Journal
SYMMETRY-BASEL
Volume 15, Issue 5, Pages -Publisher
MDPI
DOI: 10.3390/sym15051009
Keywords
non-Fourier; heat conduction; FGM; hollow cylinder; graded FEM
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In this study, a graded finite element analysis is used to solve the axisymmetric 2D hyperbolic heat conduction equation in a finite hollow cylinder made of functionally graded materials. The graded FE method is verified, and the rule of the mixture with power-law volume fraction is found to enhance the thermal properties' gradation along the radial direction. The effects of Vernotte numbers and material distributions on temperature waves are investigated, and the results are discussed for different heat conduction models and material distributions.
In the present work, we implement a graded finite element analysis to solve the axisymmetric 2D hyperbolic heat conduction equation in a finite hollow cylinder made of functionally graded materials using quadratic Lagrangian shape functions. The graded FE method is verified, and the simple rule of the mixture with power-law volume fraction is found to enhance the effective thermal properties' gradation along the radial direction, including the thermal relaxation time. The effects of the Vernotte numbers and material distributions on temperature waves are investigated in depth, and the results are discussed for Fourier and non-Fourier heat conductions, and homogeneous and inhomogeneous material distributions. The homogeneous cylinder wall made of SUS304 shows faster temperature wave velocity in comparison to the ceramic-rich cylinder wall, which demonstrates the slowest one. Furthermore, the temperature profiles along the radial direction when n = 2 and n = 5 are almost the same in all Ve numbers, and by increasing the Ve numbers, the temperature waves move slower in all the material distributions. Finally, by tuning the material distribution which affects the thermal relaxation time, the desirable results for temperature distribution can be achieved.
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