**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32870

##### A Multigrid Approach for Three-Dimensional Inverse Heat Conduction Problems

**Authors:**
Jianhua Zhou,
Yuwen Zhang

**Abstract:**

A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

**Keywords:**
Conduction,
inverse problems,
conjugated gradient method,
laser.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.2643512

**References:**

[1] J.V. Beck, B. Blackwell and C.R. St-Clair, Inverse Heat Conduction: Ill Posed Problems, Wiley, New York, (1985).

[2] O. M. Alifanov, Inverse Heat Transfer Problems, Springer-Verlag, Berlin/Heidelberg, (1994).

[3] M.N. Özisik and H.R.B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor & Francis, New York, (2000).

[4] T. Lu, B. Liu and P.X. Jiang, “Inverse estimation of the inner wall temperature fluctuations in a pipe elbow,” Applied Thermal Engineering, 31, pp. 1976-1982, (2011).

[5] M. R. Golbahar Haghighi, P. Malekzadeh, H. Rahideh, M. Vaghefi, “Inverse transient heat conduction problems of a multilayered functionally graded cylinder,” Numerical Heat Transfer, Part A: Applicaitons, 61, pp. 717-733, (2012).

[6] A. Azimi, K. Bamdad, H. Ahmadikia, “Inverse hyperbolic heat conduction in fins with arbitrary profiles,” Numerical Heat Transfer, Part A: Applications, 61, pp. 220-240, (2012).

[7] S.K. Kim, “Resolving the final time singularity in gradient methods for inverse heat conduction problems,” Numerical Heat Transfer, Part B: Fundamentals, 57, pp. 74-88, (2010).

[8] M. Samaï and T. Loulou, “A comparative study of heat flux and temperature based on objective functional to solve inverse heat conduction problems,” Numerical Heat Transfer, Part B: Fundamentals, 56, pp. 75-104, (2009).

[9] J. Zhou, Y. Zhang, J.K. Chen and Z.C. Feng, “Inverse estimation of surface heating condition in a finite slab with temperature-dependent thermophysical properties,” Heat Transfer Engineering, vol. 32, pp. 861-875, 2011.

[10] J. Zhou, Y. Zhang, J.K. Chen and Z.C. Feng, “Inverse heat conduction in composites with pyrolysis effect and temperature-dependent thermophysical properties,” ASME Journal of Heat Transfer, 132(3), 034502, (2010).

[11] J. Zhou, Y. Zhang, J.K. Chen and Z.C. Feng, “Inverse estimation of surface heating condition in a three-dimensional object using conjugate gradient method,” International Journal of Heat and Mass Transfer, 53(13-14), 2643-2654, (2010).

[12] J. Zhou, Y. Zhang, J.K. Chen and Z.C. Feng, “Inverse estimation of surface temperature induced by a moving heat source in a 3-d object based on back surface temperature with random measurement errors,” Numerical Heat Transfer, Part A: Applications, 61(2), 85-100, (2012).

[13] Y. Ren, Y. Zhang, J.K. Chen and Z.C. Feng, “Inverse estimation of front surface temperature of a 3-d finite slab based on back surface temperature measured at coarse grids,” Numerical Heat Transfer, Part B: Fundamentals, 63(1), 1-17, (2013).

[14] N. Afrin, Z.C. Feng, J.K. Zhang and J.K. Chen, “Inverse estimation of front surface temperature of a locally heated plate with temperature-dependent conductivity via Kirchhoff transformation,” International Journal Thermal Sciences, 69, 53-60, (2013).

[15] J. Zhou, Y. Zhang, J.K. Chen and Z.C. Feng, “Three-dimensional inverse heat transfer in a composite target subject to high-energy laser irradiation,” ASME Journal of Heat Transfer, 134(11), 111201, (2012).

[16] Y. Zhang, Z.C. Feng and J.K. Chen, “Recovering the Front Surface Temperature of Metallic and Composite Targets Subject to Localized Heating via Inverse Heat Transfer Modeling,” The 15th International Heat Transfer Conference, Kyoto, Japan, August 10-15, 2014.