon emission effect proposed in this paper is strong. Therefore, in the follow-up building design and construction, we can start from the perspective of new energy to reduce carbon emissions and improve the sustainable development of the construction industry.

The establishment and numerical calculation of a heat transfer model of a graphene heating energy storage floor

A new type of graphene electric heating solid wood composite floor and its heat transfer model were designed to enable users to have a higher-quality and safe living experience. A heat transfer mathematical model was developed. The structural entity of the composite graphene heating floor was drawn using Solidworks software. The floor structure was abstracted as a two-dimensional model using MATLAB software to obtain the temperature rise curves and corresponding time of each group. Then, six groups of the best data were selected from the experimental data to simulate the heat storage capacity of graphene floors. The optimal group of the model was verified via experiments. According to the simulation, the comprehensive performance was optimal when the overall thickness of the floor was 18 mm, the thickness of the floor surface was 4 mm, and the thickness of the heat-accumulating layer was 2 mm. The experimental results showed a maximum difference between the measured and calculated data of only 3.2%, which shows the scientific validity, accuracy, and advancement of the model. The composite graphene electric heating energy storage floor designed in this study can be regarded as safe, reliable, environmentally friendly, and healthy.

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 Modelling of Heat Transfer in Pipes with Turbulators in the Laminar Region and in the Transition to Turbulent Flow

The article presents an analysis of mathematical modeling of heat transfer in pipes with turbulators at low Reynolds numbers characteristic of laminar and transient flow modes of heat carriers. The solution of the heat exchange problem for semicircular cross-section flow turbulators based on multi-block computing technologies based on the solution of Reynolds equations closed using the Menter shear stress transfer model and the energy equation (on multi-scale intersecting structured grids) by the factorized finite-volume method is considered. Both local and averaged characteristics of the flow and heat transfer to a pipe with a system of turbulators were obtained, which made it possible to determine the levels of heat exchange intensification for these regime ranges.

Theoretical study of a flow-through humidifier with a rotary water spray

Purpose. To formulate a mathematical description of the process of air humidification in a flow-through apparatus with a rotary water sprayer (as an automation object). Methods. The analytical method of research is applied, which is based on determining the dynamic characteristics of heat and mass transfer processes during the interaction of water droplets with an airflow. Results. A mathematical description of the dynamics of a flowing air humidifier with a rotary water sprayer is formulated as a mathematical model of the unsteady mode of heat and mass transfer of sprayed water with an air stream and a mathematical model of the movement of a droplet as a material particle in a vertical uneven air flow. The trajectories of the droplets in the air flow are determined and the air humidification graphs are obtained. The obtained solution to the system of equations allows us to determine the influence of design and operating parameters on the dynamic properties of the air humidifier. Conclusions 1. A dynamic mathematical model of heat and mass transfer in a flow-through apparatus of ideal mixing has been developed. 2. The analytical dependences of the change in air parameters in time on the operating and design parameters of the apparatus were obtained. 3. The kinetic parameters of the droplet motion are determined. Keywords: air flow, droplet, humidifier, rotary disk, heat transfer, moisture content.

A review on dryout and Post-dryout heat transfer inside tubes and tube bundles

• Detailed review on dryout mechanism and dryout and post-dryout heat transfer. • Summarizing the dryout criterions and models of dryout and post-dryout heat transfer. • Elaborating the methods of dryout and post-dryout heat transfer enhancement. • Proposing further research suggestions of dryout and post-dryout heat transfer. The working medium changes from subcooled liquid through flow boiling to superheated vapor in actual once-through thermal equipment (such as once-through steam generators, once-through boilers). Dryout heat transfer deterioration inevitably occur in this vapor-liquid two-phase flow and heat transfer process. After dryout occurs completely, vapor almost completely covers the wall, resulting in a rapid deteriorating heat transfer performance and a sharp rising wall temperature, which puts forward higher requirements on the design, manufacture, and operation of the equipment. The mechanism of dryout is elaborated, and the dryout criterion is summarized in this paper. The three methods that are used to describe the mathematical model of dryout and post-dryout heat transfer are arranged, and the dryout and post-dryout heat transfer in the straight channel is introduced. Furthermore, the methods of enhancing dryout and post-dryout heat transfer are introduced such as changing the geometric structure (including changing the shape of the flow channel and processing the surface of the flow channel) and injecting liquid droplets, etc.

Numerical study on the effect of thermal diffusivity ratio in phase change heat transfer of crude-oil using lattice Boltzmann method

When the long distance crude-oil pipe-line is stopped, the crude-oil will solidify gradually with the decrease of the temperature in the pipe-line. The solid-liquid thermal diffusivity can reflect the ability of heat diffusion in the phase change heat transfer process of crude-oil stop-transport. Based on the mathematical model of oil phase transition heat transfer established by enthalpy method, the lattice Boltzmann method is used to solve the governing equations of oil phase transition heat transfer. According to the simulation results, the phase change heat transfer process of crude-oil is divided into three-stages, and the mechanism of the phase change heat transfer process of crude-oil is studied. The results show that the influence of solid-liquid thermal diffusion ratio increase gradually with time. When Fourier number ?0.043, Nusselt number and convective heat transfer intensity of mobile phase interface slightly decrease with the increase of solid-liquid thermal diffusivity ratio. The research results of this paper can provide a reference for controlling the stoppage time of pipe-line.

Lunar regolith sintering process simulation. Analysis of computational and experimental identification method of the heat transfer mathematical model

Lunar regolith sintering process simulation. Analysis of computational and experimental identification method of the heat transfer mathematical model

Mathematical modeling and simulation analysis of different structured cored wire feeding spheroidization by finite volume method

<abstract><p>A three-dimensional dynamic heat transfer mathematical model of the process when cored wire feed in molten iron is established based on finite volume method (FVM). The calculation area is meshed with triangles and quadrilaterals to determine nodes and control volumes, and implicit time integration method is used to ensure the stability of calculating process. For exposing the dynamic heat transfer behavior, the variation of temperature field and explosion characteristics of cored wires are studied. In addition, the melt loss rate of the top end of cored wire and the correlation among melt explosion depth, molten iron temperature and feeding speed of cored wires are theoretically calculated. More importantly, the influence of different structures of cored wires on the absorption rate of magnesium are considered. The calculation results are in good agreement with the experimental data, which indicate that the existing theoretical model has good validity and can provide theoretical guidance for spheroidization process in molten iron.</p></abstract>