Mathematical modeling of the interval stochastic thermal processes in technical systems at the interval indeterminacy of the determinative parameters

Madera A.G., Kandalov P.I.
 pdf (753K)  / List of references

The currently performed mathematical and computer modeling of thermal processes in technical systems is based on an assumption that all the parameters determining thermal processes are fully and unambiguously known and identified (i.e., determined). Meanwhile, experience has shown that parameters determining the thermal processes are of undefined interval-stochastic character, which in turn is responsible for the intervalstochastic nature of thermal processes in the electronic system. This means that the actual temperature values of each element in an technical system will be randomly distributed within their variation intervals. Therefore, the determinative approach to modeling of thermal processes that yields specific values of element temperatures does not allow one to adequately calculate temperature distribution in electronic systems. The interval-stochastic nature of the parameters determining the thermal processes depends on three groups of factors: (a) statistical technological variation of parameters of the elements when manufacturing and assembling the system; (b) the random nature of the factors caused by functioning of an technical system (fluctuations in current and voltage; power, temperatures, and flow rates of the cooling fluid and the medium inside the system); and (c) the randomness of ambient parameters (temperature, pressure, and flow rate). The interval-stochastic indeterminacy of the determinative factors in technical systems is irremediable; neglecting it causes errors when designing electronic systems. A method that allows modeling of unsteady interval-stochastic thermal processes in technical systems (including those upon interval indeterminacy of the determinative parameters) is developed in this paper. The method is based on obtaining and further solving equations for the unsteady statistical measures (mathematical expectations, variances and covariances) of the temperature distribution in an technical system at given variation intervals and the statistical measures of the determinative parameters. Application of the elaborated method to modeling of the interval-stochastic thermal process in a particular electronic system is considered.

Keywords: mathematical modelling, thermal process, technical system, interval, stochastic, non-linear, unsteady, statistical measures, mathematical expectation, variance, covariance
Citation in English: Madera A.G., Kandalov P.I. Mathematical modeling of the interval stochastic thermal processes in technical systems at the interval indeterminacy of the determinative parameters // Computer Research and Modeling, 2016, vol. 8, no. 3, pp. 501-520
Citation in English: Madera A.G., Kandalov P.I. Mathematical modeling of the interval stochastic thermal processes in technical systems at the interval indeterminacy of the determinative parameters // Computer Research and Modeling, 2016, vol. 8, no. 3, pp. 501-520
DOI: 10.20537/2076-7633-2016-8-3-501-520
URL: http://crm-en.ics.org.ru/journal/article/2468/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
According to Crossref, this article is cited by:
  • Alexander Georgievitch Madera. Modeling thermal feedback effect on thermal processes in electronic systems. // Computer Research and Modeling. — 2018. — V. 10, no. 4. — P. 483. DOI: 10.20537/2076-7633-2018-10-4-483-494
Please note that citation information may be incomplete as it includes data from Crossref cited-by program partners only.
Views (last year): 15. Citations: 6 (RSCI).

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Copyright © 2009–2024 Institute of Computer Science