Mathematical and computermodeling 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 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 intervalstochastic 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.
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Adomian, G., Stochastic Systems, New York: Academic Press, 1983.
Dobronets, B.S and Zlobin, V.S., Numerical Modeling of Temperature Fields with Interval Uncertainties, Sib. Zh. Ind. Math., 2004, vol. 7, no. 3(19), pp. 95–101.
Dulnev, G.N., Teplovye rezhimy elektronnoi apparatury (Thermal Conditions of Electronics), Leningrad: Energiya, 1971.
Gyarmati, I., Non-Equilibrium Thermodynamics. Field Theory and Variational Principles, New York: Springer-Verlag, 1970.
Konstruktorsko-tekhnologicheskoe proektirovanie elektronnoi apparatury (Technological Design of Electronics), Shakhnov, V.A., Ed., Moscow: Bauman MGTU, 2005.
Madera, A.G., Modelirovanie teploobmena v tekhnicheskikh sistemakh (Modeling of Heat Transfer in Engineering Systems), Moscow: Melnikov NF, 2005.
Madera, A.G. and Kandalov, P.I., Modeling of Temperature Fields of Technical Systems under Interval Uncertainty, Tepl. Prots. Tekhn., 2014, vol. 6, pp. 225–229.
Madera, A.G. and Kandalov, P.I., Analysis of Interval-Stochastic Temperature Fields of Technical Systems, Prog. Prod. Sist., 2014, no. 4, pp. 41–45.
Madera, A.G. and Kandalov, P.I., Computer Modeling of Temperature Fields of Technical Systems under Interval-Stochastic Uncertainty of Parameters, Prikl. Inf., 2015, vol. 10, no. 1(55), pp. 106–113.
Pugachev, V.S., Teoriya sluchainykh funktsii (Theory of Random Functions), Moscow: Nauka, 1962.
Chekanov, A.N., Raschety i obespechenie nadezhnosti elektronnoi apparatury (Calculations and Reliability Control of Electronic Equipment), Moscow: KNORUS, 2012.
Campo, A. and Yishimura, T., Random Heat Transfer in Flat Channels with Timewise Variation of Ambient Temperature, Int. J. HeatMass Transfer, 1979, vol. 22, pp. 5–12.
Chantasiriwan, S., Error and Variance of Solution to the Stochastic Heat Conduction Problem by Multiguadric Collocation Method, Int. Comm. HeatMass Trans., 2006, no. 33, pp. 342–349.
Ellison, G.N., Thermal Computations for Electronics, Conductive, Radiative, and Convective Air Cooling, New York: CRC Press, 2011.
Emery, A.F., Solving Stochastic Heat Transfer Problems, Eng. An. Bound. Elem., 2004, no. 8, pp. 279–291.
Georgiadis, J.G., On the Approximate Solution on Non-deterministic Heat and Mass Transport Problems, Int. J. HeatMass Transfer, 1991, vol. 33, no. 8, pp. 2099–2105.
Keller, C.J. and Antonetti, V.W., Statistical Thermal Design for Computer Electronics, El. Pack. Prod., 1979, vol. 19, no. 3, pp. 55–62.
Madera, A.G., Modeling of Stochastic Heat Transfer in a Solid, Appl. Math. Model., 1993, vol. 17, no. 12, pp. 664–668.
Madera, A.G., Simulation of Stochastic Heat Conduction Processes, Int. J. Heat Mass Transfer, 1994, vol. 37, no. 16, pp. 2571–2577.
Madera, A.G., Heat Transfer from an Extended Surface at a Stochastic Heat-Transfer Coefficient and Stochastic Environmental Temperature, Int. J. Eng. Sci., 1996, vol. 34, no. 9, pp. 1093–1099.
Madera, A.G. and Sotnikov, A.N., Method for Analyzing Stochastic Heat Transfer in a Fluid Flow, Appl. Math.Model., 1996, vol. 20, no. 8, pp. 588–592.
Nakamura, T. and Fujii, K., Probabilistic Transient Thermal Analysis of an Atmospheric Reentry Vehicle Structure, Aero Sci., Tech., 2006, no. 10, pp. 346–354.
Padovan, J. and Guo, Y.H., Solution of Non-deterministic Finite Element and Finite Difference Heat conduction Simulations, Num. Heat Trans. A, 1989, vol. 15, pp. 383–398.
Saleh, M.M., El-Kalla, I.L., and Ehab, M.M, Stochastic Finite Element Technique for Stochastic One-Dimension Time-DependentDifferential Equations withRandomCoefficients, Dif. Eq.Nonlin. Mech., 2007, art. ID 48527.
Samuels, J.C., Heat Conduction in Solids with Random External Temperatures and/or Random Internal Heat Generation, Int. J. Heat Mass Transfer, 1966, vol. 9, pp. 301–314.
Scheerlinck, N., Verboven, P., Stigter, J.D., Baerdemaeker, J.D., Impe, J.F.V., and Nicolai, B.M., Stochastic Finite-Element Analysis of CoupledHeat and Mass Transfer Problems with Random Field Parameters, Num. Heat Transfer B, 2000, no. 37, pp. 309–330.
Srivastava, K., Modeling the Variability of Heat Flow due to the Random Thermal Conductivity of Crust, Geophys J. Int., 2005, no. 160, pp. 776–782.
Stefanou, G., The Stochastic Finite Element Method: Past, Present and Future, Comput. Meth. Appl. Mech. Eng., 2009, no. 198, pp. 1031–1051.
Tzow Da Yu, Stochastic Analysis of Temperature Distribution in a Solid with Random Heat Conductivity, Trans. ASME, J. Heat Transfer, 1988, vol. 110, pp. 23–29.
Yoshimura, T. and Campo, A., Extended Surface Heat Rejection Accounting for Stochastic Sink Temperatures, AIAA J., 1981, vol. 19, pp. 221–225.
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Madera, A.G. Interval-stochastic thermal processes in electronic systems: Analysis and modeling. J. Engin. Thermophys. 26, 17–28 (2017). https://doi.org/10.1134/S1810232817010039