A method for solving the heat conduction problem for continuously discrete rod systems

Kravchenko, V. I.; Shut, N. I.

doi:10.1007/bf02660700

Cited by 1 publication

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“…In mathematical terms, this leads to the study of boundary problems, where the solution of the problem must satisfy not only the differential equation and the boundary conditions but also an additional system of conjugation conditions, imposed on this solution. Such system takes into account the transition of the heat flow from one physical environment to another one with other physical parameters, i. e., to the study of the class of continuous-discrete boundary problems [3]- [4].…”

Section: Statement Of the Research Taskmentioning

confidence: 99%

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Continuous-Discrete Boundary Problems in the Concepts of the Construction of Foundry Rotary-Conveyor Lines

Kravchenko

Mul

Tokova³

2019

BFPCS

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The problem of mathematical construction for the process of the control of the metal casting crystallization and cooling in a foundry mold is considered. The casting is surrounded by a layer of sand mixture, which is a porous dispersed medium that conducts heat, in terms of the concepts of the construction of foundry rotary-conveyor lines (RCL). The problem of developing an interval model for determining the speed of the conveyor line from the production of metal castings is studied. Herewith, continuous processes of the transport and technological movement of the processed materials, equipment, tools, energy carriers, and final production output are combined with inevitable stops of this continuity, which lead to discreteness, and a combination with a number of accompanying continuous, discrete or reciprocating processes. The adequacy of the model for the given technological parameters is justified. The mathematical description and agreement of the values of technological parameters for regulation and finding the optimal speed of the conveyor line at the interaction of its component rotational systems, as well as the mathematical models for program control and remote monitoring of technological modes in order to obtain the casting of the given quality are considered. The possibility of selecting the corrective parameters for the change of the conveyor line speed is shown. Tiek skatīta matemātiskās konstrukcijas problēma metāla liešanas kristalizācijas un dzesēšanas kontroles procesam liešanas veidnē. Lējumu ieskauj smilšu maisījuma slānis, kas ir poraini izkliedēts materiāls, kas vada siltumu. Lietojot lietuves rotācijas konveijeru līniju (RCL) koncepciju, tiek pētīta intervāla modeļa izveides problēma konveijera līnijas ātruma noteikšanai metāla lējumu ražošanai. Tajā pašā laikā nepārtraukti apstrādājamo materiālu, iekārtu, rīku, enerģijas nesēju un gala produkcijas transportēšanas un tehnoloģiskās kustības procesi tiek apvienoti ar šīs nepārtrauktības neizbēgamajiem apstāšanās gadījumiem, kas noved pie kombinācijas ar vairākiem nepārtrauktiem, diskrētiem vai pārvietošanās procesiem. Ir pierādīta modeļa piemērotība attiecīgajiem tehnoloģiskajiem parametriem. Tiek parādīta iespēja izvēlēties koriģējošos parametrus konveijera līnijas ātruma maiņai.

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Section: Statement Of the Research Taskmentioning

confidence: 99%

“…Considering the system (6) as a structurally heterogeneous one [3]- [4], to the system of equations (6) we add the system of additional interrelations, which is the system of conjugation conditions of the following form: (7) where k = 1, 2; i = 1, … ; t  0.…”

Section: Analysis Of the Controllability Of The Thermophysical Fimentioning

confidence: 99%