Integral power balance method in heat problems with free boundary
| dc.contributor.author | Kassabek Dina | |
| dc.date.accessioned | 2025-06-24T11:07:32Z | |
| dc.date.available | 2025-06-24T11:07:32Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | One of the important areas of application of the free boundary problems is the mathematical modelling of phenomena in the low-temperature plasma of an electric arc and in contacts of electrical devices. Analysis of solutions makes it possible to verify the obtained theoretical results, to test the effectiveness of the developed algorithms for specific evolutionary processes in electrical apparatuses, and to interpret the available experimental data. The evolution of contact bridge and arcing processes is so fast (nano- and microsecond range) that their experimental study is very difficult. In some cases, only mathematical modeling can give an idea of their dynamics. Thus, the need for modeling is required not only for optimization of the experiment, but also due to the impossibility of using a some different approach. One of the most effective methods of solving heat problem is the method of heat potentials, which reduces the initial boundary value problems to integral equations. However, in the case of regions degenerating at the initial time, additional difficulties arise releted to the singularity of these integral equations. These difficulties are compounded in the case when an unknown function appears not only in the boundary condition, but also in the coefficients of the equation. This method enables us to obtain an approximate solution with desirable degree of accuracy and to evaluate the approximation error, using the maximum principle. Analytical methods for solution of heat and mass transfer problems have recently received a new stimulus to their futher development due to the growing need to solve multicriteria problems for which numerical methods are unable to estimate the influence of a large number of input parameters on the behaviour of the solution and especially on its dynamics. In particular, an integral thermal balance method, a perturbation method, and a number of other methods are widely used to solve problems of the Stefan type with a free boundary, describing heat transfer with phase transitions. The main problem with the use of this method is the estimation of the approximation error, which, as a rule, is replaced for applied problems by comparison of the analytical solution with the experimental data. | |
| dc.identifier.citation | Kassabek Dina / Integral power balance method in heat problems with free boundary / 6M060100 « Mathematics » / 2019 | |
| dc.identifier.uri | https://repository.sdu.edu.kz/handle/123456789/1802 | |
| dc.publisher | Faculty of engineering and natural sciences | |
| dc.subject | Stefan problem | |
| dc.subject | Integral power balance method | |
| dc.subject | Quasi-stationary | |
| dc.title | Integral power balance method in heat problems with free boundary | |
| dc.type | Thesis |