SOME QUESTIONS ABOUT HEAT SUPPLY IN THE SOILPLANTAIR SYSTEM

DOI 10.12737/2073046220248187 УДК 631.5

Authors

  • Ivan Ivanovich Maksimov Chuvash State Agrarian University, Cheboksary, Russia
  • Ayrat Rasimovich Valiev Kazan State Agrarian University, Kazan, Russia
  • Evgeniy Petrovich Alekseev Chuvash State Agrarian University, Cheboksary, Russia.
  • Nikita Vladimirovich Maksimov Chuvash State Agrarian University, Cheboksary, Russia.
  • Irina Vasilievnа Lukina Chuvash State Agrarian University, Cheboksary, Russia.

Keywords:

heat supply of plants, bifurcation points, growth.

Abstract

During the growing season, cultivated plants are subject to bifurcation effects such as drought, frost, ice, hail, heavy rains, etc. The dependence of mankind on the weather is quite large. The purpose of this work is to study artificial bifurcation by heat supply of plants in laboratory conditions. The thermophysical characteristics of the interaction of the "plant-soil-air" system are due to radiation heat exchange, which includes the arrival of long-wave radiation from the atmosphere to plants and reflected radiation from plants into the atmosphere; the arrival of short-wave radiation from solar radiation used by plant leaves for photosynthesis and reflection of part of this photoactive radiation; turbulent heat exchange of the soil surface with the surrounding surface air; transpiration heat exchange of the soil surface with the surrounding surface air; heat exchange in the soil. In addition, solar radiation reaching the slope surface has a different scattering effect on the functioning of the "plant-soil-air" system. Note that the vegetation cover performs the function of thermal insulation between the atmosphere and the soil. The analytical determination of the heat supply of plants is quite difficult, especially on slopes of different steepness and exposure, due to both the insufficiency of the data included in these analytical expressions, as well as the uncertainty (impossibility) of determining experimentally appropriate coefficients. Therefore, the technique of the bifurcation approach allows, as a first approximation, to design certain technologies for cultivating crops for a specific catchment area, both in terms of frost resistance, and to apply measures to protect against frost. The stability of plant seedlings to frost was checked in laboratory conditions: sowing and germination of barley seeds under the same conditions (according to ambient temperature and soil moisture) for seven days; placing in a refrigerator at -18°C; extraction from the refrigerator at intervals of 5 minutes, maximum duration of 50 minutes; visual monitoring of the condition of plants. Experimental studies have shown that the death of a plant from frost is described by the regression equation y = 0.0268x² ‒ 0.3701x + 17.232. As a result of the research, a bifurcation function has been proposed, confirmed by laboratory experiments.

Information about the authors

Ivan Ivanovich Maksimov , Chuvash State Agrarian University, Cheboksary, Russia

Doctor of Technical Sciences, Professor of the Department of Transport and Technological Machines and Complexes

Ayrat Rasimovich Valiev , Kazan State Agrarian University, Kazan, Russia

Doctor of Technical Sciences, Professor, corresponding member of Academy of Sciences of the Republic of Tatarstan, Rector

Evgeniy Petrovich Alekseev , Chuvash State Agrarian University, Cheboksary, Russia.

Ph.D. of Technical Sciences, Associate Professor of the Department of Transport and Technological Machines and Complexes

Nikita Vladimirovich Maksimov , Chuvash State Agrarian University, Cheboksary, Russia.

Рostgraduate student

Irina Vasilievnа Lukina , Chuvash State Agrarian University, Cheboksary, Russia.

Рostgraduate student

References

 1. Определение точек бифуркации в функционировании системы почва растение воздух» / И. И. Максимов, М. Н. Калимуллин, Е. П. Алексеев [и др.] // Вестник Казанского государственного аграрного университета. 2023. Т. 18, № 2(70). С. 94101. doi 10.12737/20730462202394101.

 2. Журавлева В.В. Математические модели процессов регуляции в физиологии растений // Известия Алтайского государственного университета. 2008. (57). С. 4357.

 3. Bessonov N., Volpert V. Dynamical Models of Plant Growth. Mathematics and Mathematical modeling. // Mathematics Subject Classification. 2000. P. 63.

 4. Marasco А., Giannino F. Modelling competitive interactions and plant soil feedback in vegetation dynamics // Ricerche di Matematica. 2020. 69(1). doi: 10.1007/s11587020004976.

 5. Smithers E.T., Luo J., Dyson R.J. Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis // Journal of Experimental Botany. 2019. Vol. 70. No. 14. P. 35873600. doi: 10.1093/jxb/erz253.

 6. Mathematical Modeling of the Dynamics of ShootRoot Interactions and Resource Partitioning in Plant Growth / C. Feller, P. Favre, A. Janka, et al. // Plos one. 2015. 10(7). doi: 10.1371/journal.pone.0127905.

 7. Арнольд В.И. Теория катастроф. М.: Наука, 1990. 128 с.

 8. Prigogine I., Wiame J. M. Biologie et thermodynamique des phenomenes irreversibles // Experientia. 1946. Vol. 2. Nо. 11. P. 451453.

 9. Пригожин И., Кондепуди Д. Современная термодинамика. От тепловых двигателей до диссипативных структур. М.: Мир, 2002. 461 с.

 10. Розен Р. Принцип оптимальности в биологии. М.: Мир, 1969. 215 с.

 11. Kaur D. Bifurcation induced by delay parameter in plant growth dynamics // J. Phys.: Conf. Ser. 2022. URL: https://www.iopscience.iop.org/article/10.1088/17426596/2267/1/012031 (дата обращения: 21.04.2023). doi: 10.1088/17426596/2267/1/012031

 12. Agricultural Engineering Technologies in the Control of Frost Damage in Permanent Plantations / V. Tadi´c, K. Gligorevi´c, Z. Mileusni´c, et al. . AgriEngineering, 2023. 5, P. 20792111.

 13. Гольцберг И.А. Климатическая характеристика зам зкв и метды брьбы с ними в СССР [Текст] / И.А. Гольцберг; под ред. Юдина М. И. Ленинград : Гидрометеоиздат, Труды Главной геофизической обсерватории ; вып. 17 (79). 1949. 112 с.

 14. Snyder R. L. Frost Protection: Fundamentals, Practice and Economics // Food and Agriculture Organization of the United Nations, 2005. pp. 223.

 15. Нерпин С.В., Чудновский А.Ф. Энерго и массообмен в системе растениепочвавоздух. Л. Гидрометоиздат, 1975, 359 с.

 16. Менжулин Г.В. Кметодике расчета метеорологического режима врастительном сообществе. Метеорология игидрология, 1970, № 2, с. 92−99.

 17. Дубов А.С. Турбулентность в растительном покрове / А.С. Дубов, Л.П. Быкова, С.В. Марунич. Ленинград : Гидрометеоиздат, 1978. 183 с.

 18. Estimation of soil thermal properties using conduction and conductionconvection heat transfer equations in the Brazilian Pampa biome / Zimmer, T., Souza, V. de A., Romio, L. C. et al. // Agricultural and Forest Meteorology, 2023. 338, 109517. URL: https://www.sciencedirect.com/science/article/abs/pii/S0168192323002083#previewsectioncitedby (дата обращения 11.10.2024). doi: 10.1016/j.agrformet.2023.109517.

 19. Zhu F., Zhou Y., Zhu S. Experimental study on heat transfer in soil during heat storage and release processes. Heat. Mass. Transfer. 2021. 57, P. 14851497. URL: https://link.springer.com/article/10.1007/s00231021030456 (дата обращения 11.10.2024).

 20. Wardani A. K., Purqon A. Thermal conductivity prediction of soil in complex plant soil system using artificial neural networks //Journal of Physics: Conference Series. IOP Publishing, 2016. Т. 739. №. 1. С. 012007.

 21. Agrotool a system for crop simulation / R. A. Poluektov, S. M. Fintushal, I. V. Oparina, et al. // Archives of Agronomy and Soil Science. 2002. Vol. 48(6). P. 609635.

 22. Росс Ю.К. К математическому описанию роста растений // Доклады Академии наук СССР. 1966. Т. 171. №2. С. 481483.

 23. Тооминг Х.Г. Солнечная радиация и формирование урожая [Текст] / Х.Г. Тооминг. Москва : Гидрометеоиздат, 1977. 197 с.

 24. Функционирование системы "растение почва воздух" / И. И. Максимов, В. И. Максимов, С. А. Васильев, В. В. Алексеев // Энергосберегающие агротехнологии и техника для северного земледелия и животноводства, Киров, 1214 декабря 2018 года. Киров: ООО "Кировская областная типография", 2018. С. 5463.

 1. Maksimov II, Kalimullin MN, Alekseev EP. [Determination of bifurcation points in the functioning of the soil plant air" system]. Vestnik Kazanskogo gosudarstvennogo agrarnogo universiteta. 2023; Vol.18. 2(70). 94101 p. DOI 10.12737/20730462202394101.

 2. Zhuravleva VV. [Mathematical models of regulatory processes in plant physiology]. Izvestiya Altayskogo gosudarstvennogo universiteta. 2008; 1 (57). 4357 p.

 3. Bessonov N, Volpert V. Dynamical models of plant growth. Mathematics and mathematical modeling. Mathematics Subject Classification. 2000; P. 63 p.

 4. Marasco A, Giannino F. Modelling competitive interactions and plantsoil feedback in vegetation dynamics. Ricerche di Matematica. 2020; 69(1). doi: 10.1007/s11587020004976.

 5. Smithers ET, Luo J, Dyson RJ. Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis. Journal of Experimental Botany. 2019; Vol.70. 14. 35873600 p. doi: 10.1093/jxb/erz253.

 6. Feller C, Favre P, Janka A. Mathematical modeling of the dynamics of shootroot interactions and resource partitioning in plant growth. Plos one. 2015; 10(7). doi: 10.1371/journal.pone.0127905.

 7. Arnold VI. Teoriya katastrof. [Theory of catastrophes]. Moscow: Nauka. 1990; 128 p.

 8. Prigogine I, Wiame JM. Biologie et thermodynamique des phenomenes irreversibles. Experientia. 1946; Vol.2. 11. 451453 p. French.

 9. Prigozhin I, Kondepudi D. Sovremennaya termodinamika. Ot teplovykh dvigateley do dissipativnykh struktur. [Modern termodynamics. From heat engines to dissipative structures]. Moscow: Mir. 2002; 461 p.

 10. Rozen R. Printsip optimalnosti v biologii. [The principle of optimality in biology]. Moscow: Mir. 1969; 215 p.

 11. Kaur D. Bifurcation induced by delay parameter in plant growth dynamics. J. Phys.: Conf. Ser. 2022; [cited 2023, April 21]. Available from: https://www.iopscience.iop.org/article/10.1088/17426596/2267/1/012031. doi: 10.1088/17426596/2267/1/012031

 12. Tadic V, Gligorevic K, Mileusnic Z. Agricultural engineering technologies in the control of frost damage in permanent plantations. AgriEngineering. 2023; 5. 20792111 p.

 13. Goltsberg IA. Klimaticheskaya kharakteristika zamorozkov i metody borby s nimi v SSSR. [Climatic characteristics of frosts and methods of combating them in the USSR]. Leningrad: Gidrometeoizdat. Trudy Glavnoy geofizicheskoy observatorii. 17 (79). 1949; 112 p.

 14. Snyder RL. Frost protection: fundamentals, practice and economics. Food and Agriculture Organization of the United Nations. 2005; 223 p.

 15. Nerpin SV, Chudnovskiн AF. Energo i massoobmen v sisteme rasteniepochvavozdukh. [Energy and mass transfer in the plantsoilair system]. Leningrad: Gidrometoizdat. 1975; 359 p.

 16. Menzhulin GV. [On the methodology for calculating the meteorological regime in a plant community]. Meteorologiya i gidrologiya. 1970; 2. 9299 p.

 17. Dubov AS, Bykova LP, Marunich SV. Turbulentnost v rastitelnom pokrove. [Turbulence in vegetation cover]. Leningrad: Gidrometeoizdat. 1978; 183 p.

 18. Zimmer T, Souza V. de A, Romio LC. Estimation of soil thermal properties using conduction and conduction convection heat transfer equations in the Brazilian Pampa biome. Agricultural and Forest Meteorology. 2023; 338. 109517. [cited 2024, October 11]. Available from: https://www.sciencedirect.com/science/article/abs/pii/S0168192323002083#previewsectioncitedby. doi: 10.1016/j.agrformet.2023.109517.

 19. Zhu F, Zhou Y, Zhu S. Experimental study on heat transfer in soil during heat storage and release processes. Heat. Mass. Transfer. 2021; 57. 1485 1497 p. [cited 2024, October 11]. Available from: https://link.springer.com/article/10.1007/s00231021030456.

 20. Wardani AK, Purqon A. Thermal conductivity prediction of soil in complex plant soil system using artificial neural networks. Journal of Physics: Conference Series. IOP Publishing. 2016; Vol.739. 1. 012007 p.

 21. Poluektov RA, Fintushal SM, Oparina IV. Agrotool a system for crop simulation. Archives of Agronomy and Soil Science. 2002; Vol.48(6). 609635 p.

 22. Ross YuK. [Towards a mathematical description of plant growth]. Doklady Akademii nauk SSSR. 1966; Vol.171. 2. 481483 p.

 23. Tooming KhG. Solnechnaya radiatsiya i formirovanie urozhaya. [Solar radiation and crop formation]. Moscow: Gidrometeoizdat. 1977; 197 p.

 24. Maksimov II, Maksimov VI, Vasilev SA, Alekseev VV. Funktsionirovanie sistemy rasteniepochvavozdukh". Energosberegayushchie agrotekhnologii i tekhnika dlya severnogo zemledeliya i zhivotnovodstva. [Functioning of the plantsoilair" system. Energysaving agricultural technologies and equipment for northern agriculture and animal husbandry]. Kirov. 1214 dekabrya 2018 goda. Kirov: OOO Kirovskaya oblastnaya tipografiya". 2018; 5463 p

Published

2026-07-24

How to Cite

Maksimov И. И., Valiev . А. Р., Alekseev . Е. П. ., Maksimov Н. В. ., & Lukina И. В. (2026). SOME QUESTIONS ABOUT HEAT SUPPLY IN THE SOILPLANTAIR SYSTEM: DOI 10.12737/2073046220248187 УДК 631.5. Vestnik of Kazan State Agrarian University, 19(4). Retrieved from http://vestnik-kazgau.ru/index.php/vestnik/article/view/131