On the issues of optimization and regulation of the convective drying process of materials in drying units
Keywords:
Mathematical modeling, drying, capillary-porous body, dispersed materials, gas-suspended state, fluidization, relative moisture content, stress, optimization, heat and mass transfer, deformation, anisotropy, numerical methodsSynopsis
The chapter presents the main approaches to optimizing and regulating the drying process of materials, taking into account the structural characteristics and operating principles of drying equipment. An essential factor in optimizing such processes is the consideration of the drying object and the mathematical methods used to describe drying problems. To this end, widely applied practical methods of mathematical modeling of capillary-porous and dispersed materials are analyzed, along with the specific features of models that describe heat and mass transfer in such materials.
Particular attention is given to the role of diffusion and thermo-diffusion mechanisms in moisture transfer regulation. Optimization strategies are developed using fundamental drying principles, where the Kirpichov criterion provides a quantitative assessment of moisture transport dynamics, while Nusselt numbers serve as key parameters for controlling temperature gradients and ensuring efficient moisture removal. Additionally, the Postnov criterion is used as a means of evaluating the balance between temperature gradients and moisture content distribution, helping to prevent excessive stress accumulation that may lead to cracking. The study further explores empirical relationships between these criteria and essential process parameters, including moisture content, temperature, and airflow velocity, to enhance drying efficiency and maintain structural integrity.
The study investigates the peculiarities of constructing mathematical models of non-isothermal moisture transfer and deformation during the drying of capillary-porous, dispersed, and fractal-structured materials from the perspective of continuum mechanics, mixture theory, and statistical approaches. This allows for the broadest possible range of model implementations, accounting for the anisotropy of thermomechanical properties, elastic and viscoelastic behavior, material shrinkage, and other relevant factors.
References
Nigmatulin, R. I. (1978). Osnovy mekhaniki geterogennykh sred. Moscow: Nauka, 336.
Gamaiunov, S. N., Misnikov, O. S. (1988). Usadochnye iavleniia pri sushke prirodnykh organomineralnykh dispersii. Inzhenerno-fizicheskii zhurnal, 71 (2), 233–236.
Mushtaev, V. I.; Planovskii, A. N. (Ed.) (1971). Osnovnye teoreticheskie polozheniia konvektivnoi sushki i utochnennyi metod rascheta sushilnykh apparatov. Moscow: MIKhM, 81.
Mushtaev, V. I., Ulianov, V. M. (1988). Sushka dispersnykh materialov. Moscow: Khimiia, 352.
Likov, A. V. (1968). Teoriia sushki. Moscow: Energiia, 472.
Sazhin, B. S. (1984). Osnovy tekhniki sushki. Moscow: Khimiia, 320.
Laitfud, U. (1977). Iavleniia perenosa v zhivykh sistemakh. Moscow: Mir, 210.
Tutova, E. G., Grinchik, N. N. (1984). Mekhanizm massoperenosa pri obezvozhivanii slozhnykh biologicheskikh sistem. Teplomassoobmen – 6. Vol. 7. Minsk: ITMO AN BSSR, 25–28.
Grinchik, N. N. (1991). Protcessy perenosa v poristykh sredakh, elektrolitakh i membranakh. Minsk: ITMO im. A. V. Likova AN BSSR, 251.
Lutcik, L. P., Litevchuk, D. P. (1984). Vliianie porovoi struktury na pronitcaemost kapilliarno-poristykh tel. Teplomassoobmen – 6. Vol. 7. Minsk: ITMO AN BSSR, 74–77.
Likov, A. V. (1970). Metody resheniia nelineinykh uravnenii nestatcionarnoi teploprovodnosti. Izv. AN SSSR, Energetika i transport, 25, 109.
Zhuravleva, V. P. (1972). Masso-teploperenos pri termoobrabotke i sushke kapilliarno-poristykh stroitelnykh materialov. Minsk, 189.
Zhuravleva, V. P. (1971). Issledovanie protcessa obrazovaniia dispersnykh struktur. Minsk, 5, 35–40.
Kutc, P. S., Grinchik, N. N. (1984). Teplo- i massoperenos v kapilliarno-poristykh telakh pri intensivnom paroobrazovanii s uchetom dvizheniia fronta ispareniia. Teplomassoobmen – 6. Vol. 7. Minsk: ITMO AN BSSR, 93–96.
Lutcik, P. P. (1985). Uravneniia teorii sushki deformiruemykh tverdykh tel. Promyshlennaia teplotekhnika, 7 (6), 20.
Lutcik, P. P. (1984). Massotermicheskoe deformirovanie kapilliarno-poristykh kolloidnykh tel v protcessakh sushki. Teplomassoobmen – VII. Vol. 6. Minsk: ITMO AN BSSR, 90.
Haivas, B. I. (2010). Pro opys lokalnoho stanu kapiliarno-porystykh ta shchilno upakovanykh zernystykh materialiv v protsesi sushinnia. Chastyna I. Modeliuvannia ta informatsiini tekhnolohii. Kyiv: Instytut problem modeliuvannia v enerhetytsi im. H.Ie. Pukhova NAN Ukrainy, 57, 95–104.
Haivas, B. I. (2010). Kliuchova systema rivnian dlia doslidzhennia protsesu sushinnia porystykh til. Chastyna 2. Modeliuvannia ta informatsiini tekhnolohii. Kyiv: Instytut problem modeliuvannia v enerhetytsi im. H. Ye. Pukhova NAN Ukrainy, 58, 116–125.
Haivas, B. (2010). Matematychne modeliuvannia konvektyvnoho sushinnia materialiv z urakhuvanniam mekhanotermodyfuziinykh protsesiv. Fizyko-matematychne modeliuvannia ta informatsiini tekhnolohii. Lviv: TsMM IPPMM im. Ya.S. Pidstryhacha NAN Ukrainy, 12, 9–37.
Hayvas, B., Torskyy, A., Chapla, Y. (2012). On an approach to solution of problems of porous bodies drying. Fizyko-matematychne modeliuvannia ta informatsiini tekhnolohii. Lviv: TsMM IPPMM im. Ya.S. Pidstryhacha NAN Ukrainy, 16, 42–51.
Haivas, B., Boretska, I. (2011). Vplyv rezhymu sushylnoho ahenta na osushennia porystykh til. Kompiuterni tekhnolohii drukarstva, 26, 231–240.
Romankov, P. G., Rashkovskaia, N. B. (1968). Sushka vo vzveshennom sostoianii. Lvіv: Khimiia, 360.
Teplitckii, Iu. S. (2002). Diagramma fazovogo sostoianiia dispersnoi sistemy s voskhodiashchim potokom gaza. Inzhenerno-fizicheskii zhurnal, 75 (1), 117–121.
Kalenderian, V. A., Karnaraki, V. V. (1982). Teploobmen i sushka v dvizhushchemsia plotnom sloe. Kyiv: Vishcha shkola, 160.
Buevich, Iu. A., Bugkov, V. V. (1978). O sluchainykh pulsatciiakh v grubodispersnom psevdoozhizhennom sloe. Inzhenerno-fizicheskii zhurnal, 35 (6), 1089–1097.
Buevich, Iu. A., Korolev, V. N. (1991). Obtekanie tel i vneshnii teploobmen v psevdoozhizhennom sloe. Sverdlovsk: Izd. Uralskogo universiteta, 188.
Nagornov, S. A. (2002). Upravlenie protcessami perenosa teploty v neodnorodnykh psevdoozhizhennykh i vibrotcirkuliatcionnykh sredakh. Tambov: GNU VIITKN, 101.
Razumov, I. M. (1972). Psevdoozhizhenie i pnevmotransport sypuchikh materialov. Moscow: Khimiia, 240.
Antonishin, N. V., Geller, L. A., Ivaniutenko, I. I. (1982). Teploperedacha v psevdoturbulentnom sloe dispersnogo materiala. Inzhenerno-fizicheskii zhurnal, 43 (3), 360–364.
Kheifetc, L. I., Neimark, F. M. (1982). Mnogofaznye protcessy v poristykh sredakh. Moscow: Khimiia, 320.
Akulich, P. V., Milittcer, K. U. (1998). Modelirovanie neizotermicheskogo vlagoperenosa i napriazhenii v drevesine pri sushke. Inzhenerno-fizicheskii zhurnal, 71 (3), 404–411.
Shubin, G.S. (1985). Sushka i teplovaia obrabotka drevesiny. [Extended abstract of Doctoral thesis].
Shimanskii, V. M. (2015). Matematichne modeliuvannia neіzotermіchnogo vologoperenesennia ta v’iazkopruzhnogo deformuvannia u seredovishchakh z fraktalnoiu strukturoiu. [Extended abstract of PhD thesis].
Sokolovskii, Ia. І., Shimanskii, V. M. (2011). Dvovimіrna matematichna model vologoperenosu u kapіliarno-poristikh materіalakh z fraktalnoiu strukturoiu. Naukovii vіsnik NLTU Ukraini, 21 (2), 341–348.
Voronov, V. G., Mikhailetckii, Z. N. (1982). Avtomaticheskoe upravlenie protcessami sushki. Kyiv: Tekhnika, 109.
Gayvas, B., Markovych, B., Dmytruk, A., Havran, M., Dmytruk, V. (2024). The methods of optimization and regulation of the convective drying process of materials in drying installations. Mathematical Modeling and Computing, 11 (2), 546–554. https://doi.org/10.23939/mmc2024.02.546
Dmytruk, A. (2024). Modeling mass transfer processes in multicomponent capillary-porous bodies under mixed boundary conditions. Mathematical Modeling and Computing, 11 (4), 978–986. https://doi.org/10.23939/mmc2024.04.978
Sokolovskyy, Y., Drozd, K., Samotii, T., Boretska, I. (2024). Fractional-Order Modeling of Heat and Moisture Transfer in Anisotropic Materials Using a Physics-Informed Neural Network. Materials, 17 (19), 4753. https://doi.org/10.3390/ma17194753
Decker, Ž., Tretjakovas, J., Drozd, K., Rudzinskas, V., Walczak, M., Kilikevičius, A. et al. (2023). Material’s Strength Analysis of the Coupling Node of Axle of the Truck Trailer. Materials, 16 (9), 3399. https://doi.org/10.3390/ma16093399
Gayvas, B. I., Markovych, B. M., Dmytruk, A. A., Havran, M. V., Dmytruk, V. A. (2023). Numerical modeling of heat and mass transfer processes in a capillary-porous body during contact drying. Mathematical Modeling and Computing, 10 (2), 387–399. https://doi.org/10.23939/mmc2023.02.387
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Pages
158-197
Published
March 31, 2025
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Copyright (c) 2025 Bogdana Gayvas, Bogdan Markovych, Anatolii Dmytruk, Veronika Dmytruk
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ISBN-13 (15)
978-617-8360-09-2
How to Cite
Dmytruk, V., Gayvas, B., Markovych, B., & Dmytruk, A. (2025). On the issues of optimization and regulation of the convective drying process of materials in drying units. In V. Dmytruk & B. Gayvas (Eds.), DRYING PROCESSES: APPROACHES TO IMPROVE EFFICIENCY (pp. 158–197). Kharkiv: TECHNOLOGY CENTER PC. https://doi.org/10.15587/978-617-8360-09-2.ch5
