Abstract
Curved interfaces between material media with different characteristic speed for heat waves may be the basis for thermal lenses, concentrating the energy carried by parallel thermal rays on a focal point. This may be of practical use for the amplification of thermal signals and for the development of sensitive thermal sensors. When dissipative attenuation effects are taken into account, it turns out that these lenses could be of special interest in miniaturized probes, or in micro/nanosystems, and the optimization of the thermal lens for signal amplification may be calculated.
Funding statement: A. S. acknowledges the Italian “National Group of Mathematical Physics (GNFM-INdAM)” for supporting the research project “Progetto Giovani 2018/Heat-pulse propagation in FGMs”.
Acknowledgment
D. J. acknowledges Prof. A. Sellitto and the Department of Industrial Engineering of the University of Salerno for his stay and the hospitality during the period 18–28 September 2018.
References
[1] G. Lebon, D. Jou, J. Casas-Vázquez and W. Muschik, Weakly nonlocal and nonlinear heat transport in rigid solids, J. Non-Equilib. Thermodyn. 23 (1998), 176–191.10.1515/jnet.1998.23.2.176Search in Google Scholar
[2] I. Müller and T. Ruggeri, Rational Extended Thermodynamics, second ed., Springer, New York, 1998.10.1007/978-1-4612-2210-1Search in Google Scholar
[3] G. Lebon, D. Jou and J. Casas-Vázquez, Understanding Non-Equilibrium Thermodynamics, Springer, Berlin, 2008.10.1007/978-3-540-74252-4Search in Google Scholar
[4] V. A. Cimmelli, Different thermodynamic theories and different heat conduction laws, J. Non-Equilib. Thermodyn. 34 (2009), 299–333.10.1515/JNETDY.2009.016Search in Google Scholar
[5] D. Jou, J. Casas-Vázquez and G. Lebon, Extended Irreversible Thermodynamics, fourth ed., Springer, Berlin, 2010.10.1007/978-90-481-3074-0Search in Google Scholar
[6] G. Lebon, Heat conduction at micro and nanoscales: A review through the prism of extended irreversible thermodynamics, J. Non-Equilib. Thermodyn. 39 (2014), 35–59.10.1515/jnetdy-2013-0029Search in Google Scholar
[7] Y. Guo and M. Wang, Phonon hydrodynamics and its applications in nanoscale heat transport, Phys. Rep. 595 (2015), 1–44.10.1016/j.physrep.2015.07.003Search in Google Scholar
[8] S. Both, B. Czél, T. Fülöp, G. Gróf, A. Gyens, R. Kovács, et al., Deviation from the fourier law in room-temperature heat pulse experiments, J. Non-Equilib. Thermodyn. 41 (2015), 41–48.10.1515/jnet-2015-0035Search in Google Scholar
[9] A. Sellitto, V. A. Cimmelli and D. Jou, Mesoscopic Theories of Heat Transport in Nanosystems, SEMA-SIMAI Springer Series 6, Springer International Publishing, 2016.10.1007/978-3-319-27206-1Search in Google Scholar
[10] D. D. Joseph and L. Preziosi, Addendum to the paper “heat waves” [Rev. Mod. Phys. 61, 41 (1989), Rev. Mod. Phys. 62 (1990), 375–391.10.1103/RevModPhys.62.375Search in Google Scholar
[11] W. Dreyer and H. Struchtrup, Heat pulse experiments revisited, Contin. Mech. Thermodyn. 5 (1993), 3–50.10.1007/BF01135371Search in Google Scholar
[12] E. Marin (ed.), Thermal Wave Physics and Related Photo Thermal Techniques: Basic Principle and Recent Developments, Transworld Research, Kerale, India, 2009.Search in Google Scholar
[13] V. A. Cimmelli, D. Jou and A. Sellitto, Propagation of temperature waves along core-shell nanowires, J. Non-Equilib. Thermodyn. 35 (2010), 267–278.10.1515/jnetdy.2010.016Search in Google Scholar
[14] B. Straughan, Heat Waves, Springer, Berlin, 2011.10.1007/978-1-4614-0493-4Search in Google Scholar
[15] G. Lebon, M. Grmela and D. Jou, Extended reversible and irreversible thermodynamics: A Hamiltonian approach with application to heat waves, J. Non-Equilib. Thermodyn. 42 (2016), 153–168.10.1515/jnet-2016-0035Search in Google Scholar
[16] C. Cattaneo, Sulla conduzione del calore, Atti Semin. Mat. Fis. Univ. Modena 3 (1948), 83–101.10.1007/978-3-642-11051-1_5Search in Google Scholar
[17] P. Vernotte, Les paradoxes de la théorie continue de líéquation de la chaleur, C. R. Acad. Sci. 246 (1958), 3154–3155.Search in Google Scholar
[18] D. Jou and A. Sellitto, Focusing of heat pulses along nonequilibrium nanowires, Phys. Lett. A 374 (2009), 313–318.10.1016/j.physleta.2009.10.032Search in Google Scholar
[19] J. M. Ziman, Electrons and Phonons, Oxford University Press, Oxford, 2001.10.1093/acprof:oso/9780198507796.001.0001Search in Google Scholar
[20] S. Pertersson and G. Mahan, Theory of the thermal boundary resistance between dissimilar lattices, Phys. Rev. B 42 (1990), 7386–7390.10.1103/PhysRevB.42.7386Search in Google Scholar PubMed
[21] G. Chen, Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices, Phys. Rev. B 57 (1998), 14958–14973.10.1103/PhysRevB.57.14958Search in Google Scholar
[22] Z. Tian, K. Esfarjani and G. Chen, Enhancing phonon transmission across a Si/Ge interface by atomic roughness: First-principles study with the Green’s function method, Phys. Rev. B 86 (2012), 235304 (7 pages).10.1103/PhysRevB.86.235304Search in Google Scholar
[23] H. Ali and B. S. Yilbas, Phonon cross-plane transport and thermal boundary resistance: Effect of heat source size and thermal boundary resistance on phonon characteristics, Contin. Mech. Thermodyn. 28 (2016), 1373–1392.10.1007/s00161-015-0480-zSearch in Google Scholar
[24] B. S. Yilbas, S. B. Mansoor and H. Ali, Heat Transport in Micro- and Nanoscale Thin Films, Elsevier, Amsterdam, 2017.Search in Google Scholar
[25] X. Li and R. Yang, Effect of lattice mismatch on phonon transmission and interface thermal conductance across dissimilar material interfaces, Phys. Rev. B 86 (2012), 054305 (13 pages).10.1103/PhysRevB.86.054305Search in Google Scholar
[26] Z. Liang and H. -L. Tsai, Reduction of solid–solid thermal boundary resistance by inserting an interlayer, Int. J. Heat Mass Transf. 55 (2012), 2999–3007.10.1016/j.ijheatmasstransfer.2012.02.019Search in Google Scholar
[27] T. S. English, J. C. Duda, J. L. Smoyer, D. A. Jordan, P. M. Norris and L. V. Zhigilei, Enhancing and tuning phonon transport at vibrationally mismatched solid-solid interfaces, Phys. Rev. B 85 (2012), 035438 (14 pages).10.1103/PhysRevB.85.035438Search in Google Scholar
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