Calculation of the thermal fields in the three-dimensional multiphase system during non-stationary heat conduction
Finding new ways of obtaining permanent joint in the absence of powerful heat source is an actual problem related to the conduct repairs, installation of equipment, etc. There is a perspective idea of joint formation by local heating using heat source, acceding directly to the plate that will be joined to the large shell. To construct a heat source one can use materials that are able to generate heat through SHS reaction. This paper presents the mathematical model and calculation schemes in order to determine temperature, which changes in the process of plates joining. Calculation of heat flows must take into account the size of the plates, the characteristics of plates and solder material. As a result of this work we present a software based on the original, derived numerical schemes. Our software allows to monitor heating process and heating transfer during soldering plates. It gives the possibility to determine necessary conditions for soldering process implementation using independent sources of heat, depending on the characteristics of materials, and to find the optimal modes of soldering.
1. A. G. Merzhanov and A. S. Mukasyan (2007). Tverdoplamennoe Gorenie (Solidburning), Moscow: Torus Press (in Rus.)
2. Merzhanov A. G., Borovinskaya I. P. (1972). Self propagating high-temperature synthesis of refractory inorganic compounds. Dokl. Akad. Nauk. SSSR . 204, 366-369.
3. Zaporozhets T. V,· Gusak A. M., Ustinov A. I. (2010). Modeling of stationary mode SHS in multi-layer nanostructure materials (Phenomenological model). Sovremennaya electrometallurgiya (Modern electrometallurgy), 1, 40-46.
4. Kravchuk M. V., Ustinov A. I (2015) Influence of thermodynamic and structural parameters of multi-layer foils on the characteristics of the SHS reaction. Avtomat. svarka (Automatic welding) 8, 10-15.
5. Farlow S. J. (1985). Partial Differential Equations for Scientists and Engineers. John Wiley & Sons, New York.
6. Tihonov А. N., Samarsky A. A. (1977). Partial Differential Equations. Moscow: Nauka. (in Rus.)
7. Methews J. H., Fink K. K. (2004). Numerical Methods Using MATLAB (4th Edition) Prentice - Hall, Upper Saddle River, NJ.
8. Stukowski A. (2010). Visualization and analysis of atomistic simulation data with OVITO - the Open Visualization Tool. Modelling Simul. Mater. Sci. Eng., 18, 015012
9. Smith P. R. (1981). Bilinear interpolation of digital images. Ultramicroscopy, 6, 201-204.