Non-Local Partial Differential Equations for Engineering and Biology by Nikos I. Kavallaris & Takashi Suzuki

Author:Nikos I. Kavallaris & Takashi Suzuki
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

When an electric current, with local current density flows through the electrodes and the sheet metals, then owning to a significantly higher resistivity in the contact area a rapid heating up of this area occurs, which is caused by the Joule effect. The rapid heating leads to the development of a weld nugget (a mushy region where the solid and liquid phases coexist) which actually grows quite fast. Once, the electrical current is switched off the weld nugget solidifies, leading to a lasting weld joint (known also as weldment) between the metal sheets. The main physical quantities are involved in the description of the configuration of Fig. 4.1 are: the temperature u, a parameter standing for the proportion of the two phases and the applied electrical potential In the melting-solidification process in the solid phase while in the liquid phase we have

The temperature evolution of the above system is governed by the following internal energy balance equation

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