Analytical Determination of the Dynamic Temperature Field of a Steel Sample Exposed to Intense Heating by Applying a Line-Heat-Source
Abstract
The paper presents an analytical closed-form solution to the problem of dynamic change in
the temperature field of a steel sample model during a short-term heating up and thereafter intense heat removal. It is demonstrated how a relatively complex thermal problem can be solved analytically based on differential equation that describes the temperature field. Differential equation that describes the temperature field is formed via the power of several heat sources with limited action time, as shown mathematically by applying the Dirac and Heaviside functions. In the present paper the example provided includes two heat sources. In accordance with boundary conditions the differential equation is solved by applying the finite Fourier transforms and Laplace transform. Based on obtained analytical solution of the problem, a numerical model was created corresponding to the simulation of steel sample heating on a thermomechanical welding simulator. The welding thermal simulator is a device us...ed to achieve controlled heating and cooling, similar to the one in welding. Analytically calculated temperature fields were utilized to obtain the strain distribution in the heat source environment by applying the finite element method.
Keywords:
integral transforms / line heat-source / strain / temperatureSource:
Proceedings of the 13th International Conference on the Mechanical Behaviour of Materials (ICM 13), Melbourne, Australia, 2019, 613-620Funding / projects:
- Pressure equipment integrity under simultaneous effect of fatigue loading and temperature (RS-MESTD-Technological Development (TD or TR)-35011)
- Developed new methods for diagnosis and examination mechanical structures (RS-MESTD-Technological Development (TD or TR)-35040)
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Institution/Community
Mašinski fakultetTY - CONF AU - Milošević-Mitić, Vesna AU - Anđelić, Nina AU - Milović, Ljubica AU - Maneski, Taško PY - 2019 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5556 AB - The paper presents an analytical closed-form solution to the problem of dynamic change in the temperature field of a steel sample model during a short-term heating up and thereafter intense heat removal. It is demonstrated how a relatively complex thermal problem can be solved analytically based on differential equation that describes the temperature field. Differential equation that describes the temperature field is formed via the power of several heat sources with limited action time, as shown mathematically by applying the Dirac and Heaviside functions. In the present paper the example provided includes two heat sources. In accordance with boundary conditions the differential equation is solved by applying the finite Fourier transforms and Laplace transform. Based on obtained analytical solution of the problem, a numerical model was created corresponding to the simulation of steel sample heating on a thermomechanical welding simulator. The welding thermal simulator is a device used to achieve controlled heating and cooling, similar to the one in welding. Analytically calculated temperature fields were utilized to obtain the strain distribution in the heat source environment by applying the finite element method. C3 - Proceedings of the 13th International Conference on the Mechanical Behaviour of Materials (ICM 13), Melbourne, Australia T1 - Analytical Determination of the Dynamic Temperature Field of a Steel Sample Exposed to Intense Heating by Applying a Line-Heat-Source EP - 620 SP - 613 UR - https://hdl.handle.net/21.15107/rcub_machinery_5556 ER -
@conference{ author = "Milošević-Mitić, Vesna and Anđelić, Nina and Milović, Ljubica and Maneski, Taško", year = "2019", abstract = "The paper presents an analytical closed-form solution to the problem of dynamic change in the temperature field of a steel sample model during a short-term heating up and thereafter intense heat removal. It is demonstrated how a relatively complex thermal problem can be solved analytically based on differential equation that describes the temperature field. Differential equation that describes the temperature field is formed via the power of several heat sources with limited action time, as shown mathematically by applying the Dirac and Heaviside functions. In the present paper the example provided includes two heat sources. In accordance with boundary conditions the differential equation is solved by applying the finite Fourier transforms and Laplace transform. Based on obtained analytical solution of the problem, a numerical model was created corresponding to the simulation of steel sample heating on a thermomechanical welding simulator. The welding thermal simulator is a device used to achieve controlled heating and cooling, similar to the one in welding. Analytically calculated temperature fields were utilized to obtain the strain distribution in the heat source environment by applying the finite element method.", journal = "Proceedings of the 13th International Conference on the Mechanical Behaviour of Materials (ICM 13), Melbourne, Australia", title = "Analytical Determination of the Dynamic Temperature Field of a Steel Sample Exposed to Intense Heating by Applying a Line-Heat-Source", pages = "620-613", url = "https://hdl.handle.net/21.15107/rcub_machinery_5556" }
Milošević-Mitić, V., Anđelić, N., Milović, L.,& Maneski, T.. (2019). Analytical Determination of the Dynamic Temperature Field of a Steel Sample Exposed to Intense Heating by Applying a Line-Heat-Source. in Proceedings of the 13th International Conference on the Mechanical Behaviour of Materials (ICM 13), Melbourne, Australia, 613-620. https://hdl.handle.net/21.15107/rcub_machinery_5556
Milošević-Mitić V, Anđelić N, Milović L, Maneski T. Analytical Determination of the Dynamic Temperature Field of a Steel Sample Exposed to Intense Heating by Applying a Line-Heat-Source. in Proceedings of the 13th International Conference on the Mechanical Behaviour of Materials (ICM 13), Melbourne, Australia. 2019;:613-620. https://hdl.handle.net/21.15107/rcub_machinery_5556 .
Milošević-Mitić, Vesna, Anđelić, Nina, Milović, Ljubica, Maneski, Taško, "Analytical Determination of the Dynamic Temperature Field of a Steel Sample Exposed to Intense Heating by Applying a Line-Heat-Source" in Proceedings of the 13th International Conference on the Mechanical Behaviour of Materials (ICM 13), Melbourne, Australia (2019):613-620, https://hdl.handle.net/21.15107/rcub_machinery_5556 .