New perspectives for modelling ballistic-diffusive heat conduction

被引：0
作者：
G. Balassa
P. Rogolino
Á. Rieth
R. Kovács
机构：
[1] BME,Department of Energy Engineering, Faculty of Mechanical Engineering
[2] Wigner Research Centre for Physics,Department of Theoretical Physics
[3] Institute for Particle and Nuclear Physics,Department of Mathematics and Computer Sciences, Physical Sciences and Earth Sciences
[4] Montavid Thermodynamic Research Group,undefined
[5] University of Messina,undefined
来源：
Continuum Mechanics and Thermodynamics | 2021年 / 33卷
关键词：
Ballistic heat conduction; Finite differences; Non-equilibrium thermodynamics; Analytical solution;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Among the three heat conduction modes (diffusive, second sound, and ballistic propagation), the ballistic one is the most difficult to model. In the present paper, we discuss its physical interpretations and show different alternatives to its modelling. We highlight two of them: a thermo-mechanical model in which the generalized heat equation—the so-called Maxwell–Cattaneo–Vernotte equation—is coupled to thermal expansion. The other one uses internal variables in the framework of non-equilibrium thermodynamics. For the first one, we developed a numerical solution and tested it on the heat pulse experiment performed by McNelly et al. on NaF samples. For the second one, we found an analytical solution that emphasizes the role of boundary conditions. This analytical method is used to validate an earlier developed numerical code.
引用
收藏
页码：2007 / 2026
页数：19
相关论文
共 131 条
[1]  
Tisza L(1938)Transport phenomena in Helium II Nature 141 913-28
[2]  
Landau L(1941)Two-fluid model of liquid Helium II J. Phys. USSR 5 71-1439
[3]  
Jackson HE(1970)Second sound in NaF Phys. Rev. Lett. 25 26-391
[4]  
Walker CT(1971)Thermal conductivity, second sound and phonon-phonon interactions in NaF Phys. Rev. B 3 1428-50
[5]  
McNelly TF(1989)Heat waves Rev. Mod. Phys. 61 41-602
[6]  
Jackson HE(1990)Addendum to the paper on heat waves Rev. Mod. Phys. 62 375-620
[7]  
Walker CT(1993)Heat pulse experiments revisited Continuum Mech. Thermodyn. 5 3-28
[8]  
Joseph DD(2013)A transient ballistic-diffusive heat conduction model for heat pulse propagation in nonmetallic crystals Int. J. Heat Mass Transf. 66 592-333
[9]  
Preziosi L(2015)Generalized heat conduction in heat pulse experiments Int. J. Heat Mass Transf. 83 613-478
[10]  
Joseph DD(1996)Determination of material functions through second sound measurements in a hyperbolic heat conduction theory Math. Comput. Modell. 24 19-136
12345678910