Geodesic
Algorithm for the joint solution of heat and mass transfer equations and equations of the electromagnetic field during the drying with microwave radiation
Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 2 (2017), pp. 82-93.

Voir la notice de l'article provenant de la source Math-Net.Ru

The authors develop a numerical scheme allowing to find a joint solution to the equations of diffusion of heat and moisture, A.V. Lykov and Maxwell’s equations in electromagnetic drying of a sample with a flat geometry. Calculation scheme is based on two algorithms: a) for a given distribution of the dielectric constant the problem is to estimate the field density of electromagnetic losses, reflection coefficients and transmission; b) when there are electromagnetic losses of specified field density, the problem of calculation of fields of temperature and moisture content should be solved. The role of a bridge between these two algorithms performs the formula of Debye (it determines the dielectric permittivity of each of the two components of the mixture, the solid base and water, frequency and temperature) and mixing formula of Maxwell (on the basis of the Debye formulas for the solid base and water, it determines the dielectric permittivity of the mixture of these components as a function of frequency, temperature and moisture content). The calculation according to this scheme allows to take into account the reverse impact of distributions of temperature and moisture content at some point in time, on the distribution of absorbed electromagnetic energy in the same moment. Numerical experiment (drying the moist zeolite electromagnetic radiation in the microwave range), the results of which are in good agreement with available published experimental data.
Mots-clés : A.V. Lykov’s equations
Keywords: Maxwell’s equations, drying with electromagnetic radiation, initial boundary value problem, numerical methods, complex dielectric permittivity, the method of characteristic matrices. 
@article{VVGUM_2017_2_a8,
     author = {A. M. Afanas'ev and B. N. Siplivyi},
     title = {Algorithm for the joint solution of heat and mass transfer equations and equations of the electromagnetic field during the drying with microwave radiation},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {82--93},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2017_2_a8/}
}
TY  - JOUR
AU  - A. M. Afanas'ev
AU  - B. N. Siplivyi
TI  - Algorithm for the joint solution of heat and mass transfer equations and equations of the electromagnetic field during the drying with microwave radiation
JO  - Matematičeskaâ fizika i kompʹûternoe modelirovanie
PY  - 2017
SP  - 82
EP  - 93
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VVGUM_2017_2_a8/
LA  - ru
ID  - VVGUM_2017_2_a8
ER  - 
%0 Journal Article
%A A. M. Afanas'ev
%A B. N. Siplivyi
%T Algorithm for the joint solution of heat and mass transfer equations and equations of the electromagnetic field during the drying with microwave radiation
%J Matematičeskaâ fizika i kompʹûternoe modelirovanie
%D 2017
%P 82-93
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VVGUM_2017_2_a8/
%G ru
%F VVGUM_2017_2_a8
A. M. Afanas'ev; B. N. Siplivyi. Algorithm for the joint solution of heat and mass transfer equations and equations of the electromagnetic field during the drying with microwave radiation. Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 2 (2017), pp. 82-93. http://geodesic.mathdoc.fr/item/VVGUM_2017_2_a8/

[1] D. Anderson, Dzh. Tannehill, R. Pletcher, Computational Hydromechanics and Heat Transfer, v. 1, Mir Publ., Moscow, 1990, 384 pp. | MR | Zbl

[2] Yu.\;S. Arkhangelskiy, The Installations of Dielectric Heating. Installation of Microwave, SGTU Publ., Saratov, 2008, 220 pp.

[3] A.\;M. Afanasyev, B.\;N. Siplivyy, “The Study of Quasi-Stationary Modes in Drying with Microwave Radiation”, Izvestiya vuzov. Elektromekhanika, 2008, no. 3, 3–9 | MR

[4] A.\;M. Afanasyev, B.\;N. Siplivyy, “On Boundary Conditions of Mass Transfer in the Form of Laws of Newton and Dalton”, Inzhenerno-fizicheskiy zhurnal, 80:1 (2007), 27–34

[5] A.\;M. Afanasyev, B.\;N. Siplivyy, “The Use of Conservative Difference Schemes for the Analysis of the Equations of the Electromagnetic Drying with Variable Transport Coefficients”, Izvestiya vuzov. Elektromekhanika, 2008, no. 4, 3–8

[6] A.\;M. Afanasyev, V.\;K. Mikhaylov, B.\;N. Siplivyy, “Drying with Electromagnetic Radiation: Numerical Solution of Problem for a Rectangular Domain”, Izvestiya vuzov. Elektromekhanika, 2015, no. 2, 5–11 | DOI

[7] M. Born, E. Volf, Basics of Optics, Nauka Publ., Moscow, 1970, 856 pp.

[8] M.\;B. Vinogradova, O.\;V. Rudenko, A.\;P. Sukhorukov, Theory of Waves, Nauka Publ., Moscow, 1979, 384 pp. | MR

[9] R. King, G. Smit, Antennas in Material Media, Mir Publ., Moscow, 1984, 824 pp.

[10] L.\;D. Landau, E.\;M. Lifshits, Course of Theoretical Physics. Vol. 8. Electrodynamics of Continuous Media, Nauka Publ., Moscow, 1982, 624 pp. | MR

[11] A.\;V. Lykov, Theory of Drying, Energiya Publ., Moscow; Leningrad, 1968, 471 pp.

[12] A.\;V. Markov, Yu.\;P. Yulenets, “The Mechanism of Mass Transfer in High-Intensity Drying with Internal Heat Sources”, Teoreticheskie osnovy khimicheskoy tekhnologii, 36:3 (2002), 269–274

[13] S.\;P. Kundas, N.\;N. Grinchik, I.\;A. Gishkelyuk, A.\;L. Adamovich, Modeling of Thermal Moisture Transfer in Capillary-Porous Media, Institut teplo- i massoobmena im. A.V. Lykova NAN Belarusi, Minsk, 2007, 292 pp.

[14] N.\;N. Grinchik, A.\;L. Adamovich, O.\;A. Kizina, U.\;M. Kharma, “Modeling of Heat and Moisture Transfer in Wood during dosushki energy of the microwave field”, Inzhenerno-fizicheskij zhurnal, 2015, no. 1, 37–42

[15] S.\;P. Rudobashta, Je.\;M. Kartashov, N.\;A. Zuev, “Heat and Mass Transfer during the Completion of Drying in an Oscillating Electromagnetic Field”, Teoreticheskie osnovy khimicheskoy tekhnologii, 45:6 (2011), 641–647

[16] A.\;A. Samarskiy, Introduction to Numerical Methods, Nauka, Moscow, 1987, 288 pp. | MR

[17] Dzh.\;A. Strjetton, The Theory of Electromagnetism, Gostekhizdat Publ., Moscow, 1948, 540 pp.

[18] K. Shimoni, Theoretical Electrical Engineering, Mir Publ., Moscow, 1964, 773 pp.

[19] V.\;Ya. Yavchunovskiy, Microwave and Combined Drying: Physical Basis, Technology and Equipment, SGTU Publ., Saratov, 1999, 212 pp.