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Computer Research and Modeling, 2019, Volume 11, Issue 4, Pages 613–630
DOI: https://doi.org/10.20537/2076-7633-2019-11-4-613-630
(Mi crm732)
 

This article is cited in 5 scientific papers (total in 5 papers)

MODELS IN PHYSICS AND TECHNOLOGY

Hierarchical method for mathematical modeling of stochastic thermal processes in complex electronic systems

A. G. Madera

Scientific Research Institute for System Analysis, Russia Academy of Sciences, 36/1 Nakhimovsky Prospekt, Moscow, 117218, Russia
References:
Abstract: A hierarchical method of mathematical and computer modeling of interval-stochastic thermal processes in complex electronic systems for various purposes is developed. The developed concept of hierarchical structuring reflects both the constructive hierarchy of a complex electronic system and the hierarchy of mathematical models of heat exchange processes. Thermal processes that take into account various physical phenomena in complex electronic systems are described by systems of stochastic, unsteady, and nonlinear partial differential equations and, therefore, their computer simulation encounters considerable computational difficulties even with the use of supercomputers. The hierarchical method avoids these difficulties. The hierarchical structure of the electronic system design, in general, is characterized by five levels: Level 1 — the active elements of the ES (microcircuits, electro-radio-elements); Level 2 — electronic module; Level 3 — a panel that combines a variety of electronic modules; Level 4 — a block of panels; Level 5 — stand installed in a stationary or mobile room. The hierarchy of models and modeling of stochastic thermal processes is constructed in the reverse order of the hierarchical structure of the electronic system design, while the modeling of interval-stochastic thermal processes is carried out by obtaining equations for statistical measures. The hierarchical method developed in the article allows to take into account the principal features of thermal processes, such as the stochastic nature of thermal, electrical and design factors in the production, assembly and installation of electronic systems, stochastic scatter of operating conditions and the environment, nonlinear temperature dependencies of heat exchange factors, unsteady nature of thermal processes. The equations obtained in the article for statistical measures of stochastic thermal processes are a system of 14 nonstationary nonlinear differential equations of the first order in ordinary derivatives, whose solution is easily implemented on modern computers by existing numerical methods. The results of applying the method for computer simulation of stochastic thermal processes in electron systems are considered. The hierarchical method is applied in practice for the thermal design of real electronic systems and the creation of modern competitive devices.
Keywords: stochastic, thermal process, statistical measures, mathematical modeling, electronic systems.
Received: 14.03.2019
Revised: 14.05.2019
Accepted: 22.05.2019
Document Type: Article
UDC: 536.24: 621.396
Language: Russian
Citation: A. G. Madera, “Hierarchical method for mathematical modeling of stochastic thermal processes in complex electronic systems”, Computer Research and Modeling, 11:4 (2019), 613–630
Citation in format AMSBIB
\Bibitem{Mad19}
\by A.~G.~Madera
\paper Hierarchical method for mathematical modeling of stochastic thermal processes in complex electronic systems
\jour Computer Research and Modeling
\yr 2019
\vol 11
\issue 4
\pages 613--630
\mathnet{http://mi.mathnet.ru/crm732}
\crossref{https://doi.org/10.20537/2076-7633-2019-11-4-613-630}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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