0000000000378732
AUTHOR
Andris Buikis
Mathematical modelling of alternating electromagnetic and hydrodynamic fields, induced by bar type conductors in a cylinder
The heating of buildings by ecologically clean and compact local devices is an interesting and actual problem. One of the modern areas of applications developed during last ten years is an effective usage of electrical energy by alternating current to produce heat energy. This work presents the mathematical model of one of such devices. It is a finite cylinder with viscous incompressible liquid and with metal electrodes of the form of bars placed parallel to the cylinder axis in the liquid. These conductors are connected to the alternating current. First published online: 14 Oct 2010
Heat Conduction Problem for Double-Layered Ball
Heat conduction models for double layered spherical sample are developed. Parabolic (classic, based on Fourier’s Law) and hyperbolic (based on Modified Fourier’s Law) heat conduction equations are used to describe processes in the sample during Intensive Quenching. Solution and numerical results are obtained for 1D model using Conservative Averaging method and transforming the original problem for a sphere to a new problem for a slab, with non classic boundary condition. Models include boundary conditions of third kind and non-linear BC case. Numerical results are presented for several relaxation time and initial heat flux values.
Creation of Temperature Field in a Finite Cylinder by Alternated Electromagnetic Force
One of the modern areas of applications developed during last years is effective use of electrical energy produced by alternating current in production of heat energy. This process is ecologically clean.The water is weakly electrically conducting medium (electrolyte). Devices based on this principle are developed during last ten years. Compared to classical devices with heating elements, new devices are more compact.
Hollow system with fin. Transient Green function method combination for two hollow cylinders
In this paper we develop mathematical model for three dimensional heat equation for the system with hollow wall and fin and construct its analytical solution for two hollow cylindrical sample. The method of solution is based on Green function method for one hollow cylinder. On the conjugation conditions between both hollow cylinders we construct solution for system wall with fin. As result we come to integral equation on the surface between both hollow cylinders. Solution is obtained in the form of second kind Fredholm integral equation. The generalizing of Green function method allows us to use Green function method for regular non-canonical domains.
Intensive wave power and steel quenching 3-D model for cylindrical sample. Time direct and reverse formulations and solutions
In this paper we develop mathematical models for three dimensional hyperbolic heat equations (wave equation or telegraph equation) with inner source power and construct their analytical solutions for the determination of the initial heat flux for cylindrical sample. As additional conditions the temperature and heat flux at the end time are given. In some cases we give expression of wave energy. In some cases we give expression of wave energy. Some solutions of time inverse problems are obtained in the form of first kind Fredholm integral equation, but others has been obtained in closed analytical form as series. We viewed both direct and inverse problems at the time. For the time inverse pr…
SPECIAL SPLINES OF HYPERBOLIC TYPE FOR THE SOLUTIONS OF HEAT AND MASS TRANSFER 3-D PROBLEMS IN POROUS MULTI-LAYERED AXIAL SYMMETRY DOMAIN
In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the transfer of heat process. We derive the system of two partial differential equations (PDEs) - one expressing the rate of change of concentration of water vapour in the air spaces and the other - the rate of change of temperature in every layer. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the cons…
Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains
We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coefficients are reduced with respect to one coordinate to 2-D problems. This procedure also allows to reduce the 2-D problems to 1-D problems and the solution of the approximated problemsa can be obtained analytically. In the case of constant piece-wise coefficients we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem.…
Conservative Averaging Method for Solutions of Inverse Problems for Heat Equation
Inverse problems arise in various fields of science, technology and agriculture where from measurements of state of the system or process it is required to determine a certain typesetting of the causal characteristics. It is known that infrigement of the natural causal relationships can entail incorrectness of the mathematical formulation of inverse problem. Therefore the development of efficient methods for solving such problems allow us to simplify experimental research considerably and to increase the accuracy and reliability of the obtained results due to certain complication of algoritms for processing the experemental data. The problem of the determination of the coefficient of therma…