Interval-Stochastic Thermal Processes in Electronic Systems: Analysis and Modeling

Journal of Engineering Thermophysics. 2017. Vol. 26. No. 1. P. 17–28.

Madera A. G.

Mathematical and computer modeling of the 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 stochastic and nonlinearly depend on both the stochastic determining factors and on 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 system elements with given statistical measures of the initial interval-stochastic determining factors.

Keywords: mathematical modeling, thermal processes, expectations, electronic systems, interval stochastic, variances, covariances