Two-Dimensional C-V Heat Conduction Investigation of an FG-Finite Axisymmetric Hollow Cylinder
Abstract
:1. Introduction
2. Mathematical and Material Models
2.1. FGM Material Distribution
2.2. Numerical Scheme
3. Numerical Results and Discussions
3.1. Example 1: Verification
3.2. Example 2: Graded Finite Element Analysis of FG Axisymmetric Cylinder
4. Conclusions
- 1-
- The effective material thermal properties’ gradation, including the thermal relation time, is distributed along the radial direction by the simple rules of the mixture and power-law volume fractions.
- 2-
- Faster temperature wave velocity is related to the homogeneous cylinder wall made of SUS304 in contrast with the ceramic-rich cylinder wall, which is demonstrated to be the slowest one.
- 3-
- For n = 2 and n = 5, there is no difference in the temperature distributions along the radial direction for all Ve numbers.
- 4-
- By increasing the Ve numbers, the temperature waves move slower for all material distributions.
- 5-
- The tuning of the material distribution and, consequently, thermal relaxation time can lead to desirable results for the temperature distribution.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature and Abbreviations
1D | One-Dimensional |
B.C. | Boundary Condition |
BDF | Backward Difference Formula |
C-V | Cattaneo–Vernotte |
DQM | Differential Quadrature Method |
FEM | Finite Element Method |
FGM | Functionally Graded Material |
Fo | Fourier Number |
I.C. | Initial Condition |
LT | Laplace Transformation |
SOV | Separation of Variables |
Ve | Vernotte |
Degree of Kelvin and Centigrade | |
Heat Flux | |
Relaxation Time | |
Coefficient of Thermal Conductivity | |
Temperature, and Pulse Peak Temperature | |
Time | |
Density | |
Specific Heat Capacity | |
Power Exponent | |
Inner Radius, Outer Radius, and Length of the Cylinder | |
r and z-direction | |
Ceramic and Metal Volume Fraction | |
Effective Material Properties | |
Second-Sound (temperature) Wave Velocity | |
Matrix of Quadratic Interpolation Functions | |
Nodal Temperature | |
Boundary Flux | |
Volume | |
Non-Dimensional Temperature |
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Materials/Thermal Properties | |||
1.71 | 491 | 5670 | |
SUS304 | 14.91 | 483 | 7790 |
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Najibi, A.; Wang, G.-H. Two-Dimensional C-V Heat Conduction Investigation of an FG-Finite Axisymmetric Hollow Cylinder. Symmetry 2023, 15, 1009. https://doi.org/10.3390/sym15051009
Najibi A, Wang G-H. Two-Dimensional C-V Heat Conduction Investigation of an FG-Finite Axisymmetric Hollow Cylinder. Symmetry. 2023; 15(5):1009. https://doi.org/10.3390/sym15051009
Chicago/Turabian StyleNajibi, Amir, and Guang-Hui Wang. 2023. "Two-Dimensional C-V Heat Conduction Investigation of an FG-Finite Axisymmetric Hollow Cylinder" Symmetry 15, no. 5: 1009. https://doi.org/10.3390/sym15051009
APA StyleNajibi, A., & Wang, G.-H. (2023). Two-Dimensional C-V Heat Conduction Investigation of an FG-Finite Axisymmetric Hollow Cylinder. Symmetry, 15(5), 1009. https://doi.org/10.3390/sym15051009