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Interval-stochastic thermal processes in electronic systems: Modeling in practice


Mathematical and computer modeling of thermal processes, applied presently in thermal design of electronic systems, is based on the assumption that the factors determining the thermal processes are completely known and uniquely determined, that is, they are deterministic. Meanwhile, practice shows that the determining factors are of indeterminate interval-stochastic character. Moreover, thermal processes in electronic systems are nonstationary and nonlinearly depend on both the stochastic determining factors and the temperatures of electronics elements and environment. At present, the literature does not present methods of mathematical modeling of nonstationary, stochastic, nonlinear, interval-stochastic thermal processes in electronic systems to model thermal processes, which satisfy all the above-listed requirements to modeling adequacy. The present paper develops a method of mathematical and computer modeling of the nonstationary interval-stochastic nonlinear thermal processes in electronic systems. The method is based on obtaining equations describing the dynamics of time variation of statistical measures (expectations, variances, covariances) of temperature of electronic systemelements with given statistical measures of the initial interval-stochastic determining factors. A practical example of applying the developed approach to a the real electronic system is given.

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  1. 1.

    Adomian, G., Stochastic Systems, New York: Academic Press, 1983.

    MATH  Google Scholar 

  2. 2.

    Madera, A.G., Interval-Stochastic Thermal Processes in Electronic Systems: Analysis and Modeling, J. Eng. Therm., 2017, vol. 26, no. 1, pp. 17–28.

    Article  Google Scholar 

  3. 3.

    Madera, A.G. and Kandalov, P.I., Modeling of Three-Dimensional Temperature Fields in ElectronicsModules, Prog. Prod. Syst., 2010, no. 2, pp. 29–33.

    Google Scholar 

  4. 4.

    Pugachev, V.S., Teoriya sluchainykh funktsii (Theory of Random Functions), Moscow: Nauka, 1962.

    Google Scholar 

  5. 5.

    Chekanov, A.N., Raschety i obespechenie nadezhnosti elektronnoi apparatury (Calculations and Reliability Control of Electronic Equipment), Moscow: KNORUS, 2012.

    Google Scholar 

  6. 6.

    Ellison, G.N., Thermal Computations for Electronics, Conductive, Radiative, and Convective Air Cooling, New York: CRC Press, 2011.

    Google Scholar 

  7. 7.

    Madera, A.G., Simulation of Stochastic Heat Conduction Processes, Int. J. Heat Mass Transfer, 1994, vol. 37, no. 16, pp. 2571–2577.

    Article  MATH  Google Scholar 

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Correspondence to A. G. Madera.

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Madera, A.G. Interval-stochastic thermal processes in electronic systems: Modeling in practice. J. Engin. Thermophys. 26, 29–38 (2017).

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