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Cracks formed in building walls are frequently restored by injecting specially formulated repair grouts into the damaged areas. This study examines the effect of such repaired cracks on the thermal performance of building envelopes. Heat transfer within cracked wall sections was modeled by solving the two-dimensional steady-state heat conduction equation. Convective boundary conditions of the third kind were specified on the exterior surfaces to account for heat exchange between the wall and the surrounding environment. The truncated edges of the computational domain were assigned insulated (second-kind) boundary conditions, corresponding to zero normal heat flux. At the interfaces between adjacent materials, continuity of both temperature and heat flux was enforced through fourth-kind boundary conditions. The numerical analysis was carried out using the finite element method implemented in ANSYS Workbench 2024. Based on the obtained numerical results, a procedure was developed for constructing nomograms that characterize the specific heat losses associated with wall cracks repaired by injection grouting. The temperature fields of aerated concrete, clay brick, and reinforced concrete wall assemblies were investigated. The results indicate that injecting a repair grout into a crack increases the heat flux through the examined section in brick and aerated concrete walls, whereas the opposite effect is observed for reinforced concrete walls, where the heat flux decreases after crack injection. The simulations demonstrated that replacing the air-filled crack with injection grout increases the heat flux across the repaired region of the wall. Graphical nomograms were therefore established to estimate the heat flow through repaired cracks directly from two governing parameters – the crack depth and the crack opening width – without the need for a complete numerical solution of the temperature field. In addition, the paper presents a practical algorithm describing the application of these nomograms in engineering calculations. The developed graphical tools can be employed to evaluate the overall thermal resistance of building envelopes during reconstruction, rehabilitation, and major renovation of existing buildings.
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2. Wu J., Shi Y., Wang H., Wen Y., Du Y. Surface defect detection of Nanjing city wall based on UAV oblique photogrammetry and TLS. Remote Sensing. 2023. 15 (8). P. 2089.
3. Dong X., Liu Y., Dai J. Concrete surface crack detection algorithm based on improved YOLOv8. Sensors. 2024. 24 (16). P. 5252.
4. Wang X., Li W., Shen M., Wang H. Numerical analysis of slurry–crack coupling in grouting repair process of multiple cracks in concrete material. Materials. 2025. 18 (11). P. 2472.
5. Tselios I., Vintzileou E., Karagiannaki D., Christidis K., Palieraki V., Welz G. Anchors to solid clay brick masonry in tension: behavior under monotonic and repeated loading for constant embedment depth. Applied Sciences. 2023. 13 (23). P. 12917.
6. Oladiran O.J., Oguntona O.A. Comparative assessment of the properties of normal concrete and epoxy-repaired concrete. Materials Proceedings. 2025. 27 (1). P. 1.
7. Starczyk-Kołbyk A., Łasica W., Kardaszuk E., Gregorczyk M. Eco-Friendly rapid-setting concrete incorporating waste-derived additives for post-disaster reconstruction. Materials. 2026. 19 (6). P. 1218.
8. Sun N., Shen C., Shen J., Wang Y. Mechanical properties and constitutive model of rapid-curing epoxy resin concrete under different temperature conditions. Materials. 2026. 19 (5). P. 996.
9. Chuang P.M., Yeih W.C., Huang R., Chen T.A., Chang J.J. A Study on cement-based crack injection materials using reactive ultra-fine fly ash, portland cement (Type I), and sulfoaluminate cement. Buildings. 2025. 15 (7). P. 1193.
10. Li G., Yan D., Liu J., Yang P., Zhang J. Experimental study on the crack concrete repaired via enzyme-induced calcium carbonate precipitation (EICP). Materials. 2024. 17 (13). P. 3205.
11. Chen Z., Xu X., Wei J., Guo X., Ke X. Mechanism of the EICP centrifugal cementation method for short-term brick crack rehabilitation. Buildings. 2026. 16 (6). P. 1251.
12. Adnan Y., Jaffar N., Razali H., Wooi L.K., Lim C.H. Field measurements of adaptive thermal comfort in naturally ventilated homes of Malaysia's hot–humid climate. Buildings. 2026. 16 (7). P. 1419.
13. Muhy Al Din S.S., Hafizi N., Altan H. Quantifying the relationship between mean radiant temperature and indoor air temperature across building orientations in hot and dry steppe climates. Atmosphere. 2025. 16 (10). P. 1132.
14. Takva Ç., Takva F.G., Çakıcı F.Z. Thermal analysis of the building envelope with infrared thermography and simulation in educational buildings in the cold climate region. Buildings. 2025. 15 (11). P. 1759.
15. Yang C., Misni A. Exploring comfort and efficiency: comparing vernacular and modern dwellings in rural Handan, northern China. Sustainability. 2026. 18 (3). P. 1575.
16. Hrčka R., Štompf P., Jochim S., Mikuš M.E., Iskra M. The measurement of hemp concrete thermal and moisture properties for an effective building construction proposal in region of Slovakia (central Europe). Materials. 2025. 18 (7). P. 1651.
17. Fan C., Chen J., Yu P. Feedback effects of air-conditioning anthropogenic heat on cooling energy consumption in residential buildings: a CFD–EnergyPlus co-simulation study. Buildings. 2026. 16 (8). P. 1610.
18. Ma X., Mao Z., Xuan H. Spatial performance optimization of high-altitude residential buildings based on the thermal buffer effect: a case study of new-type vernacular housing in Lhasa. Buildings. 2025. 15 (23). P. 4337.
19. Sun Y., Tana, Zhen Q., Yan C., Chasuna, Liu K. Spatiotemporal analysis of temperature distribution in semi-underground potato storage facilities in cold and arid regions of China. Sustainability. 2026. 18 (6). P. 2927.
20. Koo B.K., Jin H.S., Jeong J.-W. Deep learning-supported panoramic infrared framework for quantitative diagnosis of building envelope thermal anomalies. Buildings. 2025. 15 (24). P. 4423.
21. Iavorschi E., Milici L.D., Atănăsoae P., Ungureanu C. An experimental and numerical investigation of a passive façade and proposals for improving its energy performance. Energies. 2025. 18 (2). P. 359.
22. Jezierski W., Szczepaniak P., Leszczyński C. Optimization of thermal insulation parameters for vertical perimeters in buildings with single-layer walls. Buildings. 2025. 15 (3). P. 405.
23. Qin L., Qi J., Qi Y., Shi W. Energy consumption analysis and energy-saving renovation research on the building envelope structure of existing thermal power plants in China's hot summer and cold winter regions. Buildings. 2026. 16 (1). P. 169.
24. Zhangabay N., Oner A., Ibraimova U., Ibrahim M.N.M., Tursunkululy T., Utelbayeva A. Assessment and numerical modeling of the thermophysical efficiency of newly developed adaptive building envelopes under variable climatic impacts. Buildings. 2026. 16 (2). P. 366.
25. Rusanov A.E., Baiburin A.Kh., Baiburin D.A., Bianco V. Heat loss from defects of hinged facade systems of buildings. Magazine of Civil Engineering. 2020. 95 (3). P. 57 – 65.
Zubarev K.P., Dobshits V.L., Kazunin V.V., Sapronova Y.A., Fedoseev V.D., Kalinina O.V. Mathematical modeling of heat transfer through building envelopes with cracks Construction Materials and Products. 2026. 9 (4). 4. https://doi.org/10.58224/2618-7183-2026-9-4-4