scholarly journals Mathematical Modeling of Induction Heating of Waveguide Path Assemblies during Induction Soldering

Metals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 697
Author(s):  
Vadim Tynchenko ◽  
Sergei Kurashkin ◽  
Valeriya Tynchenko ◽  
Vladimir Bukhtoyarov ◽  
Vladislav Kukartsev ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Induction Heating ◽  
Temperature Sensors ◽  
Heating Zone ◽  
Flux Evaporation ◽  
Rectangular Tube ◽  
Different Dimensions ◽  
Physical Phenomena ◽  
Contact Sensors ◽  
Assembly Component

The waveguides used in spacecraft antenna feeders are often assembled using external couplers or flanges subject to further welding or soldering. Making permanent joints by means of induction heating has proven to be the best solution in this context. However, several physical phenomena observed in the heating zone complicate any effort to control the process of making a permanent joint by induction heating; these phenomena include flux evaporation and changes in the emissivity of the material. These processes make it difficult to measure the temperature of the heating zone by means of contactless temperature sensors. Meanwhile, contact sensors are not an option due to the high requirements regarding surface quality. Besides, such sensors take a large amount of time and human involvement to install. Thus, it is a relevant undertaking to develop mathematical models for each waveguide assembly component as well as for the entire waveguide assembly. The proposed mathematical models have been tested by experiments in kind, which have shown a great degree of consistency between model-derived estimates and experimental data. The paper also shows how to use the proposed models to test and calibrate the process of making an aluminum-alloy rectangular tube flange waveguide by induction soldering. The Russian software, SimInTech, was used in this research as the modeling environment. The approach proposed herein can significantly lower the labor and material costs of calibrating and testing the process of the induction soldering of waveguides, whether the goal is to adjust the existing process or to implement a new configuration that uses different dimensions or materials.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals LabVIEW Interface for Controlling a Test Bench for Photovoltaic Modules and Extraction of Various Parameters

2015 ◽  
Vol 6 (3) ◽  
pp. 498 ◽  
Author(s):  
Abderrezak Guenounou ◽  
Ali Malek ◽  
Michel Aillerie ◽  
Achour Mahrane
Keyword(s):  
Numerical Simulation ◽  
Mathematical Models ◽  
Energy Production ◽  
Test Bench ◽  
Graphical Interface ◽  
Detailed Report ◽  
Photovoltaic Modules ◽  
Pv Modules ◽  
Computer Controlled ◽  
Physical Phenomena

Numerical simulation using mathematical models that take into account physical phenomena governing the operation of solar cells is a powerful tool to predict the energy production of photovoltaic modules prior to installation in a given site. These models require some parameters that manufacturers do not generally give. In addition, the availability of a tool for the control and the monitoring of performances of PV modules is of great importance for researchers, manufacturers and distributors of PV solutions. In this paper, a test and characterization protocol of PV modules is presented. It consists of an outdoor computer controlled test bench using a LabVIEW graphical interface. In addition to the measuring of the IV characteristics, it provides all the parameters of PV modules with the possibility to display and print a detailed report for each test. After the presentation of the test bench and the developed graphical interface, the obtained results based on an experimental example are presented.

scholarly journals Singular and Degenerate Boundary Value Problems Related to the Electricity Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Maria-Magdalena Boureanu ◽  
Andaluzia Matei
Keyword(s):  
Sobolev Space ◽  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Weighted Sobolev Space ◽  
Nonlinear Boundary Conditions ◽  
Uniqueness Result ◽  
Physical Phenomena ◽  
Mathematical Literature ◽  
Weak Solvability

The present paper draws attention to the weak solvability of a class of singular and degenerate problems with nonlinear boundary conditions. These problems derive from the electricity theory serving as mathematical models for physical phenomena related to the anisotropic media with “perfect” insulators or “perfect” conductors points. By introducing an appropriate weighted Sobolev space to the mathematical literature, we establish an existence and uniqueness result.

Fundamentals of the Theory of Rotating Fluids

1963 ◽  
Vol 30 (4) ◽  
pp. 481-485 ◽  
Author(s):  
L. N. Howard
Keyword(s):  
Fluid Dynamics ◽  
Boundary Layer ◽  
Mathematical Models ◽  
Rotating Flows ◽  
Laboratory Studies ◽  
Geophysical Fluid Dynamics ◽  
Rotating Fluids ◽  
Ekman Boundary Layer ◽  
Physical Phenomena

This paper gives an expository survey of some of the principal mathematical models which have been used in the theory of rotating fluids, together with a discussion of several explicit examples. Some of these examples are related to geophysical fluid dynamics; others more directly to laboratory studies. In all cases the examples have been selected to illustrate some of the most important physical phenomena which are characteristic of rotating flows and distinguish them from other fluid motions. Physical concepts, such as the Taylor-Proudman effects, the Ekman boundary layer, and Rayleigh’s analogy, which have proved useful in obtaining a general understanding of rotating fluids, are presented and discussed.

scholarly journals A Lagrange Regularized Kernel Method for Solving Multi-dimensional Time-Fractional Heat Equations

2017 ◽  
Vol 18 (1) ◽  
pp. 93-102 ◽  
Author(s):  
Edson Pindza ◽  
Jules Clement Mba ◽  
Eben Maré ◽  
Désirée Moubandjo
Keyword(s):  
Mathematical Models ◽  
Numerical Experiments ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Numerical Solutions ◽  
Kernel Method ◽  
Accurate Method ◽  
Heat Equations ◽  
Exponential Integrator ◽  
Physical Phenomena

Abstract:Evolution equations containing fractional derivatives can provide suitable mathematical models for describing important physical phenomena. In this paper, we propose an accurate method for numerical solutions of multi-dimensional time-fractional heat equations. The proposed method is based on a fractional exponential integrator scheme in time and the Lagrange regularized kernel method in space. Numerical experiments show the effectiveness of the proposed approach.

scholarly journals Generalized Differentiability of Continuous Functions

2020 ◽  
Vol 4 (4) ◽  
pp. 56
Author(s):  
Dimiter Prodanov
Keyword(s):  
Mathematical Models ◽  
Measure Zero ◽  
Continuous Functions ◽  
Primitive Function ◽  
Generalized Differentiability ◽  
Differentiable Functions ◽  
Maximal Modulus ◽  
Physical Phenomena ◽  
Broad Generalization ◽  
Differentiation Theorem

Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. These derivatives are called indicial derivatives. As an application, the indicial derivatives are used to characterize the nowhere monotonous functions. Furthermore, the non-differentiability set of such derivatives is proven to be of measure zero. As a second application, the indicial derivative is used in the proof of the Lebesgue differentiation theorem. Finally, the connection with the fractional velocities is demonstrated.

scholarly journals An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 801
Author(s):  
Md. Nur Alam ◽  
Imran Talib ◽  
Omar Bazighifan ◽  
Dimplekumar N. Chalishajar ◽  
Barakah Almarri
Keyword(s):  
Parabolic Equation ◽  
Mathematical Models ◽  
Exact Solutions ◽  
Analytical Technique ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
Expansion Scheme

In this paper, the adapted (G’/G)-expansion scheme is executed to obtain exact solutions to the fractional Clannish Random Walker’s Parabolic (FCRWP) equation. Some innovative results of the FCRWP equation are gained via the scheme. A diverse variety of exact outcomes are obtained. The proposed procedure could also be used to acquire exact solutions for other nonlinear fractional mathematical models (NLFMMs).

scholarly journals Датчик скорости потока жидкости на основе волоконных брэгговских решеток с индукционным нагревом

2021 ◽  
Vol 47 (17) ◽  
pp. 22
Author(s):  
А.В. Умнова ◽  
А.С. Алейник ◽  
В.Е. Стригалев ◽  
В.А. Новикова ◽  
А.Н. Аширов
Keyword(s):  
Flow Velocity ◽  
Induction Heating ◽  
Cross Correlation ◽  
Fiber Bragg Gratings ◽  
Correlation Method ◽  
Temperature Sensors ◽  
Heat Pulse ◽  
Experimental Results ◽  
Time Response ◽  
Velocity Range

The paper presents simulating and experimental results of flowmeter operation with induction heating, where fiber Bragg gratings were used as sensitive elements of temperature sensors. The operating principle of flowmeter based on cross-correlation method. During the experiment, it was detected time response of heat pulse from 0.2 s to 0.5 s that corresponds to a flow velocity range 0.1-0.5 m/s.

scholarly journals On the correct use of mathematical constructions in physical models

2020 ◽  
pp. 7-27
Author(s):  
M. Belevich
Keyword(s):  
Mathematical Models ◽  
Physical Meaning ◽  
Fluid Model ◽  
Model Development ◽  
Physical Models ◽  
Model Modification ◽  
First Case ◽  
Viscous Fluid Model ◽  
Model Equations ◽  
Physical Phenomena

The physical limitations of the mathematical constructions used in developing or modifying mathematical models are discussed. All reasonings are illustrated by examples from fluid mechanics. The following topics are considered: means of description; correct approach to model modification and the physical meaning of model development stages. In the first case, the method of describing physical objects using numbers as well as corresponding restrictions are investigated, followed by developing general recommendations on procedures for modifying mathematical models of fluid dynamics. The well-known procedure of averaging the viscous fluid model equations to obtain the turbulent fluid model is used as an illustration. Since we are considering the models of physical phenomena, it is natural to provide physical interpretation for each stage of model development. Unfortunately, some of the transformations used are often treated as purely technical tricks, therefore denoting the lack of the physical meaning in such cases, which does not make a mathematical procedure unacceptable, but does mark out the model's place which requires reasonable interpretation. In this paper, we are considering two variants of this kind of interpretation, namely the case of using imaginary quantities, and the case of applying integral transformations. Meanwhile, all the above-mentioned restrictions are not always given due attention. Sometimes this leads to various undesirable consequences, including excessive task complication, implicit substitution of a declared problem with another one, or, finally, lack of solution to the formulated problem.

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