2013, 2013(special): 737-746. doi: 10.3934/proc.2013.2013.737

Modeling the thermal conductance of phononic crystal plates

1. 

Rudolf Peierls Center for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom

2. 

Department of Electrical Engineering and Computer Science, University of Applied Sciences Zittau/Görlitz, D-02826 Görlitz, Germany

Received  September 2012 Published  November 2013

The paper presents a model to compute the phonon thermal conductance of phononic crystal plates. The goal is the optimization of the figure of merit for these materials, which is the primary criterion for the efficiency of a thermoelectric device. Values of about three or higher allow for the construction of thermoelectric generators based on the Seebeck effect, which are more efficient than conventional electrical generators. The paper introduces a numerical method to optimize the phonon thermal conductance of a given phononic material by varying the geometrical structure with respect to the width and thickness of a sample as well as pore size, shape, and mass density.
Citation: Stefanie Thiem, Jörg Lässig. Modeling the thermal conductance of phononic crystal plates. Conference Publications, 2013, 2013 (special) : 737-746. doi: 10.3934/proc.2013.2013.737
References:
[1]

D. Y. Chung, T. Hogan, J. Schindler, L. Iordarridis, P. Brazis, C. R. Kannewurf, B. Chen, C. Uher, and M.G. Kanatzidis, Complex bismuth chalcogenides as thermoelectrics,, 16th International Conference on Thermoelectrics, 1 (1997), 459.

[2]

A. Grigorevskii, V. Grigorevskii, and S. Nikitov, Dispersion curves of bulk acoustic waves in an elastic body with a two-dimensional periodic structure of circular holes,, Acoustical Physics, 54 (2008), 289.

[3]

T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge, Quantum dot superlattice thermoelectric materials and devices,, Science, 297 (2002), 2229.

[4]

A. I. Hochbaum, C. Renkun, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Enhanced thermoelectric performance of rough silicon nanowires,, Nature, 451 (2008), 163.

[5]

J.-C. Hsu and T.-T. Wu, Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates,, Physical Review B, 74 (2006).

[6]

W. Kuang, Z. Hou and Y. Liu, The effects of shapes and symmetries of scatterers on the phononic band gap in 2D phononic crystals,, Physics Letters A, 332 (2004), 481.

[7]

M. S. Kushwaha, P. Halevi, G. Martínez, I. Dobrzynski, and B. Djafari Rouhani, Theory of acoustic band structure of periodic elastic composites,, Physical Review B, 49 (1994), 2313.

[8]

N. Mingo, Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations,, Physical Review B, 68 (2003).

[9]

G. G. Samsonidze., R. Saito, A. Jorio, M. A. Pimenta, A. G. Souza Filho, A. Grüneis, G. Dresselhaus, and M. S. Dresselhaus, The concept of cutting lines in carbon nanotube science,, Journal of Nanoscience and Nanotechnology, 3 (2003), 431.

[10]

G. A. Slack, New materials and performance limits for thermoelectric cooling,, in ''CRC Handbook of Thermoelectrics'' (ed. D. M. Rowe), (1995), 407.

[11]

Y. Tanaka, Y. Tomoyasu, and S. Tamura, Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch,, Physical Review B, 62 (2000), 7387.

[12]

J. Tang, H.-T. Wang, D. H. Lee, M. Fardy, Z. Huo, T. P. Russell, and P. Yang, Holey silicon as an efficient thermoelectric material,, Nano Letters, 10 (2010), 4279.

[13]

J. O. Vasseur, P. A. Deymier, B. Djafari Rouhani, Y. Pennec, and A.-C. Hladky Hennion, Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,, Physical Review B, 77 (2008).

[14]

R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O'Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit,, Nature, 413 (2001), 597.

show all references

References:
[1]

D. Y. Chung, T. Hogan, J. Schindler, L. Iordarridis, P. Brazis, C. R. Kannewurf, B. Chen, C. Uher, and M.G. Kanatzidis, Complex bismuth chalcogenides as thermoelectrics,, 16th International Conference on Thermoelectrics, 1 (1997), 459.

[2]

A. Grigorevskii, V. Grigorevskii, and S. Nikitov, Dispersion curves of bulk acoustic waves in an elastic body with a two-dimensional periodic structure of circular holes,, Acoustical Physics, 54 (2008), 289.

[3]

T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge, Quantum dot superlattice thermoelectric materials and devices,, Science, 297 (2002), 2229.

[4]

A. I. Hochbaum, C. Renkun, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Enhanced thermoelectric performance of rough silicon nanowires,, Nature, 451 (2008), 163.

[5]

J.-C. Hsu and T.-T. Wu, Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates,, Physical Review B, 74 (2006).

[6]

W. Kuang, Z. Hou and Y. Liu, The effects of shapes and symmetries of scatterers on the phononic band gap in 2D phononic crystals,, Physics Letters A, 332 (2004), 481.

[7]

M. S. Kushwaha, P. Halevi, G. Martínez, I. Dobrzynski, and B. Djafari Rouhani, Theory of acoustic band structure of periodic elastic composites,, Physical Review B, 49 (1994), 2313.

[8]

N. Mingo, Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations,, Physical Review B, 68 (2003).

[9]

G. G. Samsonidze., R. Saito, A. Jorio, M. A. Pimenta, A. G. Souza Filho, A. Grüneis, G. Dresselhaus, and M. S. Dresselhaus, The concept of cutting lines in carbon nanotube science,, Journal of Nanoscience and Nanotechnology, 3 (2003), 431.

[10]

G. A. Slack, New materials and performance limits for thermoelectric cooling,, in ''CRC Handbook of Thermoelectrics'' (ed. D. M. Rowe), (1995), 407.

[11]

Y. Tanaka, Y. Tomoyasu, and S. Tamura, Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch,, Physical Review B, 62 (2000), 7387.

[12]

J. Tang, H.-T. Wang, D. H. Lee, M. Fardy, Z. Huo, T. P. Russell, and P. Yang, Holey silicon as an efficient thermoelectric material,, Nano Letters, 10 (2010), 4279.

[13]

J. O. Vasseur, P. A. Deymier, B. Djafari Rouhani, Y. Pennec, and A.-C. Hladky Hennion, Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,, Physical Review B, 77 (2008).

[14]

R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O'Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit,, Nature, 413 (2001), 597.

[1]

M. Eller, Roberto Triggiani. Exact/approximate controllability of thermoelastic plates with variable thermal coefficients. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 283-302. doi: 10.3934/dcds.2001.7.283

[2]

Claude Stolz. On estimation of internal state by an optimal control approach for elastoplastic material. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 599-611. doi: 10.3934/dcdss.2016014

[3]

Liu Rui. The explicit nonlinear wave solutions of the generalized $b$-equation. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1029-1047. doi: 10.3934/cpaa.2013.12.1029

[4]

Rúben Sousa, Semyon Yakubovich. The spectral expansion approach to index transforms and connections with the theory of diffusion processes. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2351-2378. doi: 10.3934/cpaa.2018112

[5]

Naoufel Ben Abdallah, Antoine Mellet, Marjolaine Puel. Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach. Kinetic & Related Models, 2011, 4 (4) : 873-900. doi: 10.3934/krm.2011.4.873

[6]

R. Bartolo, Anna Maria Candela, J.L. Flores, Addolorata Salvatore. Periodic trajectories in plane wave type spacetimes. Conference Publications, 2005, 2005 (Special) : 77-83. doi: 10.3934/proc.2005.2005.77

[7]

Eric P. Choate, Hong Zhou. Optimization of electromagnetic wave propagation through a liquid crystal layer. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 303-312. doi: 10.3934/dcdss.2015.8.303

[8]

Bendong Lou. Traveling wave solutions of a generalized curvature flow equation in the plane. Conference Publications, 2007, 2007 (Special) : 687-693. doi: 10.3934/proc.2007.2007.687

[9]

Jerry Bona, Jiahong Wu. Temporal growth and eventual periodicity for dispersive wave equations in a quarter plane. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1141-1168. doi: 10.3934/dcds.2009.23.1141

[10]

Brenton LeMesurier. Modeling thermal effects on nonlinear wave motion in biopolymers by a stochastic discrete nonlinear Schrödinger equation with phase damping. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 317-327. doi: 10.3934/dcdss.2008.1.317

[11]

Francesco Maddalena, Danilo Percivale, Franco Tomarelli. Adhesive flexible material structures. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 553-574. doi: 10.3934/dcdsb.2012.17.553

[12]

Kai-Uwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135-156. doi: 10.3934/amc.2009.3.135

[13]

Xiao-Hong Liu, Wei Wu. Coerciveness of some merit functions over symmetric cones. Journal of Industrial & Management Optimization, 2009, 5 (3) : 603-613. doi: 10.3934/jimo.2009.5.603

[14]

Cheng-Hsiung Hsu, Ting-Hui Yang. Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 111-128. doi: 10.3934/dcdsb.2010.14.111

[15]

Sebastian Acosta. A control approach to recover the wave speed (conformal factor) from one measurement. Inverse Problems & Imaging, 2015, 9 (2) : 301-315. doi: 10.3934/ipi.2015.9.301

[16]

P. M. Jordan, Louis Fishman. Phase space and path integral approach to wave propagation modeling. Conference Publications, 2001, 2001 (Special) : 199-210. doi: 10.3934/proc.2001.2001.199

[17]

Bopeng Rao, Zhuangyi Liu. A spectral approach to the indirect boundary control of a system of weakly coupled wave equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399

[18]

Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2603-2616. doi: 10.3934/dcdsb.2014.19.2603

[19]

Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10

[20]

Maria Grazia Naso. Controllability to trajectories for semilinear thermoelastic plates. Conference Publications, 2005, 2005 (Special) : 672-681. doi: 10.3934/proc.2005.2005.672

 Impact Factor: 

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]