Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method
Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are r...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/5/2738 |
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| author | Juan-Sebastian Rincon-Tabares Juan C. Velasquez-Gonzalez Daniel Ramirez-Tamayo Arturo Montoya Harry Millwater David Restrepo |
| author_facet | Juan-Sebastian Rincon-Tabares Juan C. Velasquez-Gonzalez Daniel Ramirez-Tamayo Arturo Montoya Harry Millwater David Restrepo |
| author_sort | Juan-Sebastian Rincon-Tabares |
| collection | DOAJ |
| description | Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are required to predict the thermal response. Numerical tools are even more relevant when the number of parameters influencing the model is large, and it is necessary to isolate the most influential variables. In this regard, sensitivity analysis can be conducted to increase the process understanding and identify those variables. Here, we combine the complex-variable differentiation theory with the finite element formulation for transient heat transfer, allowing one to compute efficient and accurate first-order sensitivities. Although this approach takes advantage of complex algebra to calculate sensitivities, the method is implemented with real-variable solvers, facilitating the application within commercial software. We present this new methodology in a numerical example using the commercial software Abaqus. The calculation of sensitivities for the temperature and heat flux with respect to temperature-dependent material properties, boundary conditions, geometric parameters, and time are demonstrated. To highlight, the new sensitivity method showed step-size independence, mesh perturbation independence, and reduced computational time contrasting traditional sensitivity analysis methods such as finite differentiation. |
| first_indexed | 2024-03-09T20:46:43Z |
| format | Article |
| id | doaj.art-733a614a584e4327a65aa8d6ceb9d922 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T20:46:43Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-733a614a584e4327a65aa8d6ceb9d9222023-11-23T22:45:32ZengMDPI AGApplied Sciences2076-34172022-03-01125273810.3390/app12052738Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element MethodJuan-Sebastian Rincon-Tabares0Juan C. Velasquez-Gonzalez1Daniel Ramirez-Tamayo2Arturo Montoya3Harry Millwater4David Restrepo5Department of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USADepartment of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USADepartment of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USADepartment of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USADepartment of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USADepartment of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USASolving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are required to predict the thermal response. Numerical tools are even more relevant when the number of parameters influencing the model is large, and it is necessary to isolate the most influential variables. In this regard, sensitivity analysis can be conducted to increase the process understanding and identify those variables. Here, we combine the complex-variable differentiation theory with the finite element formulation for transient heat transfer, allowing one to compute efficient and accurate first-order sensitivities. Although this approach takes advantage of complex algebra to calculate sensitivities, the method is implemented with real-variable solvers, facilitating the application within commercial software. We present this new methodology in a numerical example using the commercial software Abaqus. The calculation of sensitivities for the temperature and heat flux with respect to temperature-dependent material properties, boundary conditions, geometric parameters, and time are demonstrated. To highlight, the new sensitivity method showed step-size independence, mesh perturbation independence, and reduced computational time contrasting traditional sensitivity analysis methods such as finite differentiation.https://www.mdpi.com/2076-3417/12/5/2738finite differencesfinite elementstransient conductioncomplex-variable differentiationsensitivity analysisheat conduction |
| spellingShingle | Juan-Sebastian Rincon-Tabares Juan C. Velasquez-Gonzalez Daniel Ramirez-Tamayo Arturo Montoya Harry Millwater David Restrepo Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method Applied Sciences finite differences finite elements transient conduction complex-variable differentiation sensitivity analysis heat conduction |
| title | Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method |
| title_full | Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method |
| title_fullStr | Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method |
| title_full_unstemmed | Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method |
| title_short | Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method |
| title_sort | sensitivity analysis for transient thermal problems using the complex variable finite element method |
| topic | finite differences finite elements transient conduction complex-variable differentiation sensitivity analysis heat conduction |
| url | https://www.mdpi.com/2076-3417/12/5/2738 |
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