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In this paper, based on the hyperbolic equation of heat conduction, utilizing the image method and the wave function expansion method, the temperature distributions on the surface of a functionally graded material(FGM) containing a cylindrical inclusion are investigated. According to the model of thermal waves, a general solution of scattered fields of thermal waves is obtained. Effects of different physical parameters (such as the depth of buried inclusion, the thermal conductivity, the thermal diffusion length, the thermal diffusivity, and the thermal relaxation time) on the distribution of temperature are analyzed. The thermal waves are excited on the surface of the FGM by a periodically modulated laser. A cylindrical defect is taken as an inclusion under a thermal conduction condition. Results are expected to provide calculation methods and reference data for infrared thermal wave nondestructive evaluation of an FGM and the inverse problems in mathematical physics.
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Keywords:
- functionally graded material /
- hyperbolic equation of heat conduction /
- temperature distributions /
- cylindrical inclusion
[1] Asemi K, Ashrafi H, Salehi M, Shariyat 2013 Acta Mech. 224 1849
[2] Li Q H, Chen S S, Zeng J H 2013 Chin. Phys. B 22 120204
[3] Akbarzadeh A H, Chen Z T 2012 Int. J. Thermophys. 33 1100
[4] Chen D P, Xing C F, Zhang Z, Zhang C L 2012 Acta Phys. Sin. 61 024202(in Chinese) [陈大鹏, 邢春飞, 张铮, 张存林 2012 61 024202]
[5] Wang Y Z, Song X N 2012 Acta Phys. Sin. 61 234601(in Chinese) [王颖泽, 宋新南 2012 61 234601]
[6] Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273
[7] Cattaneo C 1958 Atti Sem. Mat. Fis. Univ. Modena 3 83
[8] Terron J M, Sanchez-Lavega A, Salazar A 2001 J. Appl. Phys. 89 5696
[9] Atefi G, Talaee M R 2011 Arch. Appl. Mech. 81 569
[10] Mishra S C, Sahai H 2012 Int. J. Heat Mass Transfer 55 7015
[11] Yu J G, Wu B, He C F 2010 Int. J. Eng. Sci. 48 1709
[12] Liu X Z, Zhu Y, Zhang F, Gong X F 2013 Chin. Phys. B 22 024301
[13] Xu H Y, Qi H T, Jiang X Y 2013 Chin. Phys. B 22 014401
[14] Zhao W T, Wu J H 2013 Acta Phys. Sin. 62 184401(in Chinese) [赵伟涛, 吴九汇 2013 62 184401]
[15] Ma X B, Tan H P 2006 J. Funct. Mater. 37 1507(in Chinese) [马晓波, 谈和平 2006 功能材料 37 1507]
[16] Bakkali A, Azrar L, Aljinaidi A A 2013 J. Intell. Mater. Syst. Struct. 24 1754
[17] Gray L J, Kaplan T, Richardson J D 2003 J. Appl. Mech.-T. ASME 70 543
[18] Sutradhar A, Paulino G H, Gray L J 2002 Eng. Anal. Bound. Elem. 26 119
[19] Wang Z X, Guo D R 1979 Special Functions (Beijing: Science Press) pp437-438 (in Chinese) [王竹溪, 郭敦仁 2003 特殊函数概论(北京: 科学出版社)第437–438页]
[20] Wu Q R, Wu J Q 1996 J. Inorg. Mater. 2 343 (in Chinese) [吴清仁, 吴建青 1996 无机材料学报 2 343]
[21] Wu Q R, Liu Z Q 2003 Thermal Physics of Inorganic functional materials (Guangzhou: South China University of Technology Press) pp108-420 (in Chinese) [吴清仁, 刘镇群 2003 无机功能材料热物理(广州: 华南理工大学出版社)第108–420页]
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[1] Asemi K, Ashrafi H, Salehi M, Shariyat 2013 Acta Mech. 224 1849
[2] Li Q H, Chen S S, Zeng J H 2013 Chin. Phys. B 22 120204
[3] Akbarzadeh A H, Chen Z T 2012 Int. J. Thermophys. 33 1100
[4] Chen D P, Xing C F, Zhang Z, Zhang C L 2012 Acta Phys. Sin. 61 024202(in Chinese) [陈大鹏, 邢春飞, 张铮, 张存林 2012 61 024202]
[5] Wang Y Z, Song X N 2012 Acta Phys. Sin. 61 234601(in Chinese) [王颖泽, 宋新南 2012 61 234601]
[6] Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273
[7] Cattaneo C 1958 Atti Sem. Mat. Fis. Univ. Modena 3 83
[8] Terron J M, Sanchez-Lavega A, Salazar A 2001 J. Appl. Phys. 89 5696
[9] Atefi G, Talaee M R 2011 Arch. Appl. Mech. 81 569
[10] Mishra S C, Sahai H 2012 Int. J. Heat Mass Transfer 55 7015
[11] Yu J G, Wu B, He C F 2010 Int. J. Eng. Sci. 48 1709
[12] Liu X Z, Zhu Y, Zhang F, Gong X F 2013 Chin. Phys. B 22 024301
[13] Xu H Y, Qi H T, Jiang X Y 2013 Chin. Phys. B 22 014401
[14] Zhao W T, Wu J H 2013 Acta Phys. Sin. 62 184401(in Chinese) [赵伟涛, 吴九汇 2013 62 184401]
[15] Ma X B, Tan H P 2006 J. Funct. Mater. 37 1507(in Chinese) [马晓波, 谈和平 2006 功能材料 37 1507]
[16] Bakkali A, Azrar L, Aljinaidi A A 2013 J. Intell. Mater. Syst. Struct. 24 1754
[17] Gray L J, Kaplan T, Richardson J D 2003 J. Appl. Mech.-T. ASME 70 543
[18] Sutradhar A, Paulino G H, Gray L J 2002 Eng. Anal. Bound. Elem. 26 119
[19] Wang Z X, Guo D R 1979 Special Functions (Beijing: Science Press) pp437-438 (in Chinese) [王竹溪, 郭敦仁 2003 特殊函数概论(北京: 科学出版社)第437–438页]
[20] Wu Q R, Wu J Q 1996 J. Inorg. Mater. 2 343 (in Chinese) [吴清仁, 吴建青 1996 无机材料学报 2 343]
[21] Wu Q R, Liu Z Q 2003 Thermal Physics of Inorganic functional materials (Guangzhou: South China University of Technology Press) pp108-420 (in Chinese) [吴清仁, 刘镇群 2003 无机功能材料热物理(广州: 华南理工大学出版社)第108–420页]
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