Araştırma Makalesi
Yıl 2019,
Cilt: 68 Sayı: 2, 2050 - 2063, 01.08.2019
Öz
In this paper, the fuzzy Markov chain method is proposed as a new discrete solution of a population balance equation for an aggregation process. In order to validate the proposed method, analytical solution of an aggregation equation is compared with the fuzzy Markov chain method for the constant aggregation kernel. According to the results, if the size range of the system is divided into a sufficient number of states and an appropriate transition time step is chosen, then the fuzzy Markov chain method displays a good approximation for the particle size distribution(PSD) while the main equation is driven by a constant aggregation kernel.
Anahtar Kelimeler
Kaynakça
- Hidy, G. M., and Lilly, D.K., Solutions to the Equations for the Kinetics of Coagulation, Journal of Colloid Science. 20 (1965), 867.
- Gelbard, F.M., and Seinfeld, J.H., Simulation of Multicomponent Aerosol Dynamics, Journal of Colloid and Interface Science.78 (1980), 485.
- Hounslow, M.J., The population balance as a tool for understanding particle rate processes, Kona. 16 (1998). 179-193.
- Hill, P. J., and Ka M. Ng., New discretization procedure for the agglomeration equation, AIChE journal. 42.3 (1996), 727-741.
- Vanni, M., Approximate Population Balance Equations for Aggregation-Breakage Processes, Journal of Colloid and Interface Science, 221 (2000), 143-160.
- Ramkrishna, D., Population Balances Theory and applications to Particulate Systems in Engineering, Academic Press, USA, 2000.
- Snow, R.H., Terry, A., Ennis, B., J., and Lister, J.D., Size reduction and size en-largement. Perry's chemical engineering's' handbook, 7th edition, McGraw-Hill, USA, 1997.
- Berthiaux, H., and Mizonov, V., Applications of Markov Chains in Particulate Process Engineering: A Review, The Canadian Journal of Chemical Engineering. 82, (2004),1143-1168.
- Norris, J.R.,Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 1997.
- Farina, L., and Rinaldi, S., Positive Linear Systems: Theory and Application, Wiley, 2000.
- Starczewski, J. T., Defuzzification of uncertain fuzzy sets in Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty, Springer, 2013.
Yıl 2019,
Cilt: 68 Sayı: 2, 2050 - 2063, 01.08.2019
Öz
Kaynakça
- Hidy, G. M., and Lilly, D.K., Solutions to the Equations for the Kinetics of Coagulation, Journal of Colloid Science. 20 (1965), 867.
- Gelbard, F.M., and Seinfeld, J.H., Simulation of Multicomponent Aerosol Dynamics, Journal of Colloid and Interface Science.78 (1980), 485.
- Hounslow, M.J., The population balance as a tool for understanding particle rate processes, Kona. 16 (1998). 179-193.
- Hill, P. J., and Ka M. Ng., New discretization procedure for the agglomeration equation, AIChE journal. 42.3 (1996), 727-741.
- Vanni, M., Approximate Population Balance Equations for Aggregation-Breakage Processes, Journal of Colloid and Interface Science, 221 (2000), 143-160.
- Ramkrishna, D., Population Balances Theory and applications to Particulate Systems in Engineering, Academic Press, USA, 2000.
- Snow, R.H., Terry, A., Ennis, B., J., and Lister, J.D., Size reduction and size en-largement. Perry's chemical engineering's' handbook, 7th edition, McGraw-Hill, USA, 1997.
- Berthiaux, H., and Mizonov, V., Applications of Markov Chains in Particulate Process Engineering: A Review, The Canadian Journal of Chemical Engineering. 82, (2004),1143-1168.
- Norris, J.R.,Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 1997.
- Farina, L., and Rinaldi, S., Positive Linear Systems: Theory and Application, Wiley, 2000.
- Starczewski, J. T., Defuzzification of uncertain fuzzy sets in Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty, Springer, 2013.
Toplam 11 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Ağustos 2019 |
| Gönderilme Tarihi | 21 Mart 2018 |
| Kabul Tarihi | 27 Haziran 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 68 Sayı: 2 |
Kaynak Göster
Cited By
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
