本文分別針對等向熱黏彈流體與剛體和等向熱黏彈流體與等向熱線彈固體兩種情形的共同邊界進行無滑移邊界條件之數學分析。透過本文的分析可以得出此兩種情況的無滑移邊界條件為數學推導的結果。藉由引入拉格朗日乘子，可以將守恆方程式作為限制條件與熵增不等式結合為一體，使分析可以同時滿足各項物理定律。並透過非平衡熱力學和連體力學的概念，可以得出等向熱黏彈流體與剛體和等向熱黏彈流體與等向熱線彈固體兩種情況的無滑移邊界條件在數學上為自然推導的結果。要言之，無滑移邊界條件是自然結論，而非人為假設。

In the thesis, the no-slip boundary conditions between isotropic viscous thermoelastic fluids and rigid bodies, and those between isotropic viscous thermoelastic fluids with isotropic linear thermoelastic solids, are demonstrated to be thermodynamically consistent as a natural mathematical derived result. By using the method of Lagrangian multipliers, the natural and revised balance equations of physical laws are combined with the entropy inequality. By following the concepts of rational thermodynamics and continuum mechanics, the no-slip boundary conditions on the interfaces between isotropic viscous thermoelastic fluids with rigid bodies and isotropic linear thermoelastic solids are derived as a natural mathematical consequence. The results show that the no-slip boundary conditions need not be assumed a pirori, instead, they are simply direct mathematical derived results.

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