1. MMC
  2. All Volumes and Issues
  3. Volume 8, Number 4, 2021
  4. Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

MMC.
2021;
Volume 8, Number 4
: pp. 830–841
https://doi.org/10.23939/mmc2021.04.830
Received: March 29, 2021
Revised: October 15, 2021
Accepted: November 09, 2021

Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 830–841 (2021)

Authors:
  1. Ya. I. Sokolovskyy
  2. I. B. Boretska
  3. B. I. Gayvas
  4. I. M. Kroshnyy
  5. A. V. Nechepurenko
1
Lviv Polytechnic National University, Lviv, Ukraine
2
Ukrainian National Forestry University
3
Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
4
Ukrainian National Forestry University
5
Ukrainian National Forestry University

The article deals with constructing and implementing mathematical models of non-isothermal moisture transfer during drying of anisotropic capillary-porous materials, in particular wood, taking into account the movement of the evaporation zone for non-steady drying schedules, as well as to the development of effective analytical and numerical methods for their implementation.  An analytical-numerical method for the determination of non-isothermal moisture transfer under non-steady schedules of the drying process has been developed, taking into account the dynamics of the phase transition boundary change.  Calculation relationships are established for determining the phase transition temperature taking into account transport gradients and time for which the relative saturation reaches the boundaries of the phase transition.

boundary of phase transition
non-isothermal moisture transfer
mathematical model
  1. John F. Sian.  Wood: influence of moisture on physical properties.  Virginia (2004).
  2. Lykov A. V.  Heat and mass transfer: a reference.  Energy, Moscow (1971), (in Russian).
  3. Grinchik N. N., Adamovich A. L., Kizina O. A., Kharma U. M.  Modeling of heat and moisture transfer in wood in finish drying by the energy of a microwave field.  Journal of Engineering Physics and Thermophysics. 88, 35–41 (2015).
  4. Igoshin D. E.  Model of drying a thin layer of moisture-porous medium.  Bulletin of Tyumen State University. 7, 20–28 (2013).
  5. Chemkhi S., Zagrouba F., Bellagi A.  Modelling and simulation of drying phenomena with rheological behavior.  Brazilian Journal of Chemical Engineering. 22 (2), 153–163 (2005).
  6. Arutunyan R. V.  Modeling of stochastic filtration processes in lattice systems.  Mathematical Modeling and Numerical Methods. 16, 17–30 (2017).
  7. De la Cruz-Lefevre R., Remond R., Aleon D., Perre P.  Effect of oscillating drying conditions on variations in the moisture content field inside wood boards.  Wood Material Science and Engineering. 5, 84–90 (2019).
  8. Kartashov E. M.  Heat conduction at a variable heat-transfer coefficient.  High Temperature. 57 (5), 663–670 (2019).
  9. Kostrobij P. P., Markovych B. M., Tokarchuk M. V.  Generalized diffusion equation with nonlocality of space-time. Memory function modelling.  Condensed Matter Physics. 23 (2), 23003 (2020).
  10. Gupta S. C.  The Classical Stefan Problem. 2nd edition.  Elsevier, USA (2017).
  11. Vasilyev V. I., Vasilyev M. V., Stepanov S. P., et al.  Mathematical modeling of the temperature regime of soil of foundations in conditions of perennially frozen rocks.  The Natural Science series. 1 (70), 142–159 (2017).
  12. Skopetskyi V. V., Bulavatskyi V. M., Kryvonos U. G.  Nonclassical mathematical models of heat and mass transfer processes.  Scientific thought (2005).
  13. Oztop F. H., Akpinar E. K.  Numerical and experimental analysis of moisture transfer for convective drying of some products.  International Communications in Heat and Mass Transfer. 35 (2), 169–177 (2008).
  14. Li X., Thomas H. R.  Finite element method and constitutive modeling and computation for unsaturated soils.  Computer Methods in Applied Mechanics and Engineering. 169 (1–2), 135–159 (1999).
  15. Krylov D. A., Sydnev N. I., Fedotov A. A.  Mathematical modeling of the distribution of temperature fields.  Mathematical modeling. 25 (7), 3–27 (2013).
  16. Sokolovskyy Ya., Boretska I., Yatsyshyn S., Kaspryshyn Y.  Mathematical modeling of deformation-relaxation processes under phase transition.  CEUR Workshop Proceedings. 2300, 83–86 (2018).
  17. Sokolovskyy Y., Boretska I., Kroshnyy I., Gayvas B.  Mathematical models and analysis of the heat-mass-transfer in anisotropic materials taking into account the boundaries of phase transition.  15th International Conference "The Experience of Designing and Application of CAD Systems". 28–33 (2019).
  18. Samarskii A. A.  The theory of difference schemes.  Science, Moscow (1989), (in Russian).
  19. Shymanskyi V., Protsyk Y.  Simulation of the heat conduction process in the claydite-block construction with taking into account the fractal structure of the material.  Proceedings of the 2018 IEEE XIII-th International Scientific and Technical Conference "Computer Sciences and Information Technologies''. 151–154 (2018).
  20. Sokolovskyy Ya., Boretska I., Gayvas B., Kroshnyy I.  Mathematical modeling of the heat-mass-exchange in anisotropic environments taking into account the boundary of phase transition.  Proceedings of the 2018 IEEE XIII-th International Scientific and Technical Conference "Computer Sciences and Information Technologies''. 147–150 (2018).
  21. Kostrobij P., Markovych B., Viznovych B., Zelinska I., Tokarchuk M.  Generalized Cattaneo–Maxwell diffusion equation with fractional derivatives. Dispersion relations.  Mathematical Modeling and Computing. 6 (1), 58–68 (2019).
  22. Kostrobij P. P., Markovych B. M., Ryzha I. A., Tokarchuk M. V.  Generalized kinetic equation with spatiotemporal nonlocality.  Mathematical Modeling and Computing. 6 (2), 289–296 (2019).
  23. Sokolovskyy Y., Kroshnyy I., Yarkun V.  Mathematical modeling of visco-elastic-plastic deformation in capillary-porous materials in the drying process.  The X-th International Conference on Computer Science and Information Technologies. 52–56 (2015).
  24. Sokolovskyy Y., Sinkevych O.  Software for automatic calculation and construction of chamber drying wood and its components.  The XII International Conference "Perspective Technologies and Methods in MEMS Design". 209–213 (2016).
  25. Sokolovskyy Y., Boretska I., Gayvas B., Shymanskyi V., Gregus M.  Mathematical modeling of heat transfer in anisotropic biophysical materials, taking into account the phase transition boundary.  CEUR Workshop Proceedings. 2488, 121–132 (2019).
  26. Sokolovskyy Y., Levkovych M., Sokolovskyy I.  The study of heat transfer and stress-strain state of a material, taking into account its fractal structure.  Mathematical Modeling and Computing. 7 (2), 400–409 (2020).