Method for numerical simulation of the temperature of
granule with internal heat release in a medium with random temperature
fluctuations is proposed. The method utilized the solution of a system of
ordinary stochastic differential equations describing temperature fluctuations
of the surrounding and granule. Autocorrelation function of temperature fluctuations
has a finite decay time. The suggested method is verified by the comparison
with exact analytical results. Random temperature behavior of granule with
internal heat release qualitatively differs from the results obtained in the
deterministic approach. Mean first passage time of granules temperature
intersecting critical temperature is estimated at different regime parameters.
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