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Heat flux determination in gas-tungsten-arc welding process by using a three- dimensional model in inverse heat conduction problem
Sandro Lima e Silva, Louriel Vilarinho, Americo Scotti, Tiong Ong, Gilmar Guimaraes

Heat input measurement during the welding process is a highly complex task, primarily because the welding arc is a non-uniform heat source. To solve this problem, various analytical and numerical approaches have been proposed. They can be divided into two categories, the direct and the inverse problems of heat transfer. The problem is considered direct when all the boundary conditions are given for the outside surface of the domain. In an inverse problem, information concerning one or more boundary conditions is unknown. Thus, an inverse problem requires the knowledge of temperature at a fixed point inside the domain, in order to provide the temperature profile at the surface. Here, a methodology is proposed to calculate the heat flux delivered to the workpiece during the welding process. The inverse-problem technique is based on the conjugated gradient method with an adjoint problem. The proposed model is based on three-dimensional heat transfer with spatial and temporal heat source variation. To assess the proposed technique, different welding conditions were used in the gas – tungsten-arc welding process. The arc heat input was estimated by temperature measurement at the surface at the rear of the weld, with ten thermocouples equally spaced along the middle line of the plate.

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