scholarly journals The Non-Stationary Thermal Mode for Barrier Building Constructions in Non-Symmetric Boundary Conditions

2018 ◽  
Vol 7 (3.2) ◽  
pp. 535
Author(s):  
Olena Borshch ◽  
Volodymyr Borshch ◽  
Dmytro Guzyk
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mathematical Model ◽  
Boundary Conditions ◽  
Thermal Diffusion ◽  
Thermal State ◽  
Thermal Mode ◽  
Temperature Mode ◽  
Deep Layers

In barrier building constructions the heat transfer occurs both at the expense of thermal conductivity and as a result of liquid and air vapors resistance. The mechanism of such resistance differs from classical processes of diffusion and the laws of hydrodynamics for integral medium.The temperature mode of the surface and deep layers of barrier building constructions in non-symmetric boundary conditions was     analyzed. A mathematical model was developed that characterizes the change in the thermal state of barrier constructions during thermal diffusion. The method for calculating the non-stationary thermal modes of flat walls was presented.  

Mathematical Simulation of the Gas Turbine Packages Thermal State

2018 ◽  
Author(s):  
Olena Kyrylash ◽  
Volodymyr Kostiuk ◽  
Andrii Smirnov ◽  
Dmytro Tkachenko ◽  
Igor Loboda
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Mathematical Simulation ◽  
Gas Turbine ◽  
Thermal State ◽  
Thermal Mode ◽  
Temperature State ◽  
Complex Heat Transfer ◽  
Heat Transfer Simulation ◽  
Full Scale Tests

The paper is devoted to the use of mathematical simulation to investigate the possibilities of ensuring the admissible thermal mode of gas turbine packages equipped with aircraft and marine derivative gas turbine engines. The method proposed for complex heat transfer simulation in the gas turbine packages includes some models. A generalized mathematical model is formed to describe the thermophysical processes taking place in the gas turbine packages. A particular mathematical model of gas turbine engine casing heat transfer and a method to correct the boundary conditions are also developed. These models have been validated with the data collected from the heat transfer measurements in simple objects and from full-scale tests of turbo-compressor units. The proposed method of complex heat transfer simulation has been used to evaluate a temperature state of the gas turbine packages, in particular to ensure the effectiveness of covering the engine casing by thermal insulation.

Evaluation of boundary conditions for a mathematical model of heat transfer in a glass furnace

1996 ◽  
Vol 53 (3) ◽  
pp. 69-71 ◽  
Author(s):  
V. G. Lisienko ◽  
V. B. Kut'in ◽  
S. N. Gushchin ◽  
B. A. Fetisov
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Boundary Conditions ◽  
Glass Furnace

scholarly journals CONCEPTION QUASIDERIVATIVES IN THE PROBLEMS OF MATHEMATICAL MODELING OF HEAT TRANSFER

2020 ◽  
Vol 21 ◽  
pp. 79-85
Author(s):  
R. Tatsii ◽  
M. Stasiyk ◽  
O. Pazen ◽  
L. Shypot
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Closed Form ◽  
Critical Radius ◽  
Internal Heat ◽  
Heat Sources ◽  
Internal Heat Sources

In this paper, in closed form, the problems of determining stationary temperature fields in multilayer (flat, cylindrical and spherical) structures in the presence of discrete-continuous internal and point heat sources are solved. The one-dimensional differential equation of thermal conductivity in different coordinate systems is given through one parametric family of quasi-differential equations. It is assumed that the coefficients of the differential equation of thermal conductivity are piecewise constant functions. A system of two linearly independent boundary conditions is added to the equation, which in the general case are nonlocal. The solutions of such problems are constructive and are expressed exclusively through their initial data. The basic provisions of the concept of quasi-derivatives, the provisions of the theory of heat transfer, the theory of generalized systems of linear differential equations, elements of the theory of generalized functions are used. For the mathematical model of stationary thermal conductivity, the practical use of the concept of quasi-derivatives is illustrated, for the efficient construction, in a closed form, of solutions of boundary value problems with the most general boundary conditions. As an example, the problem of finding the critical radii of thermal insulation of multilayer hollow cylinders and spheres, taking into account the internal heat sources in the layers. Boundary conditions of the first and third kind. It is established that the value of the critical radius does not depend on the number of layers and the intensity of internal heat sources, but only on the thermal conductivity of the outer layer of the structure and the heat transfer coefficient between the structure and the environment. The formula for determining the critical radius of thermal insulation for a multilayer cylindrical and spherical structure is derived. The methods developed in this work have the prospect of further development and can be used in engineering calculations.

scholarly journals Mathematical model of heat transfer in roll caliber

2019 ◽  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Rolling Mill ◽  
Thermal Process ◽  
Stationary Heat

A physical model of the thermal process in the roll caliber during the rolling of the tape on a two-roll rolling mill was constructed. A mathematical model of the temperature field of a rolling hollow roll of a rolling state of a cylindrical shape rotating about its axis with constant angular velocity is proposed. The mathematical model takes into account different conditions of heat exchange of the inner and outer surfaces of the roll with the belt and its surrounding environment. The temperature field of a hollow roll of a rolling mill is considered as an initial boundary-value problem for a homogeneous non-stationary heat equation with inhomogeneous, nonlinear boundary conditions, which also depend on the angle of rotation of the roll around its axis. The equation describes the temperature field of the rolls during uncontrolled heat transfer during rolling. It significantly depends on the time and number of revolutions around its axis. With a large number of revolutions of the roll around its axis, a quasi-stationary temperature distribution occurs. Therefore, the simplified problem of determining a quasistationary temperature field, which is associated with a thermal process that is time-independent, is considered further in the work. In this case, the temperature field is described using the boundary value problem in a ring for a homogeneous stationary heat equation with inhomogeneous boundary conditions and heat transfer conditions outside the ring, which lie from the angular coordinate. After the averaging operation, the solution of this problem is reduced to solving the equivalent integral equation of Hammerstein type with a kernel in the form of the Green's function. The Mathcad computer mathematical system builds the temperature distribution of the roll surface. An algorithm for solving a inhomogeneous problem was developed and the temperature distribution of the roll was constructed.

scholarly journals Modeling of the shape of the deflector of the shell blade of marine gas turbine engines with varying parameters of thermal protection

2021 ◽  
pp. 111-116
Author(s):  
И.К. Андрианов ◽  
М.С. Гринкруг
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Gas Turbines ◽  
Thermal Protection ◽  
Thermal State ◽  
Turbine Blades ◽  
Internal Cooling ◽  
Cooling Channels ◽  
Transfer Equations ◽  
Uniform Temperature Field

Работа посвящена исследованию проблемы управления тепловым состоянием оболочечных лопаток судовых турбин, находящихся в условиях высокотемпературного нагружения. В работе рассматривались вопросы сочетания внешней тепловой защиты с помощью теплоизоляционного покрытия и внутреннего охлаждения. Математическая модель теплопереноса строилась на основании дифференциальных уравнений теплопроводности Фурье, условия теплоотдачи в каналах охлаждения. Проведена оценка влияния состава покрытия не изменение формы оболочки дефлектора с целью интенсификации охлаждения при неизменных параметрах скорости и температуры хладагента на входе в канал. Решение системы нелинейных уравнений теплопереноса проведено с помощью метода конечных разностей. Проведен численный эксперимент при реализации равномерного температурного поля на поверхности тела лопатки. Предложенная математическая модель позволяет рассчитать геометрию дефлекторов охлаждаемых лопаток судовых газовых турбин. Применение модели и результатов расчетов позволит рационализировать процесс охлаждения лопаток турбин, выбирая оптимальные сочетания внешней тепловой защиты и расхода хладагента. The work is devoted to the study of the problem of controlling the thermal state of the shell blades of marine turbines under high-temperature loading conditions. The paper deals with the combination of external thermal protection with the help of thermal insulation coating and internal cooling. The mathematical model of heat transfer was built on the basis of the Fourier differential equations of thermal conductivity, the conditions of heat transfer in cooling channels. The influence of the coating composition on the change in the shape of the deflector shell was evaluated in order to intensify cooling at constant parameters of the speed and temperature of the refrigerant at the inlet to the channel. The solution of the system of nonlinear heat transfer equations is carried out using the finite difference method. A numerical experiment is performed for the realization of a uniform temperature field on the surface of the blade body. The proposed mathematical model allows us to calculate the geometry of the deflectors of the cooled blades of marine gas turbines. The application of the model and the results of the calculations will allow to rationalize the cooling process of the turbine blades, choosing the optimal combination of external thermal protection and refrigerant consumption.

scholarly journals Characteristics of supercritical heat transfer during filmboiling of nanofluids on a vertical heated wall

2018 ◽  
pp. 29-35
Author(s):  
А. Avramenko ◽  
M. Kovetskaya ◽  
A. Tyrinov ◽  
Yu. Kovetska
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Heat Flux ◽  
High Temperature ◽  
Heat And Mass Transfer ◽  
Heated Surface ◽  
Heated Wall ◽  
Film Boiling

Nanofluid using for intensification of heat transfer during boiling are analyzed. The using boiling nanofluids for cooling high-temperature surfaces allows significantly intensify heat transfer process by increasing the heat transfer coefficient of a nanofluid in comparison with a pure liquid. The properties of nanoparticles, their concentration in the liquid, the underheating of the liquid to the saturation temperature have significant effect on the rate of heat transfer during boiling of the nanofluid. Increasing critical heat flux during boiling of nanofluids is associated with the formation of deposition layer of nanoparticles on heated surface, which contributes changing in the microcharacteristics of heat exchange surface. An increase in the critical heat flux during boiling of nanofluids is associated with the formation of a layer of deposition of nanoparticles on the surface, which contributes to a change in the microcharacteristics of the heat transfer of the surface. Mathematical model and results of calculation of film boiling characteristics of nanofluid on vertical heated wall are presented. It is shown that the greatest influence on the processes of heat and mass transfer during film boiling of the nanofluid is exerted by wall overheating, the ratio of temperature and Brownian diffusion and the concentration of nanoparticles in the liquid. The mathematical model does not take into account the effect changing structure of the heated surface on heat transfer processes but it allows to evaluate the effect of various thermophysical parameters on intensity of deposition of nanoparticles on heated wall. The obtained results allow to evaluate the effect of nanofluid physical properties on heat and mass transfer at cooling of high-temperature surfaces. The using nanofluids as cooling liquids for heat transfer equipment in the regime of supercritical heat transfer promotes an increase in heat transfer and accelerates the cooling process of high-temperature surfaces. Because of low thermal conductivity of vapor in comparison with the thermal conductivity of the liquid, an increase in the concentration of nanoparticles in the vapor contributes to greater growth in heat transfer in the case of supercritical heat transfer.

scholarly journals Grain crops extrusion process mathematical model at a non-isothermal flow of their melt up to the temperature of the Maillard reaction start

2021 ◽  
Vol 83 (1) ◽  
pp. 23-29
Author(s):  
V. A. Afanasiev ◽  
L. N. Frolova ◽  
K. A. Sizikov ◽  
A. N. Ostrikov ◽  
S. N. Zobova
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mathematical Model ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Maillard Reaction ◽  
Flow Direction ◽  
Viscous Medium ◽  
Isothermal Flow ◽  
Grain Crops

The equations of motion, the equation of continuity, the equation of energy (heat balance), the rheological equation were chosen to describe the non-isothermal flow of the cereals melt in the extruder as the initial equations. The following assumptions were made to solve the model: the flow of a moving viscous medium is assumed to be laminar and steady; the forces of inertia and gravity are so small compared to the forces of friction and pressure that they can be neglected; a viscous medium (melt) is an incompressible liquid characterized by constant thermal conductivity and thermal diffusivity; the change in thermal conductivity in the longitudinal direction was neglected due to the fact that convective heat transfer in the flow direction is higher than the heat transfer by thermal conductivity; heat transfer in the direction perpendicular to the flow of the melt occurs only due to thermal conductivity. The numerical finite difference method was used to solve a system of equations taking into account convective heat transfer. Its essence of use lies in the fact that the considered area (extruder channel) is divided into calculated cells using a grid. The grid consisted of rectangular cells with a constant step between nodes, which exactly lie on the boundaries of the integration region. In this case, the differential equations were transformed into difference equations by replacing the derivatives at a point with finite differences along the cell boundaries. The mathematical model of non-isothermal melt flow in the extruder channel was obtained as a result of the solution. To solve a mathematical model of the process of grain crops extrusion with a non-isothermal flow of their melts, a program in the algorithmic language C ++ was compiled. A non-isothermal mathematical model of the process of extrusion of grain crops at temperatures of the beginning of the Maillard reaction, i.e., up to 120–125 ?, was obtained. It allows us to identify the nature of the temperature change along the length of the extruder. Comparative analysis of the results of the numerical solution and experimental data showed good convergence: the standard deviation did not exceed 12.7%.

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