Some Analytic Solutions for Stochastic Reactor Models Based on the Joint Composition PDF
Authors
- Fey, Harald
- Kraft, Markus
ORCID: 0000-0002-4293-8924
2010 Mathematics Subject Classification
- 60K40 35L99
Keywords
- Probability density function transport equation, analytic solution, stochastic reactor models, partially stirred reactor, partially stirred plug flow reactor
DOI
Abstract
The stochastic reactor models Partially Stirred Reactor (PaSR) and Partially Stirred Plug Flow Reactor (PaSPFR) have been investigated. These models are based on a simplified joint composition PDF transport equation. Analytic solutions for five different Cauchy problems for the PDF transport equation as given by the stochastic reactor models are presented. In all cases, molecular mixing in the stochastic reactor models is described by the LMSE mixing model. The analytic solutions have been found by combining the method of characteristics with a set of ordinary differential equations for the statistical moments to account for the functional dependence of the coefficients in the corresponding PDF transport equation. For each case an example problem is discussed to illustrate the behavior of the analytic solution.
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