Abstract
In this paper, temperature distribution in the continuous and pulsed end-pumped Nd:YAG rod crystal is determined using nonclassical and classical heat conduction theories. In order to find the temperature distribution in crystal, heat transfer differential equations of crystal with consideration of boundary conditions are derived based on non-Fourier’s model and temperature distribution of the crystal is achieved by an analytical method. Then, by transferring non-Fourier differential equations to matrix equations, using finite element method, temperature and stress of every point of crystal are calculated in the time domain. According to the results, a comparison between classical and nonclassical theories is represented to investigate rupture power values. In continuous end pumping with equal input powers, non-Fourier theory predicts greater temperature and stress compared to Fourier theory. It also shows that with an increase in relaxation time, crystal rupture power decreases. Despite of these results, in single rectangular pulsed end-pumping condition, with an equal input power, Fourier theory indicates higher temperature and stress rather than non-Fourier theory. It is also observed that, when the relaxation time increases, maximum amounts of temperature and stress decrease.
Similar content being viewed by others
References
D. Carroll, Overview of high energy lasers: past, present, and future, in: 42nd AIAA Plasmadynamics and Lasers Conference in conjunction with the 18th International Conference on MHD Energy Conversion (ICMHD), 2011, pp. 3102
M. Sobhy, Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations. Int. J. Appl. Mech. 7, 1550082 (2015)
B.S. Yilbas, Quality assessment of drilled holes, in: laser drilling, Springer, 2013, pp. 51–60
D. Vij, K. Mahesh, Medical applications of lasers, Springer Science & Business Media, 2013
M. Endo, R.F. Walter, Gas lasers (CRC Press, Boca Raton, 2016)
M. Jie, G. Zhao, X. Zeng, L. Su, H. Pang, X. He, J. Xu, Crystal growth and optical properties of Gd1.99−xYxCe0.01SiO5 single crystals. J. Cryst. Growth 277, 175–180 (2005)
Y. Gao, Management information and optoelectronic engineering: Proceedings of the 2015 International Conference on Management, Information and Communication & Proceedings of the 2015 International Conference on Optics and Electronics Engineering, World Scientific, 2016
P. Hello, E. Durand, P.K. Fritschel, C.N. Man, Thermal effects in Nd: YAG slabs: 3D modelling and comparison with experiments. J. Mod. Opt. 41, 1371–1390 (1994)
Z. Ma, J. Gao, D. Li, J. Li, N. Wu, K. Du, Thermal stress effects of the diode-end-pumped Nd: YLF slab. Opt. Commun. 281, 3522–3526 (2008)
K.S. Shibib, M.A. Minshid, N.E. Alattar, Thermal and stress analysis in Nd: YAG laser rod with different double end pumping methods. Therm. Sci. 15, S399–S407 (2011)
M. Babaei Bavil, E. Safari, Thermal and stress analyses in an end-pumped Nd: YAG slab laser using finite element method. J. Mech. Sci. Technol. 28, 3231–3236 (2014)
L. Zhang, X. Shang, Analytical solution to non-Fourier heat conduction as a laser beam irradiating on local surface of a semi-infinite medium. Int. J. Heat Mass Transf. 85, 772–780 (2015)
A. Akbarzadeh, Z. Chen, Dual phase lag heat conduction in functionally graded hollow spheres. Int. J. Appl. Mech. 6, 1450002 (2014)
D. Chang, B. Wang, Transient thermal fracture and crack growth behavior in brittle media based on non-Fourier heat conduction. Eng. Fract. Mech. 94, 29–36 (2012)
W. Koechner, Solid-state laser engineering (Springer, Germany, 2013)
W. Koechner, Thermal lensing in a Nd: YAG laser rod. Appl. Opt. 9, 2548–2553 (1970)
T. Kane, J. Eggleston, R. Byer, The slab geometry laser—part II: thermal effects in a finite slab. IEEE J. Quantum Electron. 21, 1195–1210 (1985)
M. Raffel, C.E. Willert, S. Wereley, J. Kompenhans, Particle Image Velocimetry: a Practical Guide (Springer, Göttingen, 2013)
B.L. Wang, J.C. Han, A finite element method for non-Fourier heat conduction in strong thermal shock environments. Frontiers of Materials Science in China 4, 226–233 (2010)
B. Dai, J. Cheng, B. Zheng, A moving kriging interpolation-based meshless local Petrov–Galerkin method for elastodynamic analysis. Int. J. Appl. Mech. 5, 1350011 (2013)
R. Hołubowski, K. Jarczewska, The combination of multi-step differential transformation method and finite element method in vibration analysis of non-prismatic beam. Int. J. Appl. Mech., 1750010 (2016)
D.L. Logan, A first course in the finite element method, Cengage Learning, 2011
M.H. Sadd, Elasticity: Theory, Applications, and Numerics (Academic Press, Cambridge, 2009)
J.N. Reddy, An introduction to nonlinear finite element analysis: with applications to heat transfer, fluid mechanics, and solid mechanics, OUP Oxford, 2014
A.H. Farhadian, H. Saghafifar, M. Dehghanbaghi, Calculation of thermal lensing in end-pumped YVO4/Nd: YVO4 composite crystals in view of the temperature distribution. J. Russ Laser Res 36, 350–355 (2015)
Y.-S. Huang, H.-L. Tsai, F.-L. Chang, Thermo-optic effects affecting the high pump power end pumped solid state lasers: modeling and analysis. Opt. Commun. 273, 515–525 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mojahedi, M., Shekoohinejad, H. Thermal Stress Analysis of a Continuous and Pulsed End-Pumped Nd:YAG Rod Crystal Using Non-Classic Conduction Heat Transfer Theory. Braz J Phys 48, 46–60 (2018). https://doi.org/10.1007/s13538-017-0538-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13538-017-0538-4