Determining of the laser heat flux for three-dimensional conduction model by the sequential method




laser processing, laser flux, 3-D heat conduction model, modified Newton–Raphson (MNR) method, sequential method


When performing a laser processing, one of the parameters to consider is the laser heat flux. This is a very important parameter of the processing. It is difficult to directly and correctly measure this parameter during the processing. Therefore, to estimate this parameter, a solution has been implemented. In this study, the Newton–Raphson method has been calibrated as an operational algorithm to evaluate the laser heat flux value accurately in the 3-D conduction model. The outstanding features in this algorithm: the unaware absorption coefficient's functional form is no preset, and the nonlinear least-squares are no necessary. To confirm the effectiveness of the presented method, the paper has given two specific applications. Indeed, in this research, based on the results that have been achieved in two illustrations, the sequential method to determine the inversely laser heat flux in the three-dimensional conduction model is a reasonable, correct, and powerful method.


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S. Katayama. Handbook of laser welding technologies. Elsevier, (2013).

W. M. Steen and J. Mazumder. Laser material processing. Springer Science & Business Media, (2010).

J.-T.Wang, C.-I.Weng, J.-G. Chang, and C.-C. Hwang. The influence of temperature and surface conditions on surface absorptivity in laser surface treatment. Journal of Applied Physics, 87, (7), (2000), pp. 3245–3253.

H.-T. Chen and X.-Y. Wu. Estimation of surface absorptivity in laser surface heating process with experimental data. Journal of Physics D: Applied Physics, 39, (6), (2006).

Y.-C. Yang, T.-S. Wu, and E.-J. Wei. Modelling of simultaneous estimating the laser heat flux and melted depth during laser processing by inverse methodology. International Communications in Heat and Mass Transfer, 34, (4), (2007), pp. 440–447.

Y.-S. Sun, C.-I.Weng, T.-C. Chen, andW.-L. Li. Estimation of surface absorptivity and surface temperature in laser surface hardening process. Japanese Journal of Applied Physics, 35, (6R), (1996).

Q. Nguyen and C.-Y. Yang. Inverse determination of laser power on laser welding with a given width penetration by a modified Newton–Raphson method. International Communications in Heat and Mass Transfer, 65, (2015), pp. 15–21.

Q. Nguyen and C.-Y. Yang. A modified Newton–Raphson method to estimate the temperature-dependent absorption coefficient in laser welding process. International Journal of Heat and Mass Transfer, 102, (2016), pp. 1222–1229.

L. N. P. Nguyen, Q. Nguyen, S. H. Nguyen, and T. T. Le. A sequential method in inverse estimation of the absorption coefficient for the spot laser welding process. In The 9th International Conference on Computational Methods (ICCM2018), (2018),

B. Conahan, H. A. Luther, and J. O. Wilkes. Applied numerical methods. John Wiley and Sons, New York, (1969).

M. N. Nguyen, T. T. Truong, and T. Q. Bui. An enhanced nodal gradient finite element for non-linear heat transfer analysis. Vietnam Journal of Mechanics, 41, (2), (2019), pp. 127–139.

B. X. Thang, N. X. Hung, and N. T. Phong. On stabilization of the node-based smoothed finite element method for free vibration problems. Vietnam Journal of Mechanics, 32, (3), (2010), pp. 167–181.

J. V. Beck, B. Blackwell, and C. R. S. Clair Jr. Inverse heat conduction: Ill-posed problems. James Beck, (1985).

IMSL. Library edition 10.0, User’s manual: Math library version 1.0. Houston, Tex, (1987).




How to Cite

Long, N. N. P., Nguyen, S. H., & Quan, N. (2020). Determining of the laser heat flux for three-dimensional conduction model by the sequential method. Vietnam Journal of Mechanics, 42(2), 95–103.



Research Paper