Reconstructing the effective coefficient of thermal conductivity of asbestos-textolite from the solution of the inverse problem

1983 ◽  
Vol 45 (5) ◽  
pp. 1281-1286 ◽  
Author(s):  
E. A. Artyukhin ◽  
V. E. Killikh ◽  
A. S. Okhapkin
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Effective Coefficient ◽  
Coefficient Of Thermal Conductivity

scholarly journals On investigation of the inverse problem for a parabolic integro-differential equation with a variable coefficient of thermal conductivity

2020 ◽  
Vol 30 (4) ◽  
pp. 572-584
Author(s):  
D.K. Durdiev ◽  
J.Z. Nuriddinov
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Variable Coefficient ◽  
Direct Problem ◽  
Local Existence ◽  
Problem Solution ◽  
Volterra Type ◽  
Integral Term ◽  
Local Existence And Uniqueness ◽  
Coefficient Of Thermal Conductivity

The inverse problem of determining a multidimensional kernel of an integral term depending on a time variable $t$ and $ (n-1)$-dimensional spatial variable $x'=\left(x_1,\ldots, x_ {n-1}\right)$ in the $n$-dimensional heat equation with a variable coefficient of thermal conductivity is investigated. The direct problem is the Cauchy problem for this equation. The integral term has the time convolution form of kernel and direct problem solution. As additional information for solving the inverse problem, the solution of the direct problem on the hyperplane $x_n = 0$ is given. At the beginning, the properties of the solution to the direct problem are studied. For this, the problem is reduced to solving an integral equation of the second kind of Volterra-type and the method of successive approximations is applied to it. Further the stated inverse problem is reduced to two auxiliary problems, in the second one of them an unknown kernel is included in an additional condition outside integral. Then the auxiliary problems are replaced by an equivalent closed system of Volterra-type integral equations with respect to unknown functions. Applying the method of contraction mappings to this system in the Hölder class of functions, we prove the main result of the article, which is a local existence and uniqueness theorem of the inverse problem solution.

scholarly journals INVERSE PROBLEM FOR INTEGRO-DIFFERENTIAL HEAT EQUATION WI TION WITH A VARIABLE COEFFICIEN ABLE COEFFICIENT OF THERM T OF THERMAL CONDUCTIVITY

2020 ◽  
Vol 4 (5) ◽  
pp. 3-12
Author(s):  
Durdimurod Kalandarovich Durdiev ◽  
◽  
Zhavlon Zafarovich Nuriddinov
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Heat Equation ◽  
Contraction Mapping ◽  
Cauchy Problems ◽  
Convolution Integral ◽  
Differential Heat ◽  
Memory Kernel ◽  
Coefficient Of Thermal Conductivity ◽  
Type Integral

Background. The inverse problem of finding a multidimensional memory kernel of a time convolution integral depending on a time variable t and (n-1)-dimensional spatial variable. 2-dimensional heat equation with a time-dependent coefficient of thermal conductivity is studied. Methods. The article is used Cauchy problems for the heat equation, resolvent methods for Volterra type integral equation and contraction mapping prinsiple.

scholarly journals THEORETICAL METHOD ALLOWING CALCULATING AND ANALYZE THE EFFECTIVE COEFFICIENT OF THERMAL CONDUCTIVITY, NONWOVEN HEAT-SHIELDING MATERIALS

2017 ◽  
Vol 51 (07) ◽  
pp. 21-27
Author(s):  
Viktir Yureivich Mishakov ◽  
◽  
Dimitry Anatolievich Sovetnikov ◽  
Maxim Andreevich Pavlov ◽  
Elena Aleksandrovna Kirsanova ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Theoretical Method ◽  
Effective Coefficient ◽  
Coefficient Of Thermal Conductivity ◽  
Heat Shielding

scholarly journals EFFECTIVE COEFFICIENT OF THERMAL CONDUCTIVITY OF BIOFUEL IN THE CONDITIONS OF HIGH-TEMPERATURE DRYING

2018 ◽  
Vol 40 (2) ◽  
pp. 49-55
Author(s):  
D.M. Korinchuk
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
High Temperature ◽  
Biofuel Production ◽  
Effective Coefficient ◽  
Drying Process ◽  
Average Value ◽  
Coefficient Of Thermal Conductivity ◽  
Kinetics Of ◽  
High Temperature Drying

The paper is devoted to determining the effective thermal conductivity coefficient of a mathematical model of high temperature drying biomass. The method of experimental research kinetics of drying and theoretical processing of the results is developed. The results of the research are presented. The average value of the effective coefficient of thermal conductivity is calculated and the possibility of its application in calculations of high temperature drying of biomass is substantiated. The modeling of high-temperature drying of biomass and peat will allow developing and substantiat-ing the methods of intensification of the drying process, developing engineering methods for calculating the equipment and ensuring the creation of the most rational designs of drying plants. Increasing the accuracy of mathematical modeling requires conducting experimental studies and de-termining the value of the effective coefficient of thermal conductivity of materials in the dry zone, as well as the influence of the temperature regime and properties of biomass on its value. The aim of the work is to determine the effective coefficient of heat conductivity of biomass in con-ditions of high temperature drying in biofuel production technologies. The methodology of determination of the effective coefficient of thermal conductivity for use in cal-culations of drying process under the model of high temperature drying of biomass is developed. The article presents the results of an experimental study of the kinetics of high- temperature drying of biomass samples of pine, willow and poplar of flat form. The theoretical model of flat particle drying was developed and cal-culations of the process of high-temperature drying of flat bodies were conducted. According to the results of the research, the value of the effective coefficient of thermal conductivity for a series of experiments is de-termined by the method of minimizing the relative error of theoretical and experimental results. The average value of the effective coefficient of thermal conductivity is calculated and the its applicability in the calcula-tions of high temperature drying of biomass using the mathematical model is substantiated. Based on these studies, the validity of the provisions of the developed mathematical model is concluded. The results can be used to upgrade and optimize processes in aerodynamic dryers.

Determination of the Thermal Properties of a PCB by Coupled Numerical and Experimental Approach

2020 ◽  
Author(s):  
Yener Usul ◽  
Mustafa Özçatalbaş
Keyword(s):  
Thermal Conductivity ◽  
Heat Capacity ◽  
Thermal Properties ◽  
Numerical Analysis ◽  
Specific Heat ◽  
Specific Heat Capacity ◽  
Thermal Analyses ◽  
Analysis Model ◽  
Linear Temperature ◽  
Coefficient Of Thermal Conductivity

Abstract Increasing demand for usage of electronics intensely in narrow enclosures necessitates accurate thermal analyses to be performed. Conduction based FEM (Finite Element Method) is a common and practical way to examine the thermal behavior of an electronic system. First step to perform a numerical analysis for any system is to set up the correct analysis model. In this paper, a method for obtaining the coefficient of thermal conductivity and specific heat capacity of a PCB which has generally a complex composite layup structure composed of conductive layers, and dielectric layers. In the study, above mentioned properties are obtained performing a simple nondestructive experiment and a numerical analysis. In the method, a small portion of PCB is sandwiched from one side at certain pressure by jaws. A couple of linear temperature profiles are applied to the jaws successively. Unknown values are tuned in the analysis model until the results of FEM analysis and experiment match. The values for the coefficient of thermal conductivity and specific heat capacity which the experiment and numerical analysis results match can be said to be the actual values. From this point on, the PCB whose thermal properties are determined can be analyzed numerically for any desired geometry and boundary condition.

scholarly journals PECULIARITIES OF KINETICS OF THE COEFFICIENT OF THERMAL CONDUCTIVITY DEPENDING ON THE HUMIDITY RATE OF WALL BLOCKS MADE OF AGRICULTURAL WASTES

2019 ◽  
Vol 4 (10) ◽  
pp. 19-28 ◽  
Author(s):  
А. Должонок ◽  
A. Dolzhonok ◽  
А. Бакатович ◽  
A. Bakatovich
Keyword(s):  
Thermal Conductivity ◽  
Building Materials ◽  
Moisture Absorption ◽  
Coarse Aggregate ◽  
Sustainable Use ◽  
Agricultural Wastes ◽  
Hygroscopic Moisture ◽  
Relative Air Humidity ◽  
Coefficient Of Thermal Conductivity ◽  
Kinetics Of

The article considers the prospect of plant wastes usage as aggregates while constructing new building materials in the form of wall blocks. The results of the research on water absorption of the wall blocks at the relative air humidity of 97 % are presented. The kinetics of change in humidity and the coefficient of thermal conductivity of the blocks with the rye and buckwheat straw coarse aggregate, and also the blocks with fine coarse aggregate of flax boon and atomized buckwheat are analyzed. Empirical dependences of the coefficient of thermal conductivity on the rate of humidity of wall blocks are obtained from experimental observations. After the maximum rate of hygroscopic moisture absorption, the best indexes are recorded on the blocks made of flax and straw. The humidity rate of the composite does not exceed 10,9 % with the increase of thermal conductivity up to 0.104 W/(m•°С). In the result of the research, the solution to the sustainable use of agricultural wastes to get environmental responsible building materials is proposed. Blocks can be are used in the erection of supporting and filler walls in one-story buildings and multistoried frame housing construction when filling exterior wall openings.

scholarly journals Thermal conductivity of silicon doped by phosphorus: ab initio study

2018 ◽  
Vol 35 (4) ◽  
pp. 717-724
Author(s):  
B. Andriyevsky ◽  
W. Janke ◽  
V.Yo. Stadnyk ◽  
M.O. Romanyuk
Keyword(s):  
Thermal Conductivity ◽  
Heat Conductivity ◽  
Phonon Scattering ◽  
Theoretical Calculations ◽  
Doped Semiconductors ◽  
Silicon Crystals ◽  
Coefficient Of Thermal Conductivity ◽  
Silicon Doped ◽  
Scattering Time ◽  
Phosphorus Doped

Abstract An original approach to the theoretical calculations of the heat conductivity of crystals based on the first principles molecular dynamics has been proposed. The proposed approach exploits the kinetic theory of phonon heat conductivity and permits calculating several material properties at certain temperature: specific heat, elastic constant, acoustic velocity, mean phonon scattering time and coefficient of thermal conductivity. The method has been applied to silicon and phosphorus doped silicon crystals and the obtained results have been found to be in satisfactory agreement with corresponding experimental data. The proposed computation technique may be applied to the calculations of heat conductivity of pure and doped semiconductors and isolators.

scholarly journals XVI Международная конференция "Термоэлектрики и их применения --- 2018" (ISCTA 2018), Санкт-Петербург, 8-12 октября 2018 г. Влияние неидеальности геометрической формы образца на неопределенность измерений теплопроводности методом лазерной вспышки

2019 ◽  
Vol 53 (6) ◽  
pp. 731
Author(s):  
А.В. Асач ◽  
Г.Н. Исаченко ◽  
А.В. Новотельнова ◽  
В.Е. Фомин ◽  
К.Л. Самусевич ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Measurement Uncertainty ◽  
Conductivity Measurement ◽  
Laser Flash ◽  
Comsol Multiphysics ◽  
Flash Method ◽  
Cylindrical Shape ◽  
Plane Parallel ◽  
Coefficient Of Thermal Conductivity ◽  
Truncated Cylinder

The influence of the geometric shape of the samples on the uncertainty of the coefficient of thermal conductivity measurement of materials by the method of a laser flash has been studied. Using a method of mathematical modeling in the Comsol Multiphysics software, a model that simulates the process of measuring the coefficient of thermal conductivity of samples made of graphite, Mg2Si0.4Sn0.6 and bismuth telluride using a laser flash method has been created. Samples of cylindrical shape with plane-parallel sides and samples in the form of a truncated cylinder, as well as samples in the form of a parallelepiped with a square base, were investigated. It is shown that the measurement uncertainty of samples with plane-parallel sides and sizes up to 12.7 mm, does not exceed 2%. For samples in the form of a truncated cylinder with a diameter of 3 mm and at an angle of ϕ= 1.5°, the measurement uncertainty does not exceed 3%. With an increase in the sample diameter and the ϕ angle, the measurement uncertainty increases significantly.

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