Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach
Thermal loading, especially in fire scenarios, challenges the safety and long-term durability of concrete structures. The resulting heat propagation within the structure is governed by the heat conduction equation, which can be difficult to solve analytically because of the nonlinearity related to t...
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MDPI AG
2023-03-01
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| Online Access: | https://www.mdpi.com/1099-4300/25/4/583 |
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| author | Hui Wang Xi Chen Eduardus Koenders Ying Dai Xingchun Huang Qing Ai Yong Yuan |
| author_facet | Hui Wang Xi Chen Eduardus Koenders Ying Dai Xingchun Huang Qing Ai Yong Yuan |
| author_sort | Hui Wang |
| collection | DOAJ |
| description | Thermal loading, especially in fire scenarios, challenges the safety and long-term durability of concrete structures. The resulting heat propagation within the structure is governed by the heat conduction equation, which can be difficult to solve analytically because of the nonlinearity related to the thermophysical properties of concrete. A semi-analytical approach for the transient nonlinear heat conduction problem in concrete structures was established in the present work. The nonlinearity related to the temperature-dependent thermal conductivity, mass density, and specific heat capacity of heated concrete was taken into consideration. A Taylor series approximate solution was first established within a small neighborhood, employing the Boltzmann transformation in combination with the mean value theorem. Thereafter, it was extended to the whole domain by utilizing the Bernstein polynomial. The semi-analytical approach was validated by comparing it with the numerical results of two independent Finite Element simulations of nonlinear heat conduction along concrete plates, subjected to either moderate or fierce thermal loading. Absolute values of the relative errors are smaller than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>%</mo></mrow></semantics></math></inline-formula>. The validated semi-analytical approach was further applied to prediction of the temporal evolution of the temperature field of a scaled model of a subway station, subjected to fire disaster. The nonlinearities, related to the time-dependent surface temperature and the temperature-dependent thermophysical properties of concrete, were taken into consideration. The predictions agree well with the experimental measurements. The established semi-analytical approach exhibits good accuracy and stability, providing insight into the interaction between the thermophysical properties of concrete in the heat conduction process. |
| first_indexed | 2024-03-11T05:03:10Z |
| format | Article |
| id | doaj.art-77533852b658485f84d840d989857fff |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T05:03:10Z |
| publishDate | 2023-03-01 |
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| spelling | doaj.art-77533852b658485f84d840d989857fff2023-11-17T19:08:07ZengMDPI AGEntropy1099-43002023-03-0125458310.3390/e25040583Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical ApproachHui Wang0Xi Chen1Eduardus Koenders2Ying Dai3Xingchun Huang4Qing Ai5Yong Yuan6School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, ChinaCollege of Civil Engineering and Architecture, Jiaxing University, Jiaxing 314001, ChinaInstitute of Construction and Building Materials, Technical University of Darmstadt, 64287 Darmstadt, GermanySchool of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, ChinaSchool of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, ChinaSchool of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, ChinaCollege of Civil Engineering, Tongji University, Shanghai 200092, ChinaThermal loading, especially in fire scenarios, challenges the safety and long-term durability of concrete structures. The resulting heat propagation within the structure is governed by the heat conduction equation, which can be difficult to solve analytically because of the nonlinearity related to the thermophysical properties of concrete. A semi-analytical approach for the transient nonlinear heat conduction problem in concrete structures was established in the present work. The nonlinearity related to the temperature-dependent thermal conductivity, mass density, and specific heat capacity of heated concrete was taken into consideration. A Taylor series approximate solution was first established within a small neighborhood, employing the Boltzmann transformation in combination with the mean value theorem. Thereafter, it was extended to the whole domain by utilizing the Bernstein polynomial. The semi-analytical approach was validated by comparing it with the numerical results of two independent Finite Element simulations of nonlinear heat conduction along concrete plates, subjected to either moderate or fierce thermal loading. Absolute values of the relative errors are smaller than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>%</mo></mrow></semantics></math></inline-formula>. The validated semi-analytical approach was further applied to prediction of the temporal evolution of the temperature field of a scaled model of a subway station, subjected to fire disaster. The nonlinearities, related to the time-dependent surface temperature and the temperature-dependent thermophysical properties of concrete, were taken into consideration. The predictions agree well with the experimental measurements. The established semi-analytical approach exhibits good accuracy and stability, providing insight into the interaction between the thermophysical properties of concrete in the heat conduction process.https://www.mdpi.com/1099-4300/25/4/583concrete heat conductionsemi-analytical approachhigh temperaturenonlinearfire loading |
| spellingShingle | Hui Wang Xi Chen Eduardus Koenders Ying Dai Xingchun Huang Qing Ai Yong Yuan Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach Entropy concrete heat conduction semi-analytical approach high temperature nonlinear fire loading |
| title | Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach |
| title_full | Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach |
| title_fullStr | Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach |
| title_full_unstemmed | Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach |
| title_short | Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach |
| title_sort | transient nonlinear heat conduction in concrete structures a semi analytical approach |
| topic | concrete heat conduction semi-analytical approach high temperature nonlinear fire loading |
| url | https://www.mdpi.com/1099-4300/25/4/583 |
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