thermal conductivity equation
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2021 ◽  
Vol 2052 (1) ◽  
pp. 012005
Author(s):  
V V Burkhovetskiy ◽  
A O Kamaev ◽  
A Yu Kiselev ◽  
D V Kurushkin ◽  
V M Khanaev ◽  
...  

Abstract The paper analyzes the behavior of the deformation characteristics of welded joints made of TiNi alloy with a shape memory effect. Comparison of the level of tensile strength of welded samples made by the TIG method in an Ar and He atmosphere was carried out using a Instron 5985 universal machine. The study of the material structure in the weld zone and the heat-affected zone was carried out on longitudinal sections using a JSM-6490LV electron microscope. To estimate the mechanical parameters PMT-3 microhardness tester was used. The calorimetric parameters of the welded samples were obtained using a differential scanning calorimeters METTLER TOLEDO 822e and TA Instruments Q20. To analyze the gradient properties at the weld zone and the heat-affected zone, the temperature fields were calculated using the thermal conductivity equation included in the model of the residual stress mechanism.


2021 ◽  
Vol 20 ◽  
pp. 156-165
Author(s):  
Alexander Zemliak ◽  
Eugene Machusky

Some nonlinear models are presented for modeling and analyzing IMPATT high-power pulse diodes. These models are suitable for analyzing different operating modes of the oscillator. The first model is a precise one, which describes all important electrical phenomena on the basis of the continuity equations and Poisson´s equation, and it is correct until 300 GHz. The second approximate mathematical model suitable for the analysis of IMPATT diode stationary operation oscillator and for optimization of internal structure of the diode. The temperature distribution in the semiconductor structure is obtained using the special thermal model of the IMPATT diode, which is based on the numerical solution of the non-linear thermal conductivity equation. The described models can be applied for the analysis, optimization and practical design of pulsedmode millimetric IMPATT diodes. It can also be used to evaluate the thermal behavior of diodes, to correctly select the shape and amplitude of a supply pulse, and to design various types of high-power pulsed millimeter IMPATT diodes with a complex doping profile with improved characteristics.


2021 ◽  
Vol 63 (11-12) ◽  
pp. 960-964
Author(s):  
O. S. Lekhov ◽  
A. V. Mikhalev

The article describes the main loads affecting shaped backups of the unit of combined process of continuous casting and deformation in billets production. Importance of determining the temperature fields and thermoelastic stresses in shaped backups with collars is provided at formation of several billets, at slab compression and at idle during water cooling of backups. The authors describe strength and thermophysical properties of steel from which the backups are made. Geometry of backups with collars used for obtaining billets of three different shapes in one pass is shown. Initial data of the temperature field calculation are given for backups with collars of the combined unit. Temperature boundary conditions are considered for calculation of temperature fields of backups with collars. Boundary conditions determining temperature of such backups are described and values of the heat flow and effective heat transfer coefficient are given. The results of calculation of temperature fields are performed in four sections and are given for typical lines and points located on contact surface of backups with collars and in contact layer at depth of 5 mm from the working surface. The sizes of finite elements grid which is used at calculation of temperature field of backups with collars are provided. Temperature field of backups with collars is determined on the basis of solution of unsteady thermal conductivity equation corresponding initial and boundary conditions. Values and regularities of temperature distribution in bases and in tops of the middle and extreme edges of the shaped backups are presented during slab compression and at idle when obtaining billets of three shapes in one pass at the unit of combined continuous casting and deformation.


Author(s):  
М.Х. Бештоков ◽  
З.В. Бештокова ◽  
М.З. Худалов

В прямоугольной области исследуется нелокальная краевая задача для одномерного по пространственной переменной нагруженного уравнения теплопроводности дробного порядка с сосредоточенной на границе теплоемкостью, выступающего в качестве математической модели, возникающего, в частности, в практике регулирования солевого режима почв с фрактальной организацией, когда расслоение верхнего слоя достигается сливом слоя воды с поверхности, затопленного на некоторое время участка. Основным методом исследования является метод энергетических неравенств. При предположении существования регулярного решения дифференциальной задачи получена априорная оценка, откуда следуют единственность и непрерывная зависимость решения от входных данных задачи. На равномерной сетке в соответствие дифференциальной задаче ставится разностная схема второго порядка аппроксимации по параметрам сетки. Для решения разностной задачи получена априорная оценка в разностной форме, из чего следуют единственность и устойчивость решения по правой части и начальным данным. В силу линейности рассматриваемой задачи полученное неравенство позволяет утверждать сходимость приближенного решения к точному (в~предположении существования последнего в классе достаточно гладких функций) со скоростью, равной порядку погрешности аппроксимации. Проведены численные эксперименты, иллюстрирующие полученные теоретические результаты.


Author(s):  
Ilkizar V. Amirkhanov ◽  
Nil R. Sarker ◽  
Ibrohim Sarkhadov

In this paper, we report a numerical simulation of laser ablation of a material by ultrashort laser pulses. The thermal mechanism of laser ablation is described in terms of a one-dimensional nonstationary heat conduction equation in a coordinate system associated with a moving evaporation front. The laser action is taken into account through the functions of the source in the thermal conductivity equation that determine the coordinate and time dependence of the laser source. For a given dose of irradiation of the sample, the profiles of the sample temperature at different times, the dynamics of the displacement of the sample boundary due to evaporation, the velocity of this boundary, and the temperature of the sample at the moving boundary are obtained. The dependence of the maximum temperature on the sample surface and the thickness of the ablation layer on the radiation dose of the incident laser pulse is obtained. Numerical calculations were performed using the finite difference method. The obtained results agree with the results of other works obtained by their authors.


2020 ◽  
Vol 17 (4) ◽  
pp. 498-513
Author(s):  
Yu. P. Boronenko ◽  
◽  
B. A. Abdullaev ◽  

Objective: To choose materials and technical solutions for thermal insulation in the structure of the fencing of refrigerated car and container bodies. Methods: Experimental studies of the thermal properties of the selected materials were carried out on a physical model using climatic and test chambers, analytical calculations using thermal conductivity equation. Results: The thermal properties of the thermal fencing structures of the body of refrigerated cars and containers were determined. Practical importance: New materials reduce the heat transfer coeffi cient of the fence, which will reduce fuel consumption and increase the safety of perishable goods, reduce weight and increase the volume of the body


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