Dergiler / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 2

FUZZY MARKOV CHAINS MODELING OF AGGREGATION PROCESSES

FUZZY MARKOV CHAINS MODELING OF AGGREGATION PROCESSES

Nursin BAŞ ÇATAK

Sayfa
2050–2063
DOI
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Abstract

In this paper, the fuzzy Markov chain method is proposed as a newdiscrete solution of a population balance equation for an aggregation process.In order to validate the proposed method, analytical solution of an aggregationequation is compared with the fuzzy Markov chain method for the constantaggregation kernel. According to the results, if the size range of the systemis divided into a su¢ cient number of states and an appropriate transitiontime step is chosen, then the fuzzy Markov chain method displays a goodapproximation for the particle size distribution(PSD) while the main equationis driven by a constant aggregation kernel.