Stability and Stabilization of the Solidification Front for Melt Flow in Cylindrical Channel with Phase Change on a Wall. Part 2 IVAN V. KAZACHKOV 1,2 1 Dept of Energy Technology, Royal Institute of Technology, Stockholm, 10044, SWEDEN, Ivan.Kazachkov@energy.kth.se, http://www.kth.se/itm/inst?l=en_UK 2 Dept of Applied Mathematics, Informatics and Educational Measurements, Nizhyn Gogol State University, UKRAINE, http://www.ndu.edu.ua Abstract: - Based on the mathematical model developed and analyzed in the Part 1, further analysis and computer simulation is performed as concern to peculiarities of the stability and possible stabilization of the unstable modes for interfacial boundary in the cylindrical channel, where melt is moving with solidification on the walls. Thin solid film on the walls is called garnissage, which is useful for the walls’ protection against destroying from high-temperature and chemically aggressive melts and for the keeping the transported melt in a pure state, without pollution from the particles of the walls. The results may be of interest both theoretically (in stabilization of the processes in continua), as well as practically (in metallurgical aggregate machines). Key-Words: - Control, Garnissage, Instability, Stabilization, Solidification, Melt, Wall, Protection, Channel 1 Introduction More complex physical situations comparing to the ones considered in the Part 1, in which suppression of the parametric oscillations of the system by considered simple approaches is impossible, is analyzed in this paper. As an example the results of calculations by the model obtained for the following values of parameters: 1 4, 33 cal / ( ) ms К    , 3 2 7,8 10    kg/m 3 , 0 R =0,1m, 21 65   kcal/kg are presented in the Table 1: Table 1 Dependence of exponential ( e  ) by different crystallization temperatures: values decrease exponentially e  times k  , Hz by T  , К 293 333 373 10 0,17 0,51 0,85 10 2 1,70 5,10 8,50 10 3 17,0 51,0 85,0 From the table it is visible, which is the influence of physical statements of the problem on the fading rate of parameters’ perturbations of the studied system. So, at 3 10 k  in time, equal to one second, the perturbation amplitude of parameters decreases in e 85 time if temperature of crystallization makes 373K. With increase of T  (decrease of entropy of system), stability of system increases. According to the Table 1 it is possible to estimate characteristic fading time of fluctuations of the parameters of physical system (technological process) in each case. Even when the system is steady, at slow fading of casual (or regular) perturbations of its parameters it is expedient to use the automatic heat flux control systems for acceleration of the process of parametric fluctuations’ suppression. Because the technological mode in some cases demands maintenance of characteristics of process in strictly set limits (special metallurgy, protection of lining of metallurgical units against thermal and chemical destruction, etc.). As shown in the Part 1, general information about the nature of spreading of parametric oscillations on the boundaries of melt crystallization and stability of system can be received from the analysis of the differential equations making mathematical model of the physical phenomenon. In more complex systems considered below such analysis isn't always possible, but application of asymptotic decompositions of the functions sought in a series by the small parameter  (Eigen values of a task) is effective. In a lack of experimental data about physical process it is difficult to estimate an adequacy to the constructed mathematical model and solutions of a task received on its basis to the real physical object. Therefore especially important is the question of reliability of the applied technique of researches, which is closely connected with adequacy of I. V. Kazachkov International Journal of Theoretical and Applied Mechanics http://www.iaras.org/iaras/journals/ijtam ISSN: 2367-8984 124 Volume 1, 2016