Abstract
Light amplification by stimulated emission of radiation (laser) is an organized monochromatic electromagnetic radiation beam which can proliferate linearly with negligible disparity and the source of energy is found in broad spectrum of wavelength. Laser has been witnessed as ample applications in thermal processing right from material processing to thermal therapy for cancer treatment. The laser processing of materials can be classified as: laser assisted machining, forming, joining and surface engineering. The emitted energy source from laser can be spotlighted into a small spot and it caters a large amount of intense energy which is quintessential for penetration in materials for surface treatment. In this book chapter, exact analytical solution of three-dimensional dual-phase-lag heat conduction model has been developed under the influence of non-Gaussian time and space dependent laser heat source. The corresponding mathematical solution is obtained with implementation of ‘Finite integral transform’ and ‘Duhamel’s theorem’. The consequence of lagging behaviour on laser heating has been studied. The laser heating process variables such as laser exposure, power density have been investigated with temperature variation. The development of surface thermal contours defines the heat flow in the substrate domain. The accuracy of present mathematical modelling has been justified based on the physical phenomena observed under laser heating.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bäuerle, D.: Laser Processing and Chemistry. Springer, Berlin (2000)
Schaff, P.: Laser Processing of Materials: Fundamentals, Applications and Developments. Springer, Berlin, Heidelberg (2010)
Dowden, J.M.: The Mathematics of Thermal Modelling: An Introduction to the Theory of Laser Material Processing. Chapman & Hall/CRC (2001)
Yilbas, B.: Laser Heating Applications: Analytical Modelling. Elsevier (2012)
Heller, J., Bartha, J.W., Poon, C.C., Tam, A.C.: Temperature dependence of the reflectivity of silicon with surface oxide at wavelengths of 633 and 1047 nm. Appl. Phys. Lett. 75(1), 41–43 (1999)
Brown, M.S., Arnold, C.B.: Fundamentals of Laser-Material Interaction and Application to Multiscale Surface Modification. Springer, Berlin, Heidelberg (2000)
Yilbas, B.S., Al-Dweik, A.Y., Al-Aqeeli, N., Al-Qahtani, H.M.: Laser Pulse Heating of Surfaces and Thermal Stress Analysis. Springer International Publishing, Switzerland (2014)
Maiman, T.H.: Stimulated optical radiation in ruby. Nature 187(4736), 493–499 (1960)
Fourier, J.: The Analytical Theory of Heat. Cambridge University Press, Cambridge Warehouse, London (1878)
Arpaci, V.S.: Conduction Heat Transfer. Addison-Wesley Pub. Co., the University of Michigan, Addisson Wesley Pub (1966)
Qiu, T.Q., Tien, L.: Femtosecond laser heating of multi-layer metals—I analysis. Int. J. Heat Mass Transf. 37, 2789–2797 (1994)
Yilbas, B.S., Apalak, K.: The basic concepts of heat transfer mechanism during laser drilling of metals. Egypt J. Phys. 18(1), 25–34 (1987)
Yilbas, B.S., Kalyon, M.: Formulation of laser pulse heating: a closed form solution including heating and cooling cycles with pulse parameter variation. Laser Eng. 14(3–4), 213–228 (2004)
Yilbas, B.S.: Analytical solution for time unsteady laser pulse heating of semi-infinite solid. Int. J. Mech. Sci. 39(6), 671–672 (1997)
Yilbas, B.S.: 3-Dimensional laser heating model including a moving heat source consideration and phase change process. Heat Mass Transf. 33, 495–505 (1998)
Yilbas, B.S., Kalyon, M.: Analytical solution for pulsed laser heating process: convective boundary condition case. Int. J. Heat Mass Transf. 45, 1571–1582 (2002)
Yilbas, B.S., Pakdemirli, M., Mansoor, S.B.: Analytical solution for temperature field in thin film initially heated by a short-pulse laser source. Heat Mass Transf. 41, 1077–1084 (2005)
Kalyon, M., Yilbas, B.S.: An approach for analytical solution pertinent to lattice temperature variation due to laser short-pulse heating. Heat Mass Transf. 42, 1111–1117 (2006)
Hsiao, F.B., Jen, C.P., Wang, D.B., Chuang, C.H., Lee, Y.C., Liu, C.P., Hsu, H.J.: An analytical modeling of heat transfer for laser-assisted nanoimprinting processes. Comput. Mech. 37, 173–181 (2006)
Bouaziz, M.N., Boutalbi, N.: Laser heating of a material with time-dependent laser source. Int. J. Thermophys. 32, 1047–1059 (2011)
Yilbas, B.S., Al-Dweik, A.Y., Mansour, S.B.: Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating. Phys. B 406, 1550–1555 (2011)
Yilbas, B.S., Al-Dweik, A.Y.: Short-pulse heating and analytical solution to non equilibrium heating process. Phys. B 417, 28–32 (2013)
Qi, H.T., Xu, H.Y., Guo, X.W.: The Cattaneo-type time fractional heat conduction equation for laser heating. Comput. Math. Appl. 66, 824–831 (2013)
Zhang, L., Shang, X.: 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)
Peng, Q.: An analytical solution for a transient temperature field during laser heating a finite slab. Appl. Math. Model. 40, 4129–4135 (2016)
Chen, G., Wang, Y., Zhang, J., Bi, J.: An analytical solution for two-dimensional modeling of repetitive long pulse laser heating material. Int. J. Heat Mass Transf. 104, 503–509 (2017)
Kashani, M.M., Movahhedy, M.R., Ahmadian, M.T.: Analytical solution of transient three-dimensional temperature field in a rotating cylinder subject to a localized laser beam. J Heat Transf. 139, 062701–1–062701–8 (2017)
Chen, G.: Semi-analytical solutions for 2-D modeling of long pulsed laser heating metals with temperature dependent surface absorption. Optik 132, 46–51 (2017)
Chen, G., Bi, J.: Analytical solutions for three-dimensional modeling of temperature rise inside solid material induced by laser irradiation. Optik 132, 80–88 (2017)
Chen, G.: Axisymmetric modeling of long pulsed laser heating with convective boundary conditions using analytical solutions. Optik 130, 1038–1044 (2017)
Feng, S., Huang, C., Wang, J., Zhu, H., Yao, P., Liu, Z.: An analytical model for the prediction of temperature distribution and evolution in hybrid laser-waterjet micro-machining. Prec. Eng. 47, 33–45 (2017)
Ma, J., Sun, Y., Yang, J.: Analytical solution of dual-phase-lag heat conduction in a finite medium subjected to a moving heat source. Int. J. Therm. Sci. 125, 34–43 (2018)
Dutta, J., Kundu, B.: Two-dimensional closed-form model for temperature in living tissues for hyperthermia treatments. J. Therm. Biol. 71, 41–51 (2018)
Dutta, J., Kundu, B.: A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments. J. Therm. Biol. 66, 33–48 (2017)
Xu, F., Seffen, K.A., Liu, T.J.: Non-Fourier analysis of skin biothermomechanics. Int. J. Heat Mass Transf. 51, 2237–2259 (2008)
Cattaneo, C.: A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte. Rendus 247, 431–433 (1958)
Vernotte, P.: Les paradoxes de la theorie continue de l’ equation de la chaleur. Compte. Rendus 246, 3154–3155 (1958)
Tzou, D.Y.: A unified field approach for heat conduction from macro- to microscales. J Heat Transf. 117, 8–16 (1995)
Hooshmand, P., Moradi, A., Khezry, B.: Bioheat transfer analysis of biological tissues induced by laser irradiation. Int. J. Therm. Sci. 90, 214–223 (2015)
Zhou, J., Zhang, Y., Chen, J.K.: An axisymmetric dual-phase-lag bioheat model for laser heating of living tissues. Int. J. Therm. Sci. 48(8), 1477–1485 (2009)
Ma, J., Yang, X., Sun, Y., Yang, J.: Thermal damage in three-dimensional vivo bio-tissues induced by moving heat sources in laser therapy. Sci. Rep. (Nature) 9, 10987 (2019)
Tzou, D.Y.: Macro- To Micro-Scale Heat Transfer: The Lagging Behavior (Chemical and Mechanical Engineering Series). CRC Press (1996)
Ozisik, M.N.: Heat conduction. Wiley, Canada (1976)
Hahn, D.W., Ozisik, M.N.: Heat conduction. Wiley, New Jersey (2012)
Dutta, J., Kundu, B.: Exact analysis based on BDLTNE approach for thermal behaviour in living tissues during regional hyperthermia therapy. Act. Mech. 230, 2853–2871 (2019)
Conflict of interest
The authors have declared no conflict of interest.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Dutta, J., Kundu, B., Soni, H., Mashinini, P.M. (2020). Analytical Modelling for Laser Heating for Materials Processing and Surface Engineering. In: Gupta, K. (eds) Surface Engineering of Modern Materials. Engineering Materials. Springer, Cham. https://doi.org/10.1007/978-3-030-43232-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-43232-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43231-7
Online ISBN: 978-3-030-43232-4
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)