Email this article Application of the Greene function method for solving spatially one dimensional problems of the theory of electromagnetic radiation drying
- Authors: Afanasiev A.1, Siplivy B.1
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Affiliations:
- Volgograd State University
- Issue: Vol 23, No 1 (2020)
- Pages: 73-83
- Section: Articles
- URL: https://journals.ssau.ru/pwp/article/view/7817
- DOI: https://doi.org/10.18469/1810-3189.2020.23.1.73-83
- ID: 7817
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Abstract
An algorithm for constructing a new class of solutions to spatially one-dimensional problems in the theory of electromagnetic radiation drying has been developed. Its basis is the procedure for splitting the process by physical factors. In the framework of the proposed algorithm, the initial boundary value problems for the heat and moisture propagation equations are solved sequentially using the Fourier method using the Greene function apparatus on successive layers of the difference grid separated by small time intervals. The dependencies of the temperature and moisture content fields on time in such solutions are determined by the eigenvalues of the Sturm-Liouville problem, and the distributions of these fields in space are determined by the eigenfunctions of this problem. A comparison of the new calculation algorithm with known grid methods is made, and new possibilities for analysis that are opened in the drying theory due to this algorithm are indicated.
About the authors
A.M. Afanasiev
Volgograd State University
Author for correspondence.
Email: a.m.afanasiev@yandex.ru
B.N. Siplivy
Volgograd State University
Email: tf@volsu.ru
References
- Afanas’ev A.M. et al. Calculation of the thermal effects of microwave radiation on flat objects from water-containing layered structure. Physics of Wave Processes and Radio Systems, 1998, vol. 1, no. 2, pp. 83–90. (In Russ.)Afanas’ev A.M. et al. Mathematical modeling of the thermal action of intense microwave radiation onto cylindrical objects hydrous layered structure. Physics of Wave Processes and Radio Systems, 2001, vol. 4, no. 2, pp. 15–21. (In Russ.)Chast’ mi. et al. Mathematical modeling of the microwave radiation interacts with the water-containing planar lamellar cFe. Part 1. Izvestija vuzov. Elektromehanika, 2001, no. 2, pp. 14–21. (In Russ.)Chast’ mi. et al. Mathematical modeling of the microwave radiation interacts with the water-containing planar lamellar cFe. Part 2. Izvestija vuzov. Elektromehanika, 2001, no. 4, pp. 32–38. (In Russ.)Kurant R., Gil’bert D. Methods of Mathematical Physics. Vol. 2. Moscow: Gostehizdat, 1933/1945, 620 p. (In Russ.)Marchuk G.I. Mathematical Modeling in the Environmental Problem. Moscow: Nauka, 1982, 320 p. (In Russ.)Afanas’ev A.M., Bahracheva Ju.S., Siplivyj B.N. Applying Fourier method for solving electromagnetic radiation theory of drying. Physics of Wave Processes and Radio Systems, 2019, vol. 22, no. 3, pp. 27–35. DOI: https://doi.org/10.18469/1810-3189.2019.22.3.27-35. [In Russian].Lykov A.V. Heat and Mass Transfer: A Handbook. 2nd ed., rev. and additional. Moscow: Energija, 1978, 480 p. (In Russ.)Rudobashta S.P., Kartashov E.M., Zuev N.A. Heat and mass transfer in drying in an oscillating electromagnetic field. Teoreticheskie osnovy himicheskoj tehnologii, 2011, vol. 45, no. 6, pp. 641–647. (In Russ.)Afanas’ev A.M., Siplivyj B.N. The dependence of the quality of the microwave radiation drying the depth of penetration of an electromagnetic wave. Physics of Wave Processes and Radio Systems, 2008, vol. 11, no. 1, pp. 95–99. (In Russ.)Grinchik N.N. et al. Modeling of Heat and final drying of the timber with microwave energy field. Inzhenerno-fizicheskij zhurnal, 2015, vol. 88, no. 1, pp. 37–42. (In Russ.)Afanas’ev A.M., Siplivyj B.N. Analytical solution of the problem of deformations during drying electromagnetic radiation. Physics of Wave Processes and Radio Systems, 2017, vol. 20, no. 1, pp. 11–18. (In Russ.)Afanas’ev A.M., Siplivyj B.N. Asymptotic solutions of initial boundary value problems in the theory of drying by electromagnetic radiation. Modern problems of computer modeling: monograph. Volgograd: VolGU, 2018, 170 p.Lykov A.V. Drying Theory. Moscow; Leningrad: Energija, 1968, 471 p.Afanas’ev A.M., Siplivyj B.N. On boundary conditions of mass transfer in the form of laws of Newton and Dalton. Inzhenerno-fizicheskij zhurnal, 2007, vol. 80, no. 1, pp. 27–34. (In Russ.)Afanas’ev A.M., Siplivyj B.N. The concept of surface heat sources in the drying theory electromagnetic radiation. Izvestija vuzov. Elektromehanika, 2017, vol. 60, no. 2, pp. 13–20. (In Russ.)Tihonov A.N., Samarskij A.A. Equations of Mathematical Physics. Moscow: Nauka, 1966, 724 p. (In Russ.)Sveshnikov A.G., Bogoljubov A.N., Kravtsov V.V. Lectures on Mathematical Physics. Moscow: Izd-vo MGU, 1993, 352 p. (In Russ.)Arsenin V.Ja. Methods of Mathematical Physics and Special Functions. Moscow: Nauka, 1984, 384 p. (In Russ.)Lykov A.V. The Theory of Heat Conduction. Moscow: Vysshaja shkola, 1967, 600 p. (In Russ.)Budak B.M., Fomin S.V. Multiple Integrals and Series. Moscow: Fizmatlit, 2002, 512 p. (In Russ.)Samarskij A.A. Introduction to Numerical Methods. Moscow: Nauka, 1987, 288 p. (In Russ.)Afanas’ev A.M., Siplivyj B.N. The theory of electromagnetic drying: asymptotic solution of the initial boundary value problem for the cylinder. Teoreticheskie osnovy himicheskoj tehnologii, 2014, vol. 48, no. 2, pp. 222–227. (In Russ.)Afanas’ev A.M., Siplivyj B.N. The problem of drying of the ball electromagnetic radiation. Inzhenerno-fizicheskij zhurnal, 2013, vol. 86, no. 2, pp. 322–330. (In Russ.)Afanas’ev A.M., Siplivyj B.N. The theory of electromagnetic drying: asymptotic solution of the initial boundary value problem for a rectangular area. Physics of Wave Processes and Radio Systems, 2012, vol. 15, no. 1, pp. 77–83. (In Russ.)Afanas’ev A.M., Siplivyj B.N. Asymptotic distributions of temperature and moisture at drying electromagnetic specimen having a rectangular parallelepiped shape. Izvestija vuzov. Elektromehanika, 2012, no. 3, pp. 3–8. (In Russ.)
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