直角斜方形穴を有する平板の直流電流下における角部近傍定常熱伝導問題

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  • Electro-Thermal Problems near the Corner of Diamond-Shaped Hole Having Right-Angle in a Plate under a Direct Current Flow
  • チョッカク シャホウケイケツ オ ユウスル ヘイバン ノ チョクリュウ デンリュウカ ニ オケル カドブ キンボウ テイジョウ ネツ デンドウ モンダイ

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The damage of electronic devices is often due to the generation of heat within the components. When the current is supplied to electronic components, their temperature rises because of the fact of Joule-heating. To evaluate the reliability of components subjected to Joule-heating, it is essential to analyze the associated current density and temperature distributions in the components. In this study, two-dimensional electro-thermal problems concerned with steady current flow near the corner of a hole were treated, where the shape of the hole was assumed to be a right-angled diamond. Distribution of current density near the corner was analyzed theoretically based on the Schwarz-Christoffel transformation. Electrical potential, which was calculated from the current density analyzed, was compared with FE analysis. Temperature near the corner was analyzed based on the electrical potential calculated. For the case when the heat flux related to the gradient of the temperature field associated with the problem without Joule-heating equals to zero, the temperature near the corner was verified to remain constant although current density decreased gradually far from the corner.

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