### 3D MATHEMATICAL MODEL CHARACTERIZING THE DYNAMICS OF THE TEMPERATURE FIELD OF A WALL STRUCTURE WITH A DOUBLE-SIDED FACING FROM A SAPROPEL-HEMP COMPOSITE MATERIAL

#### Abstract

*In this paper, a 3D mathematical model is proposed to determine the dynamics of the temperature field in a three-layer composite sapropel-hemp slab. The proposed model consists of a system of three initial-boundary value problems with respect to the temperature function for each layer, respectively, and one initial-boundary value problem with respect to the unknown velocity of heat propagation along the thickness dimension of the composite sapropel-hemp slab.*

#### Keywords

#### Full Text:

PDF#### References

P. Germain, Cours de mécanique des milieux continus: Théorie générale. Paris: Masson et Cie, Éditeurs, 1973.

Yu. I. Burchakov, V. E. Gnedin, and V. M. Denisov, Structural mechanics. Moscow: Higher School, 1983.

A. V. Lykov, Heat conduction theory. Moscow: Higher School, 1967.

R. I. Nigmatulin, Continuum mechanics: Kinematics, dynamics, thermodynamics, statistical dynamics. Moscow: GEOTAR-Media, 2014.

D. A. Frank-Kamenetsky, Diffusion and heat transfer in chemical kinetics. Moscow: Nauka, 1987.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids. Oxford: Oxford University Press, 1986.

V. S. Zarubin, Modelling. Moscow: "Academy" Publishing Centre, 2013.

V. S. Zarubin, A. V. Kotovich, and G. N. Kuvyrkin, "Temperature state of a plate with temperature-dependent thermal conductivity and energy-release," Mathematics and Mathematical Modeling, vol. 16, no. 3, pp. 18-28, 2016.

V. V. Vasiliev, Mechanics of structures made of composite materials. Moscow: Mechanical Engineering, 1988.

L. N. Tyalina, A. M. Minaev, and V. A. Pruchkin, New composite cmaterials. Tambov: Tambov State Technical University Press, 2011.

M. L. Kerber, Polymer composite materials: Structure, properties, technology. St. Petersburg: Profession, 2008.

V. R. Bensman, "Classification problems for peat bogs and sapropels," Young scientist, vol. 1, no. 1-2, pp. 146-147, 2010.

A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics. Moscow: Nauka, 1977.

Th. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. Dewitt, Fundamentals of Heat and Mass Transfer. New Jersey: John Wiley & Sons, 2011.

J. H. Lienhard IV and J. H. Lienhard V, A Heat Transfer Textbook. – Massachusetts, Cambridge: Phlogiston Press, 2019.

Y. Ashida, Ke. Saito, and M. Ueda, "Thermalization and heating dynamics in open generic many-body systems," Physical Review Letters, vol. 121, no. 7, pp. 402-408, 2018.

P. P. Volosevich and E. I. Levanov, "Analysis of heat transfer processes taking into account the relaxation of heat flux and bulk energy sources in the medium," Transactions of Russian Higher Educational Institutions: Mathematics, vol. 47, no. 1, pp. 36-42, 2003.

E. I. Levanov, "Heat transfer taking into account the relaxation of the heat flux and energy sources," Mathematical Modelling, vol. 9, no. 2, pp. 53-56, 1997.

D. S. P. Salazar, A. M. S. Macedo, and G. L. Vasconcelos, "Quantum heat distribution in thermal relaxation processes," Physical Review E, vol. 99, no. 2, pp. 2133-2138, 2019.

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman lectures on physics: Mainly mechanics, radiation, and heat. California: California Institute of Technology Press, 1963.

K. Micadei, J. P. S. Peterson, A. M. Souza, R. S. Sarthour, I. S. Oliveira, G. T. Landi, T. B. Batalhao, R. M. Serra, and E. Lutz, "Reversing the direction of heat flow using quantum correlations," Nature Communications, vol. 10, paper no. 2456, 6 p, 2019.

Sh. E. Guseynov, R. Aleksejevs, J. V. Aleksejeva, "On a 3D initial-boundary value problem for determining the dynamics of impurities concentration in a horizontal layered fine-pore medium," in Proceedings of the 12th International Scientific and Practical Conference "Environment. Technology. Resources", vol. III, Rezekne: Rezekne Academy of Technologies Press, 2019, pp. 60-69.

Sh. E. Guseynov, R. Aleksejevs, J. V. Aleksejeva, and J. S. Rimshans, "On the impurities concentrations dynamics in multicomponent semidisperse semicolloid-high-molecular system: a case study of two-layered anisotropic peat block," Advanced Mathematical Models & Applications, vol.4, no. 2, pp. 99-126, 2019.

A. Zettl, Sturm-Liouville Theory. Providence, Rhode Island: American Mathematical Society Press, 2005.

A. N. Kolmogorov, I. G. Petrovsky, and N. S. Piscounov, "Investigation of the diffusion equation combined with an increase in matter and its application to a biological problem," Bulletin of Moscow State University, Series A: Mathematics and Mechanivs, vol. 1, pp. 1-25, 1937.

R. A. Fisher, "The wave of advance of advantageous genes," Annals of Eugenics, vol. 7, pp. 355-369, 1937.

M.El-Hachem, S.W.McCue, W.Jin, Y.Du, and M.J.Simpson, "Revisiting the Fisher-Kolmogorov-Petrovsky-Piskunov equation to interpret the spreading-extinction dichotomy," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 475, no. 2229, Paper ID: 0378, 2019.

S. M. Shtin, Lacustrine sapropels and their complex development. Moscow State Mining University Press, 2005.

N. Brakss, B. Vimba, and A. Kalnins, "On the properties and ways of using sapropels of the Latvian SSR," Transactions of Latvian Academy of Sciences, vol. 133, no. 8, pp. 43-50, 1958.

Central Statistical Bureau of Latvia, "Geographical data," 2009. [Online]. Available: https://data.stat.gov.lv/pxweb/lv/OSP_PUB/START__ENV__DR__DRT/DRT020/. [Accessed: March 19, 2021].

Database, "Lakes," 2009. [Online]. Available: https://www.ezeri.lv/?l=en. [Accessed: March 19, 2021].

R. M. Christensen, Mechanics of composite materials. Mineola: Dover Publications, 2005.

G. L. Gorynin and Yu. V. Nemirovsky, "Mathematical modelling of heat conduction process for 2D-periodic anisotropic composite materials," Mathematical Methods and Physico-Mechanical Field, vol. 57, no. 2, pp. 142-151, 2014.

N. S. Bakhvalov and G. P. Panasenko, Averaging processes in periodic media. Mathematical problems in the mechanics of composite materials. Moscow: Science 1984.

L. C. King, The morphology of the Earth: A study and synthesis of world scenery. Edinburgh: Oliver & Boyd, 1962.

I. P. Baranov, "Using the concept of plastics relief in solving problems modern city planning and architectural planning," in International Conference "InterCarto. InterGIS. Geoinformation Support of Sustainable Development of Territories", vol. 20, 2014, pp. 575-587.

V. I. Gorbachev, "The Bakhvalov-Pobedri averaging method in the mechanics of composites," Bulletin of Lomonosov Moscow State University, Series 1: Mathematics and Mechanics, no. 6, pp. 41-45, 2016.

DOI: https://doi.org/10.17770/etr2021vol3.6648

### Refbacks

- There are currently no refbacks.