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A lagging response in time exists between the propagation of heat flux and the establishment of temperature gradient and it is affected by the space effect during the heat conduction with the micro-scale property. Based on the general heat conduction law of thermal mass, the dynamic model of generalized thermoelasticity is established by Clausius inequality and Helmholtz free energy, where the inertia effect on the time and space of heat flux and temperature is involved. The guiding equations are derived and given for the isotropic and homogeneous materials. By comparison with the existing models of generalized thermoelasticity, the guiding equations can reduce to the L-S, G-L and G-N models when the heat flux is not very high, so that the inertia effect on space of heat flux and temperature can be ignored. For micro-scale heat conduction, the heat flux may be very high and the inertial force due to the spatial velocity variation cannot be ignored, the non-Fourier phenomenon will take place even under steady state condition. In such cases, the thermal conductivity is affected by the inertia effect of the space, which can be explained by the model established in the paper. Meanwhile, the physically impossible phenomenon that thermal conductivity changes with structure size induced by existing generalized model can also be eliminated.
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Keywords:
- thermal mass /
- general heat conduction law /
- dynamic model of generalized thermoelasticity /
- micro-scale heat conduction
[1] Herwig H, Beckert K 2000 Heat and Mass Transfer 36 387
[2] Lord H W, Shulman Y A 1967 J. Mech. Phys. Solids 15 299
[3] Green A E, Lindsay K A 1972 J. Elasticity 2 1
[4] Green A E, Naghdi P M 1993 J. Elasticity 31 189
[5] Zhou L P, Tang D W, Wu B X, Qian H S 2006 Mater. Sci. Eng. A 428 284
[6] Youssef H M 2011 J. Therm. Stresses 34 138
[7] Chandrasekharaiah D S 1998 Appl. Mech. Rev. 51 705
[8] Tian X G, Shen Y P 2012 Advances in Mechanics 42 1 (in Chinese) [田晓耕, 沈亚鹏 2012 力学进展 42 1]
[9] Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896
[10] Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601
[11] Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273 (in Chinese) [过增元, 曹炳阳 2008 57 4273]
[12] Hu R F, Cao B Y 2009 Sci. China E: Tech. Sci. 39 680 (in Chinese) [胡锐峰, 曹炳阳 2009 中国科学E辑-技术科学 39 680]
[13] Guo Z Y, Wu J, Cao B Y 2009 J. Mech. Eng. 45 10 (in Chinese) [过增元, 吴晶, 曹炳阳 2009 机械工程学报 45 10]
[14] Guo Z Y, Cao B Y, Zhu H Y, Zhang Q G 2007 Acta Phys. Sin. 56 3306 (in Chinese) [过增元, 曹炳阳, 朱宏晔, 张清光 2007 56 3306]
[15] Wang H G 1989 Introduction of Thermoealsticity (Beijing: Tsinghua University Press) p39 (in Chinese) [王洪纲 1989 热弹性力学概论 (北京: 清华大学出版社) 第39页]
[16] Dillon O W 1962 J. Mech. Phys. Solids 10 123
[17] Wang Y Z, Zhang X B, Song X N 2012 Acta Mechanica 223 735
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[1] Herwig H, Beckert K 2000 Heat and Mass Transfer 36 387
[2] Lord H W, Shulman Y A 1967 J. Mech. Phys. Solids 15 299
[3] Green A E, Lindsay K A 1972 J. Elasticity 2 1
[4] Green A E, Naghdi P M 1993 J. Elasticity 31 189
[5] Zhou L P, Tang D W, Wu B X, Qian H S 2006 Mater. Sci. Eng. A 428 284
[6] Youssef H M 2011 J. Therm. Stresses 34 138
[7] Chandrasekharaiah D S 1998 Appl. Mech. Rev. 51 705
[8] Tian X G, Shen Y P 2012 Advances in Mechanics 42 1 (in Chinese) [田晓耕, 沈亚鹏 2012 力学进展 42 1]
[9] Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896
[10] Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601
[11] Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273 (in Chinese) [过增元, 曹炳阳 2008 57 4273]
[12] Hu R F, Cao B Y 2009 Sci. China E: Tech. Sci. 39 680 (in Chinese) [胡锐峰, 曹炳阳 2009 中国科学E辑-技术科学 39 680]
[13] Guo Z Y, Wu J, Cao B Y 2009 J. Mech. Eng. 45 10 (in Chinese) [过增元, 吴晶, 曹炳阳 2009 机械工程学报 45 10]
[14] Guo Z Y, Cao B Y, Zhu H Y, Zhang Q G 2007 Acta Phys. Sin. 56 3306 (in Chinese) [过增元, 曹炳阳, 朱宏晔, 张清光 2007 56 3306]
[15] Wang H G 1989 Introduction of Thermoealsticity (Beijing: Tsinghua University Press) p39 (in Chinese) [王洪纲 1989 热弹性力学概论 (北京: 清华大学出版社) 第39页]
[16] Dillon O W 1962 J. Mech. Phys. Solids 10 123
[17] Wang Y Z, Zhang X B, Song X N 2012 Acta Mechanica 223 735
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