scholarly journals Optimization Of Parameters Of Heating Elements For Floor Panel Of Piglets Resting Places

2015 ◽  
Vol 2 ◽  
pp. 92
Author(s):  
V. Zagorska ◽  
U. Iljins
Keyword(s):  
Separation Of Variables ◽  
Mathematical Physics ◽  
Hot Water ◽  
Tube Material ◽  
Water Tube ◽  
Surrounding Environment ◽  
Floor Panel ◽  
Insulation Thickness ◽  
The Mathematical Model ◽  
Equal Temperature

The article deals with problem solving of mathematical physics using the method of separation of variables optimizing heating element – optimizing water tube parameters (tube material, radius, insulation thickness, choosing appropriate surrounding environment). For ensuring piglets comfort, concrete floor panels heated by electric current or hot water are used. If an electro-heated cable in the panels body is placed, than amount of heat conducted from the cable is the same along all the length of the cable. If hot water circulating through tube is used, than amount of heat energy taken off the heater decreases along its length. The aim of the research is to create the mathematical model of a water tube, were water temperature is gradually decreasing. This model is needed to make precise calculations of the heating panel for piglets, to ensure equal temperature distribution over the upper surface of the panel, taking into account mathematically calculated temperature decrease of the heat source.

Design of 110kV/2kA High Temperature Superconducting Cable Termination Stress Cones

2014 ◽  
Vol 1070-1072 ◽  
pp. 1011-1015
Author(s):  
Meng Song ◽  
Zuo Shuai Wang ◽  
Li Ren ◽  
Yi Zhang ◽  
Shi Feng Shen ◽  
...  
Keyword(s):  
High Temperature ◽  
Electric Field ◽  
Equivalent Circuit Model ◽  
Radial Electric Field ◽  
Internal Electric Field ◽  
Element Analysis ◽  
High Temperature Superconducting ◽  
Before And After ◽  
Insulation Thickness ◽  
The Mathematical Model

High temperature superconducting (HTS) cable termination is an important component of the HTS cable system, which functions to connect the HTS cable and the conventional cable accessory. The stress cones of the HTS cable termination can improve the internal electric field distribution and the electrical insulation strength of the cable termination. In this paper, the mathematical model and equivalent circuit model of the stress cones are built and the genetic algorithm is adopted to the design of 110-kV HTS cable terminal stress cone. The capacitance, radial electric field, axial electric field, voltage, insulation thickness and other parameters of the stress cone were compared before and after the optimization of the stress cone. Finally, the simulations of the stress cone with the optimized structure were made using finite-element analysis software COMSOL to test the optimization result.

scholarly journals Functional separable solutions of two classes of nonlinear mathematical physics equations

2019 ◽  
Vol 486 (3) ◽  
pp. 287-291
Author(s):  
A. D. Polyanin ◽  
A. I. Zhurov
Keyword(s):  
Separation Of Variables ◽  
Functional Differential Equations ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Mathematical Physics ◽  
Variable Coefficients ◽  
Reaction Diffusion Equations ◽  
Equations Of Mathematical Physics ◽  
Klein Gordon ◽  
Functional Differential

The study describes a new modification of the method of functional separation of variables for nonlinear equations of mathematical physics. Solutions are sought in an implicit form that involves several free functions; the specific expressions of these functions are determined in the subsequent analysis of the arising functional differential equations. The effectiveness of the method is illustrated by examples of nonlinear reaction-diffusion equations and Klein-Gordon type equations with variable coefficients that depend on one or more arbitrary functions. A number of new exact functional separable solutions and generalized traveling-wave solutions are obtained.

scholarly journals Modeling of the physical phenomenon of heat generation by using partial differential equations

2021 ◽  
Vol 2073 (1) ◽  
pp. 012014
Author(s):  
J J Cadena Morales ◽  
C A López Castro ◽  
H F Rojas Molano
Keyword(s):  
Heat Generation ◽  
Physical Phenomenon ◽  
Separation Of Variables ◽  
Computational Simulation ◽  
Mathematical Physics ◽  
Temperature Function ◽  
Mathematical Arguments ◽  
Solution Methods ◽  
Equations Of Mathematical Physics ◽  
Physical Phenomena

Abstract The equations of mathematical physics are a natural environment for modeling physical phenomena, an example of the above is evidenced by the heat equation in relation to its use in a variety of applications; directly related to the equations of mathematical physics are the solution methods that are used to construct the predictive models. This paper describes step by step the analytical method of separation of variables to perform a complete description of the heat conduction phenomenon in the presence of a heat generation source. The investigation by using mathematical arguments allowed to calculate the temperature function as the addition of a Fourier series and a function which represents the steady state; by performing a computational simulation, it was possible to demonstrate the accuracy of the results achieved.

scholarly journals Ensuring electromagnetic safety at high-speed maglev transport

2017 ◽  
Vol 3 (3) ◽  
pp. 90-110
Author(s):  
Stanislav M Apollonskiy
Keyword(s):  
Mathematical Programming ◽  
Electromagnetic Interference ◽  
High Speed ◽  
Electric Energy ◽  
Energy System ◽  
Practical Significance ◽  
Coordinate Systems ◽  
Surrounding Environment ◽  
Scalar Potentials ◽  
The Mathematical Model

High-speed ground maglev transport creates electromagnetic interference of wide frequency spectrum during the movement. Electromagnetic interference spreads both in the surrounding environment and within the transport itself. Mathematically, electromagnetic interference is a vector (and in some cases tensor) field, where the functions are magnetic and electrical tenseness. Purpose. The purpose of the work is to ensure electromagnetic safety of high-speed ground maglev transport’s technical means and people (passengers and staff) by means of optimisation synthesis. Objective. The objective of the works is to optimise the placement of field sources in areas with variable geometric characteristics. Methodology. The method of the work is to synthesise elements of an energy system whose characteristics depend on the behaviour of electromagnetic interference. The mathematical model of the energy system being designed should take into account technological and constructive constraints, and electromagnetic interference. Calculation of electromagnetic interference from several sources in the premises, where the energy system is located by means of solving nonlinear tasks of special type mathematical programming. The peculiarities of this type of problems do not allow using known methods of mathematical programming. Finally, methods of formalisation and algorithms for solving optimisation problems of placement. Practical significance. The search of solution of optimisation tasks became feasible owing to a number of suggestions put forward by the author: introduction of scalar potentials for describing external electromagnetic interference of the electric power plant elements; the introduction of interinfluence taking into account the influence of closely-located sources; development of screening functions in the form of harmonic decompositions; the application of addition theorems which enable describing solutions of mathematical physics equations in different coordinate systems. Conclusion. The suggested method of formation of maglev transport electric energy system may be useful.

scholarly journals Energy saving and optimum insulation thicknesses in building upgrading

2018 ◽  
Vol 240 ◽  
pp. 04007
Author(s):  
Mateusz Orzechowski ◽  
Tadeusz Orzechowski
Keyword(s):  
Renewable Energy ◽  
Renewable Energy Sources ◽  
Heat Pumps ◽  
Hot Water ◽  
Bank Loan ◽  
Existing Buildings ◽  
Historical Buildings ◽  
Renewable Energy Consumption ◽  
Insulation Thickness ◽  
Selection Of

Heat pumps are classified as ecologically friendly heat-generating devices and are one of the most suitable solutions for improving energy efficiency in buildings. Systems based on such solutions replace conventional sources very well. Household sector is one of the major energy consumers, where energy is used mainly for space heating and providing hot water. To increase renewable energy consumption levels, it is necessary to take decisive actions aimed at energy modernization of existing buildings. Particular emphasis must be put on the use of renewable energy sources. A wide selection of insulation materials is available on the market, however proper technologies are required to apply those materials, especially for historical buildings. Therefore, while planning investment, a question must be answered what type of material should be used, and what costs that will generate. The paper presents simple methodology for calculating the optimal insulation thickness so that the costs of the thermo-modernization would be covered by savings in heating expenses, when bank loan for the project is available at fixed interest rate.

scholarly journals Functional Separation of Variables in Nonlinear PDEs: General Approach, New Solutions of Diffusion-Type Equations

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 90 ◽  
Author(s):  
Andrei D. Polyanin
Keyword(s):  
Exact Solutions ◽  
Applied Mathematics ◽  
Separation Of Variables ◽  
Surface Condition ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Variable Coefficients ◽  
Nonlinear Pdes ◽  
Diffusion Type ◽  
Differential Constraint

The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematics and mathematical physics, based on a special transformation with an integral term and the generalized splitting principle. The effectiveness of this approach is illustrated by nonlinear diffusion-type equations that contain reaction and convective terms with variable coefficients. The focus is on equations of a fairly general form that depend on one, two or three arbitrary functions (such nonlinear PDEs are most difficult to analyze and find exact solutions). A lot of new functional separable solutions and generalized traveling wave solutions are described (more than 30 exact solutions have been presented in total). It is shown that the method of functional separation of variables can, in certain cases, be more effective than (i) the nonclassical method of symmetry reductions based on an invariant surface condition, and (ii) the method of differential constraints based on a single differential constraint. The exact solutions obtained can be used to test various numerical and approximate analytical methods of mathematical physics and mechanics.

scholarly journals MATHEMATICAL MODELING OF SEISMIC VIBRATIONS OF THE DAM AND UNDERFOUNDATION LAYERS OF THE SOIL MASSIF TAKING INTO ACCOUNT THE INFLUENCE OF WATER IN THE RESERVOIR

2017 ◽  
Author(s):  
Н.И. Музаев ◽  
К.С. Харебов ◽  
И.Д. Музаев
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
High Pressure ◽  
Seismic Waves ◽  
Mathematical Physics ◽  
Contact Boundary ◽  
Influence Of Water ◽  
Seismic Vibrations ◽  
The Mathematical Model ◽  
Oscillatory Processes

Составлена математическая модель совместных сейсмических колебаний высоконапорной плотины, водохранилища и двух слоев массива грунта под основаниями плотины и водохранилища. Модель представляет контактную краевую задачу математической физики в которой учтены взаимозависимости колебательных процессов в грунтовой толще, в плотине и в водохранилище при распространении гармонической сейсмической волны в рассматриваемой системе. В результате решения поставленной задачи получены расчетные формулы для вычисления относительных амплитуд сейсмических колебаний гребня и основания плотины. The mathematical model of the co-seismic vibrations of high-pressure dams, reservoirs and two layers of soil under the foundations of the dam and reservoir is created. The model represents the contact boundary value problem of mathematical physics which takes into account the interdependence of oscillatory processes in soil, in the dam and in the reservoir during the propagation of harmonic seismic waves in the system under consideration. As a result of solving the tasks the formulae are derived to calculate the relative amplitudes of the oscillations of the top and the base of the dam.

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