scholarly journals Simulation of thermal processes on the electrode of a miniature protective spark gap

2021 ◽  
Vol 12 (32) ◽  
pp. 127-138
Author(s):  
Igor A. Murog ◽  
Valery F. Gnido ◽  
Elena V. Tinina ◽  
Igor A. Ilchuk ◽  
Tatiana A. Asayeva
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Temperature Field ◽  
Cathode Spot ◽  
Balance Of Power ◽  
Nonlinear Heat Equation ◽  
Thermal Processes ◽  
Melting Points ◽  
Spark Gap ◽  
The Finite Difference Method

The article discusses the issues that arise when determining the temperature in the region of the cathode spot in miniature protective spark gaps. The modeling principle is used to study the temperature field on the spark gap electrode. A mathematical model of the process is compiled on the basis of the balance of power entering the cathode spot and its removal inside the cathode due to thermal conductivity. A numerical solution of the obtained nonlinear heat equation with inhomogeneous boundary conditions by the finite-difference method is presented. The authors compared the found temperatures in the cathode spot for metals of the fourth and fifth groups of the Mendeleev's Periodic Table with the corresponding melting points of the selected metals. A complete correlation was obtained between these temperatures. Simulation of thermal processes in the region of the cathode spot on the electrode made of 42NA-VI alloy has been carried out. The results are presented in the form of diagrams.

scholarly journals Mathematical model for calculating the temperature field of a direct-flow drying drum

2021 ◽  
Vol 2131 (5) ◽  
pp. 052067
Author(s):  
A Mamatov ◽  
A Parpiev ◽  
M Shorakhmedova
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Parabolic Type ◽  
Drying Process ◽  
Air Velocity ◽  
Direct Flow ◽  
Proposed Model ◽  
Cotton Seeds ◽  
The Finite Difference Method ◽  
Type Boundary

Abstract In this paper, one parabolic-type boundary value problem is solved for determining the temperature field of the raw cotton and air components in drum dryers. In the proposed model, convective heat transfer is used according to Newton’s law, the terms describing the evaporation of moisture from the components of raw cotton (seeds, fiber) and the influence of air velocity are taken into account. The resulting system of Galerkin’s differential equations is solved by the finite-difference method in time. It is shown that the approximate solution is estimated according to Galerkin in Sobolev space.The numerical results of the considered problem are obtained by the Bubnov–Galerkin method. A comparative analysis is carried out with experimental data. It is shown that the proposed mathematical model and its numerical algorithm adequately describe the drying process of raw cotton.

scholarly journals Numerical Model Of Binary Alloys Solidification Basing On The One Domain Approach And The Simple Macrosegregation Models

2015 ◽  
Vol 60 (3) ◽  
pp. 2431-2435 ◽  
Author(s):  
E. Majchrzak ◽  
B. Mochnacki ◽  
J. Mendakiewicz
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Finite Difference Method ◽  
Numerical Solutions ◽  
Thermal Capacity ◽  
Thermal Processes ◽  
Domain Method ◽  
The Finite Difference Method ◽  
The One ◽  
The Mathematical Model

AbstractIn the paper the thermal processes proceeding in the domain of solidifying binary alloy are considered. The mathematical model of solidification and cooling processes bases on the one domain method (or fixed domain method). In such a model the parameter called a substitute thermal capacity (STC) appears. At the stage of STC construction the macrosegregation process described by the lever arm rule or the Scheil model is taken into account. In this way one obtains the formulas determining the course of STC resulting from the certain physical considerations and this approach seems to be closer to the real course of thermal processes proceeding in domain of solidifying alloy. In the final part the examples of numerical solutions basing on the finite difference method are presented.

scholarly journals A mathematical model for determining and analyzing temperature regimes in a battery pack of electric trucks

2020 ◽  
Vol 30 (1) ◽  
pp. 132-135
Author(s):  
В. І. Гавриш ◽  
В. Б. Лоїк ◽  
О. С. Король ◽  
О. Д. Синельніков
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Temperature Field ◽  
Lithium Ion Batteries ◽  
Internal Heat ◽  
Lithium Ion ◽  
Discontinuous Coefficients ◽  
Generalized Functions ◽  
Temperature Regimes ◽  
Mathematical Relation

A mathematical model for the determination of the temperature field and the analysis of temperature regimes in lithium-ion batteries have been developed. Using the theory of generalized functions, the thermophysical parameters of the structural components of a battery are represented by a single mathematical relation. A function in the form of the product of the generalized thermal conductivity coefficient for temperature was introduced, which avoided the differentiation of the product of two generalized functions as a result of constructing the initial differential equation of thermal conductivity, which was obtained with discontinuous coefficients. An analytical solution of this equation is determined, which is expressed by the temperature value at the conjugation surfaces of the layers of the structure. A relation was obtained to determine these values ​​and expressions for constant integration. To determine the numerical values ​​of the temperature in the design of the battery nodes, as well as to analyze the temperature gradients in its environment caused by the heterogeneity of the components due to heating, an algorithm and computational programs have been developed that allow to analyze lithium-ion batteries for their normal functioning. Using numerical programs, numerical values ​​of the temperature were obtained for given values ​​of the power of the internal heat sources, which made it possible to construct curves that reflect the behavior of the temperature field depending on the spatial coordinate. The angular points on the curve are revealed, which indicate the presence of a phase transition in the design of lithium-ion battery assemblies. As a consequence, it becomes possible to determine the permissible temperature values ​​for the fire safety of these batteries.

Experiment Research on the Temperature Field and Thermal Error Distribution of NC Grinding Machine

2009 ◽  
Vol 76-78 ◽  
pp. 61-66
Author(s):  
Ya Dong Gong ◽  
Yan Guang Bai ◽  
Yue Ming Liu ◽  
Jian Qiu
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Infrared Camera ◽  
Thermal Error ◽  
Error Distribution ◽  
Measurement Technology ◽  
Actual Error ◽  
Grinding Machine ◽  
The Mathematical Model ◽  
Nc Grinding

With the help of the infrared camera temperature measurement technology, the systemic theoretical analysis and experimental research for temperature field and thermal error distribution in NC grinding machine is provided. Two different situations for temperature field and thermal error distribution are respectively measured while the free and loaded grinding by the new measurement method. The mathematical model of thermal error is built, and it shows that the actual error and the forecasted error from thermal error mathematical model have good comparability.

Mathematical model implementation in conditions of uncertainty and possible risks

2021 ◽  
pp. 137-145
Author(s):  
A. Kravtsov ◽  
◽  
D. Levkin ◽  
O. Makarov ◽  
◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Layer Structure ◽  
Boundary Value ◽  
Goal Function ◽  
Cauchy Problems ◽  
System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

Method of Lines to Solve 2-D Steady Temperature Field of FGM

2007 ◽  
Vol 353-358 ◽  
pp. 2003-2006 ◽  
Author(s):  
Wei Tan ◽  
Chang Qing Sun ◽  
Chun Fang Xue ◽  
Yao Dai
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Transfer Problem ◽  
Method Of Lines ◽  
Main Idea ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Steady Temperature ◽  
Thermal Transfer ◽  
Steady Temperature Field

Method of Lines (MOLs) is introduced to solve 2-Dimension steady temperature field of functionally graded materials (FGMs). The main idea of the method is to semi–discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs with functions of thermal properties. As numerical examples, six kinds of material thermal conductivity functions, i.e. three kinds of polynomial functions, an exponent function, a logarithmic function, and a sine function are selected to simulate spatial thermal conductivity profile in FGMs respectively. The steady-state temperature fields of 2-D thermal transfer problem are analyzed by the MOLs. Numerical results show that different material thermal conductivity function has obvious different effect on the temperature field.

scholarly journals Improving the quality of alumina-containing sinter using water-cooled furnace shell

2012 ◽  
Vol 44 (3) ◽  
pp. 281-286
Author(s):  
A.V. Aleksandrov ◽  
V.V. Aleksandrov
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Heat Exchange ◽  
Energy Balance ◽  
Cold Water ◽  
Sintering Temperature ◽  
Radiant Heat ◽  
Thermal Processes ◽  
Technical Solutions

This article deals with the use of computer modeling to develop technical solutions to ensure better quality of alumina-containing sinter. The simulation accounted for the influence of the feed materials on the thermal processes in the furnace. The energy balance (including thermal conductivity, heat convection and radiant heat exchange) was solved assuming steady state. A good correlation was observed for the actual and calculated temperatures of the solids and gases, with less than 15% discrepancy. Using the model of the furnace investigated the possibility of lowering the temperature of sintering by removing heat from the outside of the furnace shell. To reduce the sintering temperature to 1000 ?C length of the refractory lined steel is 5 m, the height of the lining should not exceed - 0.06 m, the required rate of cold water - 54.7 m3/h

scholarly journals About Two-dimensional Mathematical Model of Contaminant Migration in Unsaturated Catalytic Porous Media with Traps

2020 ◽  
pp. 25-28
Author(s):  
Anatolyy Vlasyuk ◽  
Viktor Zhukovskyy ◽  
Nataliia Zhukovska ◽  
Serhiy Kraychuk
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Moisture Transfer ◽  
Physical Problem ◽  
Two Dimensional ◽  
Contaminant Migration ◽  
Nonlinear Case ◽  
The Finite Difference Method ◽  
Saline Solutions ◽  
Assessment Strategies

This paper proposes an approach for the computer simulation of complex physical problem of contaminant migration through unsaturated catalytic porous media to the filter-trap. The corresponding mathematical model in the two-dimensional nonlinear case is presented. The model includes detailed considerations of the moisture transfer of saline solutions under the generalized Darcy’s and Cluta’s laws in different subregions of soil. The numerical solution of the boundary value problem was found by the finite difference method and proposed the algorithm for computer implementation. The proposed algorithm may be used for creating software with effective risk assessment strategies and predicting the cleaning and further useful use of the soil massifs.

scholarly journals Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

2021 ◽  
Vol 321 ◽  
pp. 03005
Author(s):  
George Kuvyrkin ◽  
Inga Savelyeva ◽  
Daria Kuvshinnikova
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Complex Structure ◽  
Modern World ◽  
Nonlocal Term ◽  
Material Structure ◽  
Two Dimensional ◽  
Differential Heat

Nonlocal models of thermodynamics are becoming more and more popular in the modern world. Such models make it possible to describe materials with a complex structure and unique strength and temperature properties. Models of nonlocal thermodynamics of a continuous medium establish a relationship between micro and macro characteristics of materials. A mathematical model of thermal conductivity in nonlocal media is considered. The model is based on the theory of nonlocal continuum by A.K. Eringen. The interaction of material particles is described using local and nonlocal terms in the law of heat conduction. The nonlocal term describes the effect of decreasing the influence of the surrounding elements of the material structure with increasing distance. The effect of nonlocal influence is described using the standard non-locality function based on the Gaussian distribution. The nonlocality function depends on the distance between the elements of the material structure. The mathematical model of heat conduction in a nonlocal medium consists of an integro-differential heat conduction equation with initial and boundary conditions. A numerical solution to the problem of heat conduction in a nonlocal plate is obtained. The numerical solution of a two-dimensional problem based on the finite element method is described. The influence of nonlocal effects and material parameters on the thermal conductivity in a plate under highintensity surface heating is analyzed. The importance of nonlocal characteristics in modelling the thermodynamic behaviour of materials with a complex structure is demonstrated.

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