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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| Vydané v: | Applied sciences Ročník 12; číslo 5; s. 2738 |
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| Hlavní autori: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Basel
MDPI AG
01.03.2022
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| ISSN: | 2076-3417, 2076-3417 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Velasquez-Gonzalez, Juan C. Rincon-Tabares, Juan-Sebastian Millwater, Harry Restrepo, David Montoya, Arturo Ramirez-Tamayo, Daniel |
| Author_xml | – sequence: 1 givenname: Juan-Sebastian orcidid: 0000-0001-6798-4532 surname: Rincon-Tabares fullname: Rincon-Tabares, Juan-Sebastian – sequence: 2 givenname: Juan C. orcidid: 0000-0003-2442-437X surname: Velasquez-Gonzalez fullname: Velasquez-Gonzalez, Juan C. – sequence: 3 givenname: Daniel surname: Ramirez-Tamayo fullname: Ramirez-Tamayo, Daniel – sequence: 4 givenname: Arturo surname: Montoya fullname: Montoya, Arturo – sequence: 5 givenname: Harry orcidid: 0000-0001-7097-9283 surname: Millwater fullname: Millwater, Harry – sequence: 6 givenname: David orcidid: 0000-0001-5462-5434 surname: Restrepo fullname: Restrepo, David |
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| SubjectTerms | Algorithms Approximation Boundary conditions complex-variable differentiation Cooling Design optimization finite differences Finite element analysis finite elements heat conduction Heat transfer Methods Partial differential equations Sensitivity analysis transient conduction |
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