Unsteady-state temperature field of building walls using building materials operating moisture values

In the presented work, the unsteady-state temperature field in the single-layer brick building wall enclosing structure was investigated. To model the nonstationary temperature field of the building wall, the differential equation of thermal conductivity was solved by the finite difference method using an explicit difference scheme, taking into account boundary conditions of the third kind. The formula using to calculate the value of operational thermal conductivity at the known value of operational moisture of building materials is given.

For the calculations, single-layer enclosing brick structures with base thicknesses of 0.12 m, 0.25 m and 0.51 m in Moscow were adopted. The results of calculating temperatures in sections of enclosing structures over time at a thermal conductivity value selected in accordance with the regulatory document are presented. The time establishing stationary temperature field is presented. For brick walls, the time of the stationary state was determined when the outside air temperature is equal to the temperature of the coldest five-day period.

1. Radin V.P., Poznyak E.V., Novikova O.V. Reaktsiya modeli zdaniya so snizheniyem zhestkosti na dlinnoperiodnyye seysmicheskiye vozdeystviya [The dynamic response of a building model with decreasing stiffness during long-period earthquakes]. Bulletin of Moscow energy institute. Bulletin of MEI. 2019. No. 6. – Pp. 124-130. – DOI 10.24160/1993-6982-2019-6-124-130.(rus.)

2. Likhachev A.A., Usoltseva O.A. Obzor i sravneniye sovremennykh otechestvennykh i zarubezhnykh metodov otsenki tekhnicheskogo sostoyaniya zdaniy i sooruzheniy [Review and comparison of modern domestic and foreign methods of assessing the technical condition of buildings and structures]. Engineering bulletin of the Don. 2022. – No. 10(94). – Pp. 1-12.

3. González-Rodrigo B., Navas-Sánchez L., Rejas-Ayuga J.G., Hernández-Rubio O., Benito M.B. Preliminary Geospatial and In Situ Reconnaissance of the 8 September 2023 Moroccan Atlas Earthquake Damage. Buildings 2024. Vol. 14(3). No. 693. https://doi.org/10.3390/buildings14030693

4. Huang Y., Tu R., Tuerxun W., Jia X., Zhang X., Chen X. A Community Information Model and Wind Environment Parametric Simulation System for Old Urban Area Microclimate Optimization: A Case Study of Dongshi Town, China. Buildings 2024. Vol. 14(3). –No. 832. https://doi.org/10.3390/buildings14030832

5. Medinilha-Carvalho T.A., Marques da Silva F.V., Bre F., Gimenez J.M., Labaki L.C. Experimental Study of Wind Pressures on Low-Rise H-Shaped Buildings. Buildings. 2024. Vol. 14(3). No. 762. https://doi.org/10.3390/buildings14030762

6. Karvelis A.C., Dimas A.A., Gantes C.J. Unsteady Numerical Simulation of Two-Dimensional Airflow over a Square Cross-Section at High Reynolds Numbers as a Reduced Model of Wind Actions on Buildings. Buildings. 2024. Vol. 14(3). No. 561. https://doi.org/10.3390/buildings14030561

7. Sazonov A.K., Sukharev G.V., Beljavskaja O.S. Trekhmernoye modelirovaniye temperaturnykh poley v uglovykh zonakh naruzhnykh sten [Three-dimensional modeling of temperature fields in the corner zones of exterior walls] Natural and technogenic risks. Safety of structures. 2023. No. 6-2(67). – Pp. 34-36.(rus.)

8. Kokaya D., Zaborova D., Koriakovtseva T. Environmental analysis of residential exterior wall construction in temperate climate. Magazine of Civil Engineering. 2023. No. 8 (124). Pp. 114-122. DOI 10.34910/MCE.124.10.(rus.)

9. Habibi A., Kahe N. Evaluating the Role of Green Infrastructure in Microclimate and Building Energy Efficiency. Buildings. 2024. Vol. 14(3). No. 825. https://doi.org/10.3390/buildings14030825

10. Sun W., Chen L., Suolang B., Liu K. An Investigation of the Energy-Saving Optimization Design of the Enclosure Structure in High-Altitude Office Buildings. Buildings. 2024. Vol. 14(3). No. 645; https://doi.org/10.3390/buildings14030645

11. Lysova E.P., Kotlyarova E.V. Osnovy obespecheniya ekologicheskoy bezopasnosti stroitel'nykh materialov na vsekh etapakh ikh zhiznennogo tsikla [Fundamentals of ensuring the environmental safety of building materials at all stages of their life cycle].Modern trends in construction, urban planning and territory planning. 2023. Vol. 2. No. 2. – Pp. 72-80. DOI 10.23947/2949-1835-2023-2-2-72-80.(rus.)

12. Samarskaya N.S., Kotlyarova E.V., Lysova E.P. Osnovnyye nauchnyye printsipy sistemnogo podkhoda k opredeleniyu negativnykh faktorov, vozdeystvuyushchikh na okruzhayushchuyu sredu gorodskikh territoriy [Main scientific principles of a systematic approach to the determination of negative factors affecting urban environment] Safety of technogenic and natural systems. 2023. Vol. 7. No. 4. – Pp. 20-29. DOI 10.23947/2541-9129-2023-7-4-20-29.(rus.)

13. Kotlyarova E. Improving the methodology for assessing the level of environmental safety of urban areas as the basis of their life cycle. E3S Web of Conferences. 2023. Vol. 389.No. 09062. https://doi.org/10.1051/e3sconf/202338909062

14. Lushin K.I. Voitovich E.V. Mul'timodal'nost' podkhoda resheniya zadach energoeffektivnosti gorodskogo khozyaystvennogo kompleksa [Multimodality of the approach to solving problems of energy efficiency of the urban economic complex]. International technical and economic journal. 2022. – No. 5-6. – Pp. 7-17. DOI 10.34286/1995-4646-2022-86-5/6-7-17.(rus.)

15. Sevryugina N.S., Apatenko A.S. Import Substitution and Monitoring of Workpiece Quality. Russian Engineering Research. 2023. Vol. 43. No. 8. Pp. 927-933. DOI 10.3103/s1068798x23080294.(rus.)

16. Minchenkov N.D., Churakova S.K. Differentsial'noye uravneniye teploprovodnosti i konvektivnogo teploobmena v tsilindricheskoy sisteme koordinat [Differential equation of thermal conductivity and convective heat transfer in a cylindrical coordinate system]. Bashkir Chemical Journal. 2024. No. 1 (31). Pp. 96-100.(rus.)

17. Nemova D., Kotov E., Andreeva D., Khorobrov S., Olshevskiy V., Vasileva I., Zaborova D., Musorina T. Experimental Study on the Thermal Performance of 3D-Printed Enclosing Structures. Energies. 2022. Vol. 15(12). No. 4230. https://doi.org/10.3390/en15124230 (rus.)

18. Musorina T., Gamayunova O., Petrichenko M., Soloveva E. Boundary Layer of the Wall Temperature Field. Advances in Intelligent Systems and Computing. 2020. Vol. 1116 AISC. Pp. 429-437. DOI:10.1007/978-3-030-37919-3_42(rus.)

19. Zaborova D.D., Kozinec G.L., Musorina T.A., Petrichenko M.R. Mathematical Model for Unsteady Flow Filtration in Homogeneous Closing Dikes. Power Technology and Engineering. 2020. Vol. 54(3). Pp. 358–364. DOI:10.1007/s10749-020-01216-9(rus.)

20. Petrichenko M.R., Musorina T.A. Fractional differentiation operation in the Fourier boundary problems. St. Petersburg State Polytechnical University Journal: Physics and Mathematics. 2020. Vol. 13(2). Pp. 41–52. DOI: 10.18721/JPM.13204(rus.)

21. Statsenko E.A., Musorina T.A., Ostrovaia A.F., Olshevskiy V.Ya., Antuskov A.L. Moisture transport in the ventilated channel with heating by coil. Magazine of Civil Engineering. 2017. No.70(2).Pp. 11–17. DOI:10.18720/MCE.70.2(rus.)

22. Gamayunova O., Petrichenko M., Mottaeva A. Thermotechnical calculation of enclosing structures of a standard type residential building. Journal of Physics: Conference Series. 2020. Vol. 1614(1). No. 012066. DOI 10.1088/1742-6596/1614/1/012066(rus.)

23. Gamayunova O., Golov R. Potential of energy saving on transport. E3S Web of Conferences. 2019. Vol. 135. No. 02025. DOI:10.1051/e3sconf/201913502025

24. Kanareykin A.I. Raspredeleniye temperatury v polom tele ellipticheskogo secheniya pri granichnykh usloviyakh pervogo i tret'yego roda [Temperature distribution in a hollow body of elliptical section under boundary conditions of the first and third kind]. Forging and stamping production. Pressure processing of materials. – 2023. – No. 9. – P. 10-14.(rus.)

25. Belov A.V., Ilyin Yu.P., Kuzmina N.Yu., Skorodumova N.V. Resheniye uravneniya teploprovodnosti dlya gorizontal'noy BGU pri vnutrennem istochnike tepla [Heat equation solution for the horizontal biogas unit with an internal heat source]. Agroindustrial complex of Russia. 2019. Vol. 26, No. 2. Pp. 177-184.(rus.)

26. Kanareikin A.I. Statsionarnoye temperaturnoye pole v pryamougol'noy plastine s peremennoy teploprovodnost'yu po odnoy koordinate [Stationary temperature field in a rectangular plate with variable thermal conductivity in one coordinate]. Bulletin of the International Academy of Refrigeration. 2023. No. 1. Pp. 99-104. – DOI 10.17586/1606-4313-2023-22-1-99-104.(rus.)

27. Kanareikin A.I. Opredeleniye temperaturnogo polya termoelementa v vide plastiny pri nestatsionarnom rezhime [Determination of the temperature field of a thermoelectric element in the form of a plate in the two-dimensional case in a non-stationary mode]. Forging and stamping production. Processing of materials by pressure. 2023. No. 4. Pp. 11-16.(rus.)

28. Vidin Yu.V., Kazakov R.V., Zlobin V.S. Protsess perenosa tepla v dvukhsloynom tsilindricheskom tele [The process of heat transfer in a two-layer cylindrical body]. News of higher educational institutions. Energy problems. 2018. Vol. 20. No. 11-12. – Pp. 93-98. – DOI 10.30724/1998-9903-2018-20-11-12-93-98.

29. Yakimov N.D., Shageev A.F., Dmitriev A.V., Badretdinova G.R. Osobennosti rascheta temperaturnogo polya v kol'tsevom poristom sloye pri beskonechnom nagreve [Features of calculating the temperature field in an annular porous layer under infinite heating]. News of higher educational institutions. Energy problems. 2023. Vol. 25. No. 6. – Pp. 54-66.

30. Beibalaev V.D., Aliverdiev A.A. Issledovaniye temperaturnogo polya v plastine odnomernym nelineynym uravneniyem teploprovodnosti [Investigation of the temperature field in a plate by a one-dimensional nonlinear heat equation]. Bulletin of Dagestan State University. Series 1: Natural Sciences. 2022. Vol. 37. No. 1. Pp. 12-17.(rus.)

31. Kubacka E., Ostrowski P., Influence of Composite Structure on Temperature Distribution—An Analysis Using the Finite Difference Method. Materials. 2023. Vol. 16. No. 5193. 32. Saadeh R, Sedeeg A.K, Ghazal B., Gharib G. Double Formable Integral Transform for Solving Heat Equations. Symmetry. 2023. Vol. 15. No. 218.

32. Zubarev K.P. Taking into account moisture in increasing the accuracy of calculating heat losses of a building. International Journal for Computational Civil and Structural Engineering. 2024. Vol. 20. No. 1. – Pp. 150-161. DOI:10.22337/2587-9618-2024-20-1-154-161(rus)

33. Zubarev K.P. Derivation of the equation of unsteady-state moisture behaviour in the enclosing structures of buildings using a discrete-continuous approach. International Journal for Computational Civil and Structural Engineering. 2021. Vol. 17. No. 4. – P. 83-90. DOI:10.22337/2587-9618-2021-17-4-83-90 (rus.)

34. Zubarev K.P. Using discrete-continuous approach for the solution of unsteady-state moisture transfer equation for multilayer building walls. International Journal for Computational Civil and Structural Engineering. 2021. Vol. 17. No. 2. Pp. 50-57. DOI:10.22337/2587-9618-2021-17-2-50-57 (rus.)