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A Multigrid Approach for Three-Dimensional Inverse Heat Conduction Problems
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.
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[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).
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[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).
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[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).
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[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.
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