Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model |
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Authors: | Xue-Qian Fang Shu-Min Duan Shu-Hong Liu Xiao-Hua Wang and Wen-Jie Feng |
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Affiliation: | (1) Department of Engineering Mechanics, Shijiazhuang Railway Institute, Shijiazhuang, 050043, China;(2) Computer and Information Engineering Department, Shijiazhuang Railway Institute, Shijiazhuang, 050043, China |
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Abstract: | In this study, a theoretical method is applied to investigate the multiple scattering of thermal waves and temperature field
resulting from a subsurface cylindrical inclusion in a semi-infinite functionally graded material (FGM). The adiabatic boundary
condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally
graded materials by modulated optical beams. The model includes the multiple scattering effects of the cylindrical thermal
wave generated by the line heat source. According to the wave equation of heat conduction, a general solution of scattered
thermal waves is presented. Numerical calculations illustrate the effect of subsurface inclusion on the temperature and phase
change at the sample surface under different physical and geometrical parameters. It is found that the temperature above the
conducting cylindrical inclusion decreases because of the existence of the inclusion. The effect of the inclusion on the temperature
and phase change at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves,
and the distance between the inclusion and the semi-infinite surface. Finally, the effect of the relaxation time of buried
inclusion on the temperature and phase change at the surface is examined. |
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Keywords: | Cylindrical inclusion Multiple scattering of thermal waves Non-Fourier heat conduction law Semi-infinite functionally graded materials |
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