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Abstract
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.
Highlights
The catalytic synthesis processes are generally accompanied by heat release
Exceeding heat generation over heat transfer leads to uncontrolled growth temperature
In this paper we propose a method for direct numerical modeling of a random temperature of granule with internal heat generation with accounted temperature fluctuations in the surrounding
Summary
The catalytic synthesis processes are generally accompanied by heat release. Synthesis of heavy hydrocarbons in the Fischer-Tropsch process (GTL technology) is associated with essential heat generation [1]. The situation drastically changes when the temperature of the environment is a random process In this case there is always a non-zero probability for a temperature fluctuation, the magnitude of which exceeds a critical value, which may lead to the loss of thermal stability. Study of random temperature fluctuations was carried out in the framework of probability density function approach [12] This approach requires the use of modern methods of stochastic processes and functional analysis and yields results which have practical importance. In this paper we propose a method for direct numerical modeling of a random temperature of granule with internal heat generation with accounted temperature fluctuations in the surrounding. We write down the equation for the temperature of the granule with internal heat source and perform the analysis of Semenov’s diagram
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