Mathematical Simulation Of Heat Transfer Research Articles

Mathematical Simulation of Heat Transfer through the Multilayer Filler Structures of Buildings

Mathematical Simulation of Heat Transfer through the Multilayer Filler Structures of Buildings

Математическое моделирование динамики тепловых ударных волн в нелинейных локально-неравновесных средах

We performed a mathematical simulation of heat transfer in a local non-equilibrium medium whose transfer characteristics are functions of the temperature distribution. A homogeneous polynomial of arbitrary degree represents nonlinearities in thermal conductivity and thermal diffusivity. The mathematical model consists of a hyperbolic nonlinear heat transfer wave equation, initial conditions and nonlinear boundary conditions of the second and first kind. To solve this problem, we used a conservative homogeneous finite-difference scheme along the upper time grid line (implicitly). We then used the tridiagonal matrix algorithm of the second order in the spatial variable and of the first order in time to solve the resulting system of linearised algebraic equations. A periodic series of rectangular temperature or heat flux pulses form the boundary conditions of the first and second kind. Computation results reveal ultimate propagation rates of temperature and heat fronts featuring pronounced first-kind discontinuities with attenuating magnitudes. As the process unfolds, the initial pulses heat the region between the boundary and the heat wave front, while the subsequent pulses traverse this region at a higher velocity due to thermal diffusivity being a function of temperature, their fronts "catching up" with the previous fronts, increasing the discontinuity magnitude at the initial pulse front, that is, forming a thermal shock wave front similar to that of a shock wave in gas dynamics. We obtained such thermal shock waves for boundary conditions of both the first and the second kind. We also analysed kinematic and dynamic characteristics of thermal waves

Mathematical simulation of inert heating and pyrolysis of forest fuel under the influence of a forest fire front, if the process of sooting is taken into account

Introduction. Large amounts of pollutants, including carbonaceous particles of soot, are released into the atmosphere during a forest fire. High concentrations of these particles in the air can lead to the development of cardiorespiratory diseases or death. It has been noticed that a certain number of soot particles is produced at the stage of forest fuel pyrolysis. In this regard, it is advisable to study the processes of pyrolysis and sooting to develop effective methods of their prediction and prevention.Goal of the study. The goal of this study is the mathematical simulation of heat transfer in an element of standard forest fuel (a birch leaf), taking into account the thermal decomposition of dry organic matter and sooting.Materials and methods. Within the framework of the work, scenario modeling of heat and mass transfer processes in an element of forest fuel (a birch leaf), subjected to the influence of a high-temperature environment, was conducted. A one-dimensional heat transfer equation and a kinetic equation, having respective initial and boundary conditions, were solved by means of numerical simulation. The finite difference method was employed to solve the resulting system of differential equations. The calculations were conducted using the RAD Studio software package. Graphical results were processed using the OriginPro software package.Results. Scenario modeling took into account the type of forest fire, the period of the fire hazard season, forest fuel properties, the degree of the forest fuel dispersion, and the initial moisture content in a forest fuel element. The authors have found that the major influence is made by the extent of dispersion and the type of forest fire. The similarity of qualitative characteristics of sooting has also been established for all types of forest fires.Conclusion. The proposed mathematical model can be used in conjunction with geoinformation systems to visualize the initial and output information in the process of assessment, monitoring and forecasting of forest fires and their environmental consequences.

Mathematical Simulation of Heat Transfer in Thermally Magnetised Oldroyd-B Fluid in Sakiadis Rheology with a Heat Reservoir

Sakiadis rheology of a generalised polymeric material, as well as a heat source or sink and a magnetic field, are all part of this study. Thermal radiations have been introduced into the convective heating process. The translation of a physical situation into a set of nonlinear equations was achieved through mathematical modelling. To convert the resulting partial differential equation into a set of nonlinear ordinary differential equations, appropriate transformations have been used. The velocity and temperature profiles are generated both analytically by HAM and numerically by the Runge–Kutta method (RK-4). In order to analyse the behaviour of the physical quantities involved, numerical and graphical depictions have been offered. To show that the acquired findings are correct, a nonlinear system error analysis has been offered. The heat flux study has been shown using bar charts. For the essential factors involved, the local Nusselt number and local Skin friction are calculated in tabular form. The fluid particles’ molecular mobility was slowed due to the magnetic field and porosity, and the heat transfer rates were demonstrated to be lowered when magnetic and porosity effects are present. This magnetic field and porosity effects regulating property has applications in MHD ion propulsion and power production, the electromagnetic casting of metals, etc. Furthermore, internal heat absorption and generation have diametrically opposed impacts on fluid temperature. The novelty of the present study is that no one has investigated the Sakiadis flow of thermal convection magnetised Oldroyd-B fluid in terms of a heat reservoir across a porous sheet. In limited circumstances, a satisfactory match is revealed when the collected values are compared to the existing work published corroborating the current attempt. The findings of this study are expected to be applicable to a wide range of technical and industrial processes, including steel extrusion, wire protective layers, fiber rolling, fabrication, polythene stuff such as broadsheet, fiber, and stainless steel sheets, and even the process of depositing a thin layer where the sheet is squeezed.

Mathematical Simulation of Heat Transfer and Chemical Reaction in a Swirling Flow of Equilibrium-Dissociating Gas

Mathematical Simulation of Heat Transfer and Chemical Reaction in a Swirling Flow of Equilibrium-Dissociating Gas

Mathematical simulation of heat transfer in nonaccessible channels of heat supply system network

High values of standard heat losses in the heating networks of central heat supply systems indicate an opportunity to increase their energy efficiency. Сurrently available mathematical models of heat networks are described in the scientific studies of Polovnikov V.Yu., Kuznetsov G.V., Tarasevich E.I. But they do not solve the problem of assessing changes of the thermal networks state when energy-saving measures are used. The purpose of the study is to determine the permissible heat perception of the device collector for utilization of heat losses in the heating main channel. The study is based on the development and research of mathematical models of heat exchange processes in the heat supply network. A mathematical modeling method is chosen to search for acceptable operating modes of this device. The method can help to determine properly changes in the operation of the heat network. A descriptive mathematical model with distributed parameters based on differential equations with partial derivatives is used in modeling heat transfer processes in the heat network. The model is implemented using the finite element method. The authors propose a device for the utilization of heat losses in the heating channel. The authors have developed mathematical models of heat transfer processes in heat networks of underground trench laying in nonaccessible channels in a traditional design with the use of a heat-reflecting screen and combined action of the network and the device for the utilization of heat losses in the heat channel. Based on the comparison of the calculation results, the permissible heat perception value of the device collector for the utilization of heat losses has been determined. It equals to 90 % of the initial thermal losses. Mathematical models have been verified by comparing the results obtained and the experimental data with an error of less than 6 %. The developed mathematical models allow us to study the influence of heat perception of the device collector and the heat-reflecting screen on the operating mode of the heat network. It can be used to determine the geometric parameters of the collector of the device.

Mathematical Simulation of Heat Transfer in the Structures of a Passenger Carriage Under the Influence of Forest Fires

Forest fires have a negative impact on the functioning of the railway. The aim of the work is a mathematical modeling of heat transfer in the structures of a passenger carriage under the influence of radiation from a forest fire front. The originality of the study is explained by modeling heat transfer in structural materials of a passenger carriage under the influence of radiation from a forest fire front. Low and high intensity surface forest fires, crown forest fires are considered. Most of the previously published works are devoted to the analysis of the causes of forest fires, including the ones near the railway. The software implementation of the mathematical model is performed in the RAD Studio software in the high-level programming language Delphi. Mathematically, heat transfer in the materials of a passenger carriage is described by non-stationary differential heat conduction equations with corresponding initial and boundary conditions. In order to solve the partial differential equations, the finite-difference method and the locally one-dimensional method are used. Difference analogs of differential equations are solved by the marching method. The main findings of the study are: 1) physical and mathematical models of heat transfer in the structures of a passenger carriage under conditions of exposure to radiation from a forest fire; 2) the obtained temperature distributions in the inhomogeneous structure of the passenger carriage wall; 3) simulation has shown that a low-intensity surface forest fire causes a relatively safe forest fire impact scenario, while a high-intensity surface forest fire impact is a potentially dangerous scenario; 4) the scenario of the impact of a crown forest fire is unambiguously dangerous at any parameters; 5) the results obtained in this paper and the expected in future investigations will create a physical basis for the development of software for fire safety systems for rolling stock on the railway. The presented results are proposed to be used for forecasting, monitoring, and assessing forest fire dangers during the operation of the rolling stock of JSC Russian Railways.

Mathematical Simulation of Heat Transfer and Chemical Reactions in an Equilibrium Dissociating Gas

Mathematical Simulation of Heat Transfer and Chemical Reactions in an Equilibrium Dissociating Gas

Mathematical simulation of heat transfer for atmospheric air cooling of heat exchange tube

The laboratory facility with horizontal, atmospheric air cooled heat exchange tube has been engineered, manufactured and put to trial. The test has proven the reliability of the employed analysis methods and hardware. Mathematical simulation of horizontal tube heat transfer process has been fulfilled with the use of ideal displacement and mixing, cellular and longitudinal diffusion models. The in-tube hot water temperature pattern has been evaluated according to the aforementioned models. The results comparison has been fulfilled for experimental determination of in-tube water temperature differential and calculation data in accordance with given models. The longitudinal diffusion model has proven itself as the most suitable for describing the heat transfer process in a horizontal, atmospheric air cooled tube. The longitudinal diffusion coefficient value has been deducted from experiments. The research data can be utilized during the development of tubular heat exchangers.

Mathematical simulation of forest fire front influence on wood-based building using one-dimensional model of heat transfer

The purpose of the present paper is to mathematical simulation of heat transfer in enclosures of wood-based building when exposed to thermal radiation from forest fire front. One-dimensional mathematical model is used. Mathematically, heat transfer in building enclosures is described by system of non-stationary equations of heat conduction with corresponding initial and boundary conditions. It is suggested to use several scenarios of forest fire impact. Temperature distribution on wall depth is obtained for different scenarios of forest fire impact on building enclosures.

Mathematical simulation of heat transfer in an elliptic channel depending on the tangential momentum accommodation coefficient

This paper considers a flow of rarefied gas with a specular-diffuse reflection of gas molecules from a model of a elliptical cross section of channel walls in the transition regime. We assume that the channel maintains a constant pressure gradient. Heat flow is obtained as a function of the tangential momentum accommodation coefficient and the ratio between the semiaxes of the ellipse in the whole range of the Knudsen number. Similar results presented in the literature are compared.

Математическое моделирование теплообмена при течении жидкости для ТВЭЛа с полизональным оребрением оболочки

Математическое моделирование теплообмена при течении жидкости для ТВЭЛа с полизональным оребрением оболочки

Mathematical simulation of heat transfer in spacecraft

We implemented a systemic scientific approach to thermal vacuum development of spacecraft, which integrates the problems of thermal calculations, thermal vacuum tests and accuracy evaluation for mathematical models of heat transfer by means of solving identification problems. As a result, the following factors increase the efficiency of spacecraft ground testing: reducing the duration of thermal vacuum tests, making autonomous thermal vacuum testing of components possible, increasing the accuracy of thermal calculations

Identification of radiative heat transfer parameters in multilayer thermal insulation of spacecraft

PurposeThe purpose of this study is to optimize multilayer vacuum thermal insulation (MLI) of modern high-weight spacecrafts. An adequate mathematical simulation of heat transfer in the MLI is impossible if there is no available information on the main insulation properties.Design/methodology/approachThe results of experiments in thermo-vacuum facilities are used to re-estimate some radiative properties of metallic foil/metalized polymer foil and spacer on the basis of the inverse problem solution. The experiments were carried out for the sample of real MLI used for the BP-Colombo satellite (ESA). The recently developed theoretical model based on neglecting possible near-field effects in radiative heat transfer between closely spaced aluminum foils was used in theoretical predictions of heat transfer through the MLI.FindingsA comparison of the computational results and the experimental data confirms that there are no significant near-field effects between the neighboring MLI layers. It means that there is no considerable contradiction between the far-field model of radiative transfer in MLI and the experimental estimates.Originality/valueAn identification procedure for mathematical model of the multilayer thermal insulation showed that a modified theoretical model developed recently can be used to estimate thermal properties of the insulation at conditions of space vacuum.

Mathematical simulation of heat transfer in an elliptic channel under the action of a pressure gradient

A method for calculating the heat flux through the cross section of an elliptic channel in the presence of a pressure gradient that is normal to the symmetry axis of the channel has been suggested. As a basic equation that describes the process kinetics, the Williams equation is taken, and the model of diffuse reflection sets boundary conditions at the channel wall. The deviation of the state of the gas from equilibrium is assumed to be small. The dependence of the heat flux through the cross section of the channel on the Knudsen number has been derived. The heat fluxes in the limiting cases of free-molecular and hydrodynamic regimes have been compared.

Mathematical simulation of heat transfer in surface soil layer at forest fire influence in three-dimension statement

Mathematical simulation of non-stationary conductive heat transfer in volume with the local centre of ignition is spent. Fields of temperatures during the different periods of time on soil section are obtained. The problem is considered in three-dimensional statement. It is used finite difference method to decision of a problem. Results of the comparative analysis of the decision of two-dimensional and three-dimensional models are presented.

Mathematical simulation of heat transfer at deciduous tree ignition by cloud-to-ground lightning discharge

Numerical research results of deciduous tree ignition by cloud-to-ground lightning discharge are presented. The problem is solved in one-dimensional statement in cylindrical system of coordinates. The typical range of influence parameters of positive and negative cloud-to-ground lightning discharges is considered. Ignition conditions for deciduous tree are established.

Mathematical simulation of heat transfer in unidirectional fiber composite

Mathematical simulation of heat transfer in unidirectional fiber composite

Evaluation Different Boundary Condition in Depth of Tissue for the Task of Mathematical Simulation of Heat Transfer in Human Skin

The problem of an estimation of thermal defeats at influence of affected factors of fire has great value for various areas of technics, industry and medicine. Results of mathematical simulation of heat transfer in layered structure of human skin influenced by the radiant thermal flux of the set value are presented in the work. The three-layer system of skin is considered. Research according to the various boundary conditions exposed in human tissue is carried out. Temperature distribution on thickness of skin is presented.

Mathematical simulation of heat transfer at coniferous tree ignition by cloud-to-ground lightning discharge

Numerical simulation results of coniferous tree heating by cloud-to-ground lightning discharge are presented. Pine tree is under consideration. The problem is solved in one-dimensional statement in cylindrical system of coordinates. Parametric investigation of volt-ampere characteristics influence on stem heating process was lead for negative and positive ground lightning discharges. Conditions of coniferous tree ignition in a typical range of influence parameters change are established.