The welding onto in-service pipeline (operation condition) results in three possibilities of high risks: leaking and/or explosion by burn-through, chemical reactions to instability, or even explosion due to the heat on internal fluid and cracking in heat affected zone (HAZ). The numerical methods have a useful role in the assessment of welding conditions for the safe in-service welding of pipelines. Only limited published works have considered direct calculation of burn-through using a combination of thermal and stress analysis. The mathematical model of the heat source is the most important part of these numerical models, and actually the mathematical model which described better the heat distribution of the arc welding through gas-shielded tungsten arc welding (GTAW) process or shielded metal arc welding process is the double ellipsoidal heat source (DEHS) model of Goldak and Akhlaghi (2010, Computational Welding Mechanics, Springer Books, New York, pp. 32–35). However, that model has considered the heat source in rectilinear motion only, and it depends on three parameters (a, b, c) which are related with the weld bead size and shape to define the geometry and co-ordinates of heat source, and they are determined empirically or experimentally. Few researchers published works that could determine these parameters mathematically, from the welding data. The publication that best analytically addressed this issue was the work of Eagar and Tsai (1983, “Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J., 62(12), pp. 346–355). First, this paper presents a new equation for heat source in double ellipsoid considering the circular motion, trying to develop a model closer to the physical situation of hot tapping onto pipeline. Second, a proposal for determination of the parameters a, b analytically from the Eagar model and Tsai (1983, “Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J., 62(12), pp. 346–355), and third, an experimental facility to get the temperature field that was used to validate the numerical finite element models.

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