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TECHNICAL PAPERS

Inverse Heat Transfer Solution of the Heat Flux Due to Induction Heating

[+] Author and Article Information
Jie Luo

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109-2125

Albert J. Shih1

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109-2125shiha@umich.edu

1

Author to whom correspondence should be addressed.

J. Manuf. Sci. Eng 127(3), 555-563 (Jul 07, 2004) (9 pages) doi:10.1115/1.1949617 History: Received July 24, 2003; Revised July 07, 2004

The explicit finite difference formulation of an inverse heat transfer model to calculate the heat flux generated by induction is developed. The experimentally measured temperature data are used as the input for the inverse heat transfer model. This model is particularly suitable for a workpiece with low cross section Biot number. Induction heating experiments are carried out using a carbon steel rod. The finite difference method and thermocouple temperature measurements are applied to estimate the induction heat flux and workpiece temperature. Compared to measured temperatures, the accuracy and limitation of proposed method is demonstrated. The effect of nonuniform temperature distribution, particularly in the heating region during the induction heating, is studied. Analysis results validate the assumption to use the uniform temperature in a cross section for the inverse heat transfer solution of induction heat flux. Sensitivity to the grid spacing, thermocouple location, and thermophysical properties are also studied.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Configuration of the induction heating a long workpiece and the cross section represented by a node m with area Am and perimeter Pm

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Figure 2

Finite difference model and nodal points in a half rod

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Figure 3

Control volume at node m and the sources of heat flux

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Figure 4

Setup of rod workpiece, water-cooled induction heating coil, and thermocouples

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Figure 5

Configuration of the induction heating experiment of the rod workpiece and thermocouple locations

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Figure 6

Experimentally measured temperatures at four thermocouples for th=25s and the selection of data points for inverse heating transfer solution of induction heat flux

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Figure 7

Comparison of the measured and calculated temperature for th=25s

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Figure 8

Effect of grid spacing on the surface heat flux qind″

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Figure 9

FEM mesh and the three cross sections

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Figure 10

Comparison of the finite element and finite difference analysis results for th=25s at three cross sections

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