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当热作用时间或受热器件结构尺寸呈现微尺度特征时, 热流运动的惯性效应将对热量的传递过程产生显著地影响. 基于热质的概念, 依据牛顿力学原理引入用于描述热质运动的热波方程, 结合各向同性材料的本构关系, 构建了计及热流运动惯性效应的广义热弹性动力学模型. 利用超常传热的微尺度特征, 采用解析的方法对半无限大体外表面受热冲击作用的一维问题进行了渐近求解. 通过对热波、热弹性波的传播和各物理场分布的分析以及与已有广义热弹性理论预测结果的对比, 揭示了热流运动的惯性效应对热弹性行为的影响. 结果表明：热量的传递除了受到热流加速的时间惯性影响之外, 热流运动的空间惯性也对传热行为产生影响, 当计及空间惯性时, 热波、热弹性波的波速、波前位置, 各物理场的建立时间、阶跃峰值及阶跃间隔均受到不同程度的影响.
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关键词:
- 热惯性 /
- 热质运动 /
- 广义热弹性动力学模型 /
- 渐近分析
The inertia effect induced by the motion of heat flow will have a significant impact on the heat transfer, when the heat pulse duration or the device structure has micro-scale characteristics. Based on the thermomass theory, the thermal wave equation is introduced to describe the motion of thermomass, and the generalized thermoelastic dynamic model involved in the thermal inertia is established by combining the constitutive relation of isotropic material. By taking into account the micro-scale characteristics for the transient heat transfer, the one-dimensional problem for the semi-infinite solid with the boundary subject to thermal impact is investigated by an analytic method, where the asymptotic solutions for thermoelastic response are obtained. With these solutions, the propagation of the thermal wave and thermal elastic wave and the distribution of the temperature, displacement and stresses are studied. By comparison with the same predictions of the L-S generalized thermoelasticity, the effect of thermal inertia on the thermal behaviors is revealed. The results show that the spatial thermal inertia induced by the motion of heat flux has an impact on the thermal behaviors, except for the temporal thermal inertia. All the velocities and wavefront locations of thermal wave and thermal elastic wave, and the time of each physical field begin to establish, the peak values of jumps and the intervals of two jumps are influenced by the spatial thermal inertia.-
Keywords:
- thermal inertia /
- thermomass motion /
- generalized thermoelastic dynamic model /
- asymptotic analysis
[1] Guo Z Y 2000 Advances in Mechanics 30 1(in Chinese) [过增元 2000 力学进展 30 1]
[2] Wang H D, Ma W G, Guo Z Y, Zhang Y, Wang W 2011 Chin. Phys. B 20 040701
[3] Wang H D, Liu J H, Guo Z Y, Takahashi K 2012 Chin. Sci. Bull. 57 1794 (in Chinese) [王海东, 刘锦辉, 过增元, 高桥厚史 2012 科学通报 57 1794]
[4] 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]
[5] Lord H W, Shulman Y A 1967 J. Mech. Phys. Solids 15 299
[6] Green A E, Lindsay K A 1972 J. Elasticity 2 1
[7] Green A E, Naghdi P M 1993 J. Elasticity 31 189
[8] Xu H Y, Qi H T, Jiang X Y 2013 Chin. Phys. B 22 014401
[9] Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601
[10] Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273 (in Chinese) [过增元, 曹炳阳 2008 物理学报 57 4273]
[11] Dong Y, Cao B Y, Guo Z Y J. Appl. Phys. 110 063504
[12] Guo Z Y, Hou Q W 2010 J. Heat and Transfer 132 072403
[13] 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 物理学报 56 3306]
[14] Cao B Y, Guo Z Y 2007 J. Appl. Phys. 102 053503
[15] Cattaneo C 1958 Comptes Renuds 247 431
[16] Vermptte P 1958 Comptes Renuds 246 3154
[17] Wang Y Z, Song X N 2012 Acta Phys. Sin. 61 234601 (in Chinese) [王颖泽, 宋新南 2012 物理学报 61 234601]
[18] Wang Y Z, Zhang X B, Song X N 2012 Acta Mechanica 223 735
[19] Bagri A, Eslami M R 2007 Int. J. Mech. Sci. 49 1325
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[1] Guo Z Y 2000 Advances in Mechanics 30 1(in Chinese) [过增元 2000 力学进展 30 1]
[2] Wang H D, Ma W G, Guo Z Y, Zhang Y, Wang W 2011 Chin. Phys. B 20 040701
[3] Wang H D, Liu J H, Guo Z Y, Takahashi K 2012 Chin. Sci. Bull. 57 1794 (in Chinese) [王海东, 刘锦辉, 过增元, 高桥厚史 2012 科学通报 57 1794]
[4] 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]
[5] Lord H W, Shulman Y A 1967 J. Mech. Phys. Solids 15 299
[6] Green A E, Lindsay K A 1972 J. Elasticity 2 1
[7] Green A E, Naghdi P M 1993 J. Elasticity 31 189
[8] Xu H Y, Qi H T, Jiang X Y 2013 Chin. Phys. B 22 014401
[9] Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601
[10] Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273 (in Chinese) [过增元, 曹炳阳 2008 物理学报 57 4273]
[11] Dong Y, Cao B Y, Guo Z Y J. Appl. Phys. 110 063504
[12] Guo Z Y, Hou Q W 2010 J. Heat and Transfer 132 072403
[13] 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 物理学报 56 3306]
[14] Cao B Y, Guo Z Y 2007 J. Appl. Phys. 102 053503
[15] Cattaneo C 1958 Comptes Renuds 247 431
[16] Vermptte P 1958 Comptes Renuds 246 3154
[17] Wang Y Z, Song X N 2012 Acta Phys. Sin. 61 234601 (in Chinese) [王颖泽, 宋新南 2012 物理学报 61 234601]
[18] Wang Y Z, Zhang X B, Song X N 2012 Acta Mechanica 223 735
[19] Bagri A, Eslami M R 2007 Int. J. Mech. Sci. 49 1325
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