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Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method

Farzad Mohebbi, Ben Evans Orcid Logo, Timon Rabczuk

International Journal of Thermal Sciences, Volume: 159

Swansea University Authors: Farzad Mohebbi, Ben Evans Orcid Logo

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DOI (Published version): 10.1016/j.ijthermalsci.2020.106629

Abstract

In this study we present a numerical approach to solve steady-state heat conduction problems in functionally graded materials (FGMs). Two different types of material gradations are considered for spatially varying thermal conductivity of FGM: (1) Quadratic material gradation; (2) Exponential materia...

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Published in: International Journal of Thermal Sciences
ISSN: 1290-0729
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa55140
first_indexed 2020-09-08T08:24:37Z
last_indexed 2020-10-31T04:07:59Z
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spelling 2020-10-30T16:01:32.7270371 v2 55140 2020-09-08 Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method 35d5780a36e2949d4a6b6268c3dc1db0 Farzad Mohebbi Farzad Mohebbi true false 3d273fecc8121fe6b53b8fe5281b9c97 0000-0003-3662-9583 Ben Evans Ben Evans true false 2020-09-08 In this study we present a numerical approach to solve steady-state heat conduction problems in functionally graded materials (FGMs). Two different types of material gradations are considered for spatially varying thermal conductivity of FGM: (1) Quadratic material gradation; (2) Exponential material gradation. The proposed numerical procedure is based on finite-difference method and is developed to solve the steady-state heat conduction equation over a general two-dimensional (irregular) heat conducting body (FGM) with Dirichlet, Neumann, and Robin boundary conditions. In addition to presenting an accurate heat conduction equation solution considering an irregular shape and a variety of boundary conditions, the other novel aspect of this study is to identify the constant parameters in the material gradations accurately by an inverse analysis thereby determining the accurate form of gradation. The novelty of the inverse analysis lies in proposing an accurate and efficient explicit sensitivity analysis scheme. The main advantage of the sensitivity analysis scheme is that it is not involved with an adjoint equation and all the sensitivity coefficients can be explicitly computed in only one direct solution. The conjugate gradient method (CGM) is used to reduce the mismatch between the computed temperature on part of the boundary and the simulated measured temperature distribution. The accuracy, efficiency, and robustness of the proposed numerical approach are demonstrated through presenting two test cases. Journal Article International Journal of Thermal Sciences 159 Elsevier BV 1290-0729 Functionally graded materials, Steady-state heat conduction, Inverse analysis, Conjugate gradient method, Spatially varying thermal conductivity, Sensitivity analysis 1 1 2021 2021-01-01 10.1016/j.ijthermalsci.2020.106629 COLLEGE NANME COLLEGE CODE Swansea University 2020-10-30T16:01:32.7270371 2020-09-08T09:22:33.6073541 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Farzad Mohebbi 1 Ben Evans 0000-0003-3662-9583 2 Timon Rabczuk 3 55140__18314__255c16078ac04c44a6cff4c2d196700e.pdf 55140.pdf 2020-10-05T12:45:06.7022347 Output 16241691 application/pdf Accepted Manuscript true 2021-09-28T00:00:00.0000000 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method
spellingShingle Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method
Farzad Mohebbi
Ben Evans
title_short Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method
title_full Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method
title_fullStr Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method
title_full_unstemmed Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method
title_sort Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method
author_id_str_mv 35d5780a36e2949d4a6b6268c3dc1db0
3d273fecc8121fe6b53b8fe5281b9c97
author_id_fullname_str_mv 35d5780a36e2949d4a6b6268c3dc1db0_***_Farzad Mohebbi
3d273fecc8121fe6b53b8fe5281b9c97_***_Ben Evans
author Farzad Mohebbi
Ben Evans
author2 Farzad Mohebbi
Ben Evans
Timon Rabczuk
format Journal article
container_title International Journal of Thermal Sciences
container_volume 159
publishDate 2021
institution Swansea University
issn 1290-0729
doi_str_mv 10.1016/j.ijthermalsci.2020.106629
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
document_store_str 1
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description In this study we present a numerical approach to solve steady-state heat conduction problems in functionally graded materials (FGMs). Two different types of material gradations are considered for spatially varying thermal conductivity of FGM: (1) Quadratic material gradation; (2) Exponential material gradation. The proposed numerical procedure is based on finite-difference method and is developed to solve the steady-state heat conduction equation over a general two-dimensional (irregular) heat conducting body (FGM) with Dirichlet, Neumann, and Robin boundary conditions. In addition to presenting an accurate heat conduction equation solution considering an irregular shape and a variety of boundary conditions, the other novel aspect of this study is to identify the constant parameters in the material gradations accurately by an inverse analysis thereby determining the accurate form of gradation. The novelty of the inverse analysis lies in proposing an accurate and efficient explicit sensitivity analysis scheme. The main advantage of the sensitivity analysis scheme is that it is not involved with an adjoint equation and all the sensitivity coefficients can be explicitly computed in only one direct solution. The conjugate gradient method (CGM) is used to reduce the mismatch between the computed temperature on part of the boundary and the simulated measured temperature distribution. The accuracy, efficiency, and robustness of the proposed numerical approach are demonstrated through presenting two test cases.
published_date 2021-01-01T14:00:15Z
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