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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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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
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa55140
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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 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.
Keywords: Functionally graded materials, Steady-state heat conduction, Inverse analysis, Conjugate gradient method, Spatially varying thermal conductivity, Sensitivity analysis
College: College of Engineering