Mathematical Model Of Heat Transfer Research Articles

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>

Mathematical modeling of the heat transfer process in a dense blown layer of granular material

The object of research: a mathematical model of unsteady heat transfer between particles forming a dense layer in a heat exchange channel and an air flow passing through the layer.
 Investigated problem: obtaining a mathematical model adequate to the physical phenomenon will significantly expand the field of research, reduce the time for determining the thermal characteristics of heat transfer and data processing.
 The main scientific results: an explicit analytical dependence is obtained that allows calculating the local temperature of the layer in an arbitrary cross-section of the channel at selected moments of time. The presented analytical dependence was verified by analyzing the calculated data on the material temperatures in the channel obtained by varying the main physical quantities: the effect of the heating duration, heat transfer coefficient, porosity, and density on the temperature distribution was studied. The temperatures along the length of the channel were calculated at different points in time with the following initial data: material - gravel: c=860, ρ=1500, λ=0.6, ε=0.4; aud=800. Based on the results of the calculations for the time τ=60 s, τ=900 s, τ=1800 s, τ=2400 s, τ=1800 s, the graphs shown in the paper are constructed. It is shown that the mathematical model adequately describes the process of heating a layer of granular material in a heat exchange channel and allows obtaining satisfactory data on the temperature distribution along the length at different points in time. The calculated data correlate satisfactorily with the experimental results.
 Innovative technological product is an analytical dependence obtained for the first time, which is necessary for inclusion in the calculation method of regenerative heat exchangers intended for the utilization of low-potential heat flows.
 The area of practical use of the research results is the heat engineering calculations of regenerative heat exchangers with a dense granular packing. The consumers of the developed regenerators are greenhouses and food industry. Such industries are characterized by a low-potential level of thermal emissions, the heat of which is difficult to utilize using existing heat exchange equipment.
 Scope of the innovative product: design bureaus focused on the design of innovative heat exchangers for the utilization of low-potential heat flows, and research laboratories studying the processes of heat exchange between a dense layer of granular material and a through gas (air) flow.

Deterministic–Probabilistic Prediction of Forest Fires from Lightning Activity Taking into Account Aerosol Emissions

Forest fires arise from anthropogenic load and lightning activity. The formation of a thunderstorm front is due to the influence of a number of factors, including the emission of aerosol particles from forest fires. The purpose of this study is mathematical modeling of heat and mass transfer in vegetation firebrand carried out from a forest fire front, taking into account the formation of soot particles to predict forest fire danger from thunderstorm activity. Research objectives: (1) development of a deterministic mathematical model of heat and mass transfer in a pyrolyzed firebrand of vegetation, taking into account soot formation; (2) development of a probabilistic criterion for assessing forest fire danger from thunderstorms, taking into account aerosol emissions; (3) scenario modeling of heat and mass transfer and the formation of a thunderstorm front; (4) and the formulation of conclusions and proposals for the practical application of the developed deterministic–probabilistic approach to the prediction of forest fires from thunderstorms, taking into account aerosol emissions. The novelty of this study lies in the development of a new model of heat and mass transfer in a pyrolyzed vegetation firebrand and a new probabilistic criterion for forest fire danger due to thunderstorm activity, taking into account aerosol emission. The distributions of temperature and volume fractions of phases in a firebrand are obtained for various scenarios. Scenarios of surface fires, crown forest fires, and a fire storm are considered for typical types of coniferous vegetation. Cubic firebrands are considered in the approximation of a two-dimensional mathematical model. To describe the heat and mass transfer in the firebrand structure, a differential heat conduction equation is used with the corresponding initial and boundary conditions, taking into account the kinetic scheme of pyrolysis and soot formation. Variants of using the developed mathematical model and probabilistic criterion in the practice of protecting forests from fires are proposed. Key findings: (1) linear deterministic–probabilistic mathematical model to assess forest fire occurrence probability taking into account aerosol emission and lightning activity; (2) results of mathematical modeling of heat and mass transfer in firebrand taking into account soot formation; (3) and results of scenario modeling of forest fire occurrence probability for different conditions of lightning activity and aerosol emission.

Analysis of the structural integrity of a frozen wall during a mine shaft excavation using temperature monitoring data

This paper describes the results of the temperature monitoring of a frozen wall (FW) around the skip shaft of a potash mine under construction. The data on temperature measurements in control-thermal boreholes were used to parameterize the mathematical model of heat transfer, which allowed for the reconstruction of the temperature field throughout the entire cooled and frozen soil volume. The resulting temperature distribution in the FW zone for greater than 1 year was used to determine the distribution of the strength properties and calculate the temporary change in the limiting value of the external lateral load on an FW of a given thickness and specified thermomechanical properties. The obtained dependencies of the maximum external load on the FW can be used to optimize the operation mode of the freezing station at the ice holding stage (or passive freezing) to increase the energy efficiency of the system and ensure the structural integrity of the FW.

Mathematical model of heat transfer of a solar chamber carrying out solar thermal treatment of precast reinforced concrete

A mathematical model of heliocamera heat exchange has been developed, designed for heat treatment of precast concrete and reinforced concrete products, which allows to determine the preferred design solutions from the standpoint of effective heating and increase the strength of concrete in them. The mathematical model allows us to estimate the efficiency of the heliocamera in different climatic zones and at different times of the year, as well as to calculate the temperature regime of the heliocamera under the conditions of the varying intensity of solar radiation and the outdoor air temperature during the day.

Dynamic mathematical heat transfer model for two-phase flow in solar collectors

In the present study, a dynamic heat transfer model is developed for two-phase flow through the absorber tube of linear solar collectors, where the heat transfer fluid is water. The model considers that thermophysical properties, such as viscosity, thermal conductivity, densities, and specific heat, depend on temperature; this dependency is reflected in the value of the convective heat transfer coefficient. The governing partial differential equations for the fluid are solved using the finite difference method in an explicit scheme, the heat transfer equation for the absorber tube uses an implicit scheme, whose solution is implemented in C++ compiler. The model is validated with experimental data from a solar collector using a Solar Fresnel Reflector type, with an error related to the steam quality lower than 4.28% at the outlet of the collector and a better fit with the temperature profile through the collector in comparison with previous studies. The results show that as the phase change occurs, increasing the quality of steam in the absorber tube, the collector efficiency decreases. This is due to that the convective heat transfer coefficient of the absorber decreases, since the thermophysical properties of the liquid-steam mixture do not favor heat transfer.

Experimental Study on Heat Transfer Characteristics of Two-Phase Flow in Square and Rectangular Channels

Two-phase flow in non-circular cross-section flow channels such as micro-heat sinks and micro-channel heat exchangers has received extensive attention due to its heat-enhancing properties. In this paper, under the boundary of constant heat flux, an experimental investigation of the heat transfer properties of gas–liquid two-phase flow in horizontal channels with cross-sections of 4 × 4 mm and 8 × 3 mm is carried out using air and water as working fluids. The effects of different inlet gas and liquid inlet Reynolds numbers on the wall temperature and Nusselt number are discussed. The results show that the effects of the liquid Reynolds number and the gas phase Reynolds number on the heat transfer coefficient of the square tube and the rectangular tube are different. Under the same gas–liquid Reynolds number, the Nusselt number of the gas–liquid two-phase flow in the square-section tube can be increased by 3.2 times compared with that in the single-phase flow, while the Nusselt number of the gas–liquid two-phase flow in the rectangular tubes can be increased by 1.87 times. The results of this paper provide a reference for the design of microchannel heat exchangers and the establishment of mathematical models for Taylor flow heat transfer in rectangular and square tubes.

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

Structural and Heat Transfer Model Analysis of Wall-Mounted Solar Chimney Inlets and Outlets in Single-Story Buildings

Wall-mounted solar chimneys use solar radiation to heat the air inside the chimney cavity and use thermal pressure to create natural convection. Applying this principle allows for the indoor ventilation of a building without energy consumption. However, in wall-mounted solar chimney designs, different air inlet and outlet design dimensions can have varying degrees of impact on the effectiveness of wall-mounted solar chimney ventilation. In order to analyze the internal airflow state and airflow temperature field distribution of wall-mounted solar chimneys, physical models of wall-mounted solar chimneys with six different air outlet-to-inlet cross-sectional area ratios were developed in this research work. Before numerical simulation analysis, heat transfer analysis of the wall-mounted solar chimney’s structural components and airflow channels was carried out, and corresponding mathematical heat transfer models were established. The internal flow state and temperature distribution characteristics of a wall-mounted solar chimney were analyzed by steady-state simulations using the computational fluid dynamics software, Ansys Fluent. Finally, transient simulation calculation analysis was conducted under six different S-value models to investigate the variation in the natural ventilation of a single-story building’s wall-mounted solar chimney for a whole day. The study showed that under the same simulation conditions, 80% ≤ S < 100% effectively avoided the formation of vortices in the internal airflow of the wall-mounted solar chimneys and kept the ventilation effect of wall-mounted solar chimneys at a high level. The results of this study provide a reference for the optimization of research on the design of the air inlet and outlet structures of wall-mounted solar chimneys for single-story buildings.

Significance of non-Fourier heat conduction in the thermal analysis of a wet semi-spherical fin with internal heat generation

The transient temperature distribution of a wet semi-spherical porous fin with convection, internal heat generation, and radiation is researched using a non-Fourier heat conduction (NFHC) model. A mathematical model for transient heat transfer in a dehumidifying environment is developed from the non-Fourier law and the corresponding governing equation is formulated. This equation is subjected to nondimensionalization using suitable dimensionless terms and is further solved by employing the finite difference method (FDM). A substantial deviation in thermal response by considering non-Fourier law under unsteady heat transmission has been analyzed graphically with the influence of various nondimensional parameters on the dry and wetted fins surface. The examination reveals the notable difference in temperature variation between the dry and wetted fins surfaces. Some important key results of the research analysis include that the transient thermal distribution through the fin decrease as the magnitude of the convective, wet porous and radiation-conduction parameters develop. For higher generating numbers, thermal distribution will be higher. The temperature in the hyperbolic model increases after some time in the existence of relaxation time and the temperature in a non-Fourier model flow in the form of a thermal wave.

A study on dual solutions for water-based hybrid nanofluids flowing through convergent channel with dissipative heat transport

Over the years, the fluid flows in conjunction with thermal transport between non-parallel surfaces having converging nature is of great significance due to their broad spectrum of applications, which include fluid flows through nozzles in petroleum engineering, blood flow in arteries, lubrication systems, automobile radiators, thermal pumps, and water purification processes. Additionally, hybrid nanofluid is a prolific topic because of its thermal properties and potentials which provide a better performance even compared with common nanofluid in optimizing heat transfer. Therefore, this article presents a numerical simulation to investigate the heat transport characteristics of hybrid nanofluids in Jeffery-Hamel flow through a convergent channel. The considered hybrid nanofluids are composed of Copper (Cu) and Graphene-oxide (Go) as suspended nanoparticles and water as base fluid. This analysis further includes the impacts of viscous dissipation and magnetic field. A mathematical model for fluid flow and heat transfer are constructed with the help of cylindrical polar coordinates. The governing equations are converted into a system of ordinary differential equations (ODEs) by Lie symmetry group transformation. A MATLAB code is exercise to get the numerical solutions for flow and thermal distributions. An interesting phenomenon is that dual solutions are obtained in the computation. Thus, a comprehensive discussion is included on the dual solutions for various involved variables. The current findings may be employed in petroleum science, r biomedical scientists, polymer industry, etc.

Thermodynamic factor and vacuum crystallization

Sucrose crystallization depends on various thermal phenomena, which makes them an important scientific issue for the sugar industry. However, the rationale and theory of sucrose crystallization still remain understudied. Among the least described problems is the effect of time and temperature on the condensation rate of sucrose molecules on crystallization nuclei in a supersaturated sugar solution. This article introduces a physical and mathematical heat transfer model for this process, as well as its numerical analysis.
 The research featured a supersaturated sugar solution during sucrose crystallization and focused on the condensation of sucrose molecules on crystallization nuclei. The study involved the method of physical and mathematical modeling of molecular mass transfer, which was subjected to a numerical analysis.
 While crystallizing in a vacuum boiling pan, a metastable solution went through an exothermal reaction. In a supersaturated solution, this reaction triggered a transient crystallization of solid phase molecules and a thermal release from the crystallization nuclei into the liquid phase. This exogenous heat reached 39.24 kJ/kg and affected the mass transfer kinetics. As a result, the temperature rose sharply from 80 to 86 °C.
 The research revealed the effect of temperature and time on the condensation of solids dissolved during crystalline sugar production. The model involved the endogenous heat factor. The numerical experiment proved that the model reflected the actual process of sucrose crystallization. The obtained correlations can solve a number of problems that the modern sugar industry faces.

The modified finite element method for heat and mass transfer of unsteady reacting flow with mixed convection

This study reveals the extension of a mathematical model of heat and mass transfer of fluid flow over a sheet by incorporating the effect of non-linear mixed convection. The governing equations of flow phenomena are expressed as partial differential equations (PDEs). Similarity transformations are employed to get a dimensionless set of boundary value problems. Most of the existing relevant literature employed some solver to solve a set of differential equations, but this study implements the finite element method to tackle the boundary value problems. The employed finite element method is based on the Galerkin approach. For verifications of the obtained results, a set of linear and non-linear boundary value problems is also solved with Matlab solverbvp4c. The results are displayed in graphs by varying Grashof number, modified (solutal) Grashof number, non-linear convection parameters in heat and mass transfer, radiation parameter, Prandtl number, Schmidt number, and reaction rate parameter. Also, numerical values for the friction at the wall and local Nusselt and Sherwood numbers are given in tables. The problem in PDEs form is also solved with software that implements the finite element method to solve problems. The simulations are also provided, which is the outcome of the software. It is shown that the velocity profile escalates by growing values of thermal and solutal Grashof numbers. Problem-solving techniques from this study may be used in future research to address other unsolved heat transfer fluid physics issues.

Heat transfer analysis of compressible laminar flow in a parallel-plates channel via integral transforms

The present work analyzes a coupled nonlinear mathematical model for heat transfer in compressible laminar flow within a parallel plates channel. The governing partial differential equations are obtained considering the conservation of mass, momentum and energy, based on a two-dimensional steady laminar flow of an ideal gas with constant physical properties and taking into account viscous dissipation. Two kinds of boundary conditions at the wall were considered, namely, prescribed arbitrary temperature or heat flux longitudinal distributions. The mathematical model was solved using the hybrid numerical-analytical method known as the Generalized Integral Transform Technique (GITT). A convergence analysis of the proposed eigenfunction expansions for velocity and temperature fields was undertaken, indicating that fairly low truncation orders are required for the accurate representation of the potentials. The proposed hybrid solution was also critically compared with the Mathematica NDSolve finite difference-based routine and additional theoretical and experimental results in the literature, with good agreement in all cases considered.

Effects of heat transfer mechanism on methane-air mixture explosion in 20 L spherical device

This study developed a model of methane one-step combustion mechanism based on the CFD code GASFLOW-MPI to understand the influence mechanism and degree of influence of heat transfer mechanism on methane explosion. Moreover, this study proposed the addition of heat transfer mathematical models using GASFLOW-MPI, including thermal radiation and convection heat transfer. Further, the effects of thermal radiation and convective heat transfer on the shock wave during a methane explosion in a 20 L spherical explosion tank were studied through numerical simulation and the results were compared with the experimental data. The numerical simulation results were found to reasonably predict the peak pressure value and pressure decay process of a methane explosion. In addition, through comparisons of the effects of adiabatic and numerical simulations considering heat loss, the peak pressure of gas explosion calculated via adiabatic simulation were found to be overestimated. Moreover, during the methane-air mixed explosion experiment in the 20 L spherical device, the heat loss was observed to be primarily caused by heat radiation, accounting for more than 76.01% of the total heat loss, followed by convection heat transfer, accounting for 23.99% of the total heat loss. The research results showed that heat loss significantly influenced the methane explosion process. Additionally, for the methane-air mixture explosion experiment in a 20 L spherical device, thermal radiation was the most critical factor that resulted in heat loss in the methane explosion process. Therefore, the influence of thermal radiation and convective heat transfer mechanism on methane explosion must be considered in the numerical simulation of a methane explosion.

Numerical investigation of heat transfer characteristics of moderator assembly employed in a low-enriched uranium nuclear thermal propulsion reactor

The design of a nuclear thermal propulsion (NTP) reactor based on low-enriched uranium (LEU) requires additional moderator elements in the core to physically meet the critical requirements. This design softens the core energy spectrum and can provide more thermal neutrons for the fission reaction, but the heat transfer characteristics between the fuel and moderator assembly are more complex. Aiming at the typical LEU unit design, the heat transfer mathematical model is established using the principle of heat flow diversion and superposition. The model adopts the heat transfer relationship based on STAR-CCM+ simulation rather than the empirical expression used in the past literature to improve the applicability of the model. The heat transfer coefficients in the proposed model are evaluated under different Reynolds numbers and thermal power. The deviations between the proposed model and CFD simulation are analyzed. The results show that the calculation of the heat transfer coefficient between the proposed model and the CFD simulation maintains a good consistency, most of which are within 10%. It may provide a reliable and conservative temperature estimation model for future LEU core design.

Study of entropy generation and heat flow through a microtube induced by the membrane-based thermofluidics systems

A mathematical model to study the thermally fully developed pressure-driven flow of Newtonian fluid in a finite length vertical microtube with a spatial–temporal dependent membrane contraction, is presented. Here, pressure is generated by the membrane propagation and is further regulated by buoyancy forces. Besides, the energy equation refers to the movement of thermal energy between two walls of the microtube. This model examines the kinematics of membrane, flow and pumping characteristics, wall shear stress, Grashof number (Buoyancy force) effects, Nusselt number, isotherms, and entropy generation in the membrane based thermofluidics system. The dimensional analysis followed by the lubrication approach (since radius of the microtube is substantially less than its length) has been utilized to derive the analytical solutions which are further simulated by using the Matlab code for the graphical illustrations. The velocity fields under the effects of thermal properties and membrane kinematics are computed and noted that magnitude to axial velocity increases by 44.8% via the Grashof number in the range 0 to 4. Further, it is observed that the convective heat flow ( N u > 1 ) is performing in the range [ − 0 . 2 , 0 . 2 ] due to the rhythmic membrane kinematics. Another side, the membrane shape parameter is a major concern for the entropy generation. Such types of analysis and membrane based thermofluidics could be applicable to control the heat transfer rate and energy in various thermal treatments of biomedical sciences and engineering, and also help to design the thermo-pneumatic micropump. • A mathematical model for heat transfer in membrane based microtube is presented. • The membrane pumping mechanism is highly motivated by insect’s respiratory system. • The direct heat source increases the temperature elevation up to 49% in microtube. • Entropy can be controlled by relative temperature and membrane shape in the system. • The findings of the present model are useful in various thermal treatments.

SPECIFIC CHARACTERISTICS OF THE APPLICATION OF MATHEMATICAL MODELING IN SOIL SCIENCE

The article talks about the use of mathematical modeling in the field of soil science. Empirical, semi-empirical, theoretical models are used in soil science, as well as their specific features. An overview, advantages and disadvantages of empirical, semi-empirical and theoretical models are analyzed. Necessary formulas and algorithms for mathematical modeling of heat transfer in the soil are compiled and their features are described.