## [JAC044] Resistance Heating Analysis of a Steel Sheet

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### Overview

In treatments like hot formed pressing, a steel sheet needs to be heated uniformly as a part of pre-processing. Resistance heating is a method of uniform heating that uses a steel sheet’s electric resistance. In resistance heating, current is run through electrodes placed on both sides of a steel sheet. The joule heat produced from the ensuing electric resistance is then used to heat the steel sheet. However, the uniformity of the range of heat generation changes depending on the arrangement of the electrodes, so whether or not the uniformity satisfies the heating conditions needs to be investigated ahead of time.
Unevenness in the current distribution flowing from the electrodes through the steel sheet is determined from the geometry and the material’s electric conductivity. Electric conductivity changes according to the temperature, though, so both the electromagnetic phenomena and the heat transfer phenomena need to be analyzed at the same time.
This Application Note presents how to obtain the calculate current density distribution, Joule loss distribution and temperature distribution of steel sheet.

### Current Density Distribution and Joule Loss Density Distribution

Fig. 1 shows the current density distribution and current flux line of the work piece immediately after heating. Fig. 2 shows the Joule loss density distribution of the work piece immediately after heating. The electrodes are shorter than the work piece in the width direction, so the current density is not uniform at the edges of the work piece, as can be seen in fig. 1. It is high near the tips of the electrodes and gets lower at the four corners of the work piece. Joule loss comes from electric resistance in the work piece, so its density has the same distribution as the current density. Their distribution is almost uniform near the center of the work piece. This joule loss becomes the heat source.

### Temperature Distribution

The work pieces temperature distribution is shown in fig. 3, and its work pieces temperature of 10 sec are shown in fig. 4 and fig. 5. Electric resistance generates heat in the work piece and heats it to about 400 deg C in 10 sec. The areas aside from the work piece’s edges are heated uniformly.