Singular integral equation for an electric dipole taking into account the finite metal conductivity from which it is made

A singular integral equation for an electric dipole has been obtained, which makes it possible to take into account the finite conductivity of the metal from which it is made. The derivation of the singular integral equation is based on the application of the Greens function for free space, written in a cylindrical coordinate system, taking into account the absence of the dependence of the field on the azimuthal coordinate, on a point source located on the surface of an electric dipole. Methods for its solution are proposed. In contrast to the well-known mathematical models of an electric dipole, built in the approximation of an ideal conductor, the use of the singular integral equation obtained in this work makes it possible to take into account heat losses and calculate the efficiency.

Finding a Fair Heat Settlement Model

In this report, we investigate optimal strategies for fair heat settlement schemes in apartment buildings heated by externally powered radiators and pipes. We use mathematical modelling to predict the distribution of heat among apartments taking into account heat flow through the building walls and external conditions. We use both deterministic and statistical approaches.

Analysis the dynamics formation of a vapor supersonic jet under outflow from thin nozzle

The dynamics formation of a vapor jet with near-critical state parameters outflowing from a high-pressure vessel through a thin nozzle is studied. The numerical modeling of this process, by using a system of model equations for gas-vapor-liquid mixture, which include conservation laws of mass, momentum, and energy of phases in accordance with one-pressure, one-velocity and two-temperature approximations, was conducted, taking into account heat and mass transfer processes of evaporation and condensation under conditions of equilibrium state with modified reactingTwoPhaseEulerFoam solver of open package OpenFOAM. The process of barrel shock formation in supersonic boiling jet with shaping Mach disk is shown. It was found that the process of boiling fluid outflow is accompanied by formation of vortex zones near axis of symmetry and leads to generation of acoustic wave pulses series preceding the main jet flow, which are the source of pulsations, observed in experiments. The justification of applied numerical method reliability is shown by comparing the computational and analytical solutions for Sedov’s problem of a point explosion in gas-water mixture at the plane case.

Thermal evolution of the Earth's core during its formation taking into account heat release from the short-lived radioisotopes 26Al and 60Fe

Research subject. Based on the two-stage mechanism of the Earth's heterogeneous accumulation, previously proposed by V.N. Anfilogov and Yu.V. Khachay, the thermal evolution of the core during its formation was studied. Account is taken of both the heat release from 26Al, the content of which was established with a fairly reliable accuracy, and that from 60Fe.Materials and methods. The methods of mathematical modelling were used. Calculations were carried out for three estimates of the fractional content of the radioisotope 60Fe to stable 56Fe at the time of CAI formation (Ca-Al-In- clusions, calcium- and aluminium-rich inclusions found in carbonaceous chondrites) based on the results of various authors.Results. As a result of numerical experiments, variants of the temperature and melting temperature distributions at different stages of the core formation for different 60Fe/56Fe ratios were obtained.Conclusions. The results show that the central region of the forming core can remain melted even by the end of its accumulation. As a consequence, in this region for this time, the conditions for free thermal convection and, accordingly, for the implementation of the MHD dynamo mechanism remain.

Analysis of Micro-Segregation of Solute Elements on the Central Cracking of Continuously Cast Bloom

On the basis of the Brody–Flemings model and modified Voller–Beckermann model, an analytical model of micro-segregation is established by considering the actual solidification cooling conditions of bloom. According to the developed model, the interdendritic solute distribution at the origin of the cracking gap is obtained. It is found that both phosphorus and sulfur have quite severe segregation, but both carbon and manganese have slight segregation; these results agree well with the semiquantitative analysis results of the scanning electron microscope (SEM). At the same time, the interdendritic segregation leads to an enhanced increase in the temperature range of crack formation; correspondingly, the possibility of cracking significantly increases and, thus, element segregation is the internal cause of crack formation. On the other hand, taking into account heat transfer, phase transformation, and metallurgical pressure, the strain of the solid shell is revealed through finite element software. When the solid shell thickness is equal to the distance of 90 mm between the opening point of the crack and the inner arc side, the tensile strain of the solid front is much bigger than the critical strain, which meets the external cause of crack formation; therefore, reasons for the cracking of blooms are successfully found.

Simulation of Electromagnetic-Acoustic Heating of the Oil Layer in Laboratory Conditions

This paper describes an experiment to study the combined effects of high-frequency electromagnetic and acoustic fields on a model of an oil reservoir. A mathematical model is described that describes the physical processes that occur in the reservoir. The heat equation takes into account heat transfer with the environment by introducing an additional term. The largest discrepancy between theoretical and experimental data does not exceed 28%. Qualitative coincidence of theoretical and experimental curves indicates the adequacy of the mathematical model.

Liquid Ring Vacuum Pumps for Heat and Mass Transfer Processes

The paper examines the calculation of a liquid ring vacuum pump, using the example of the drying process of various materials. It was found that for two-stage convective vacuum-impulse drying it is economically efficient to use a two-stage liquid ring vacuum pump with the ability to turn off the second stage. A method for calculating the specific power of one-stage and two-stage liquid ring vacuum pumps, taking into account heat and mass transfer and thermal processes that occur during operation is proposed.

The influence of the length of heat sources on the external border on the temperature distribution in profiled polar-orthotropic ring plates taking into account there heat exchange with the external environment

We study the influence of N extended heat sources at external boundaries on the nonaxisymmetric temperature distribution on profiled polar-orthotropic ring plates and take into account heat exchange with the external environment. The solution of the stationary heat conduction problem for anisotropic annular plates of a random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conductivity problem for a reverse conical polar-orthotropic ring plate is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

Numerical Simulation of Fire Resistance Test for Gas Turbine Component Using Coupled CFD/FEM Approach

The article presents the implementation of CFD/FEM approach for real oil tank of the gas turbine engine for the purposes of prediction of the component behavior under the local impact of a burner jet. The model takes into account heat and mass transfer problems as well as strength problems that are solved using a one way coupled fluid-structure interaction method. Results of the blind test simulation are compared and show good agreement with available experimental data.