Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach
A new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coefficients to estimate timewise varying heat flux in heat conduction problems over irregular geometries using the transient readings of a <i>single</i> sensor. There is no prior information ava...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/13/17/4410 |
| _version_ | 1827707478257696768 |
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| author | Farzad Mohebbi |
| author_facet | Farzad Mohebbi |
| author_sort | Farzad Mohebbi |
| collection | DOAJ |
| description | A new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coefficients to estimate timewise varying heat flux in heat conduction problems over irregular geometries using the transient readings of a <i>single</i> sensor. There is no prior information available on the functional form of the unknown heat flux; hence, the inverse problem is regarded as a function estimation problem and sensitivity and adjoint problems are involved in the solution of the inverse problem to recover the unknown heat flux. However, using the proposed sensitivity analysis scheme, one can compute all sensitivity coefficients explicitly in only one direct problem solution at each iteration without the need for solving the sensitivity and adjoint problems. In other words, the functional form of the unknown heat flux can be numerically estimated by using the parameter estimation approach. In this method, the irregular shape of heat-conducting body is meshed using the boundary-fitted grid generation (elliptic) method. Explicit expressions are given to compute the sensitivity coefficients efficiently and the steepest-descent method is used as the minimization method to minimize the objective function and reach the solution. Three test cases are presented to confirm the accuracy and efficiency of the proposed inverse analysis. |
| first_indexed | 2024-03-10T16:48:09Z |
| format | Article |
| id | doaj.art-badba28600e54fadba546e9174667e9d |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T16:48:09Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-badba28600e54fadba546e9174667e9d2023-11-20T11:29:52ZengMDPI AGEnergies1996-10732020-08-011317441010.3390/en13174410Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation ApproachFarzad Mohebbi0Zienkiewicz Centre for Computational Engineering, Bay Campus, College of Engineering, Swansea University, Fabian Way, Crymlyn Burrows, Swansea SA18EN, UKA new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coefficients to estimate timewise varying heat flux in heat conduction problems over irregular geometries using the transient readings of a <i>single</i> sensor. There is no prior information available on the functional form of the unknown heat flux; hence, the inverse problem is regarded as a function estimation problem and sensitivity and adjoint problems are involved in the solution of the inverse problem to recover the unknown heat flux. However, using the proposed sensitivity analysis scheme, one can compute all sensitivity coefficients explicitly in only one direct problem solution at each iteration without the need for solving the sensitivity and adjoint problems. In other words, the functional form of the unknown heat flux can be numerically estimated by using the parameter estimation approach. In this method, the irregular shape of heat-conducting body is meshed using the boundary-fitted grid generation (elliptic) method. Explicit expressions are given to compute the sensitivity coefficients efficiently and the steepest-descent method is used as the minimization method to minimize the objective function and reach the solution. Three test cases are presented to confirm the accuracy and efficiency of the proposed inverse analysis.https://www.mdpi.com/1996-1073/13/17/4410inverse heat transfersteepest-descent methodsensitivity analysisfunction estimationbody-fitted grid generationtimewise varying heat flux |
| spellingShingle | Farzad Mohebbi Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach Energies inverse heat transfer steepest-descent method sensitivity analysis function estimation body-fitted grid generation timewise varying heat flux |
| title | Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach |
| title_full | Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach |
| title_fullStr | Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach |
| title_full_unstemmed | Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach |
| title_short | Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach |
| title_sort | function estimation in inverse heat transfer problems based on parameter estimation approach |
| topic | inverse heat transfer steepest-descent method sensitivity analysis function estimation body-fitted grid generation timewise varying heat flux |
| url | https://www.mdpi.com/1996-1073/13/17/4410 |
| work_keys_str_mv | AT farzadmohebbi functionestimationininverseheattransferproblemsbasedonparameterestimationapproach |