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• W1521228863 abstract "We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint of a variational principle. The dynamics of the fluids satisfy the conservation laws of mass, momentum, angular momentum, and energy, and obey the second law of thermodynamics. By Noether’s theorem, these conservation laws are associated with the corresponding symmetries. On the other hand, the equation for entropy gives a nonholonomic constraint. Then Lagrangians and this nonholonomic constraint of the fluids satisfy these symmetries. The dynamics of fluid are given as a weak solution, minimizing an action subject to this constraint. For the existence of the weak solution, all the surface terms appearing in the variational calculus have to vanish with the aid of the nonholonomic constraint. In this study, we show that the equation for entropy is determined to be consist to “the second law of thermodynamics”, “the symmetries”, and “the necessary condition of the existence of the weak solution”. Our method gives a general scheme to derive the equation of motion for fluids in inhomogeneous temperature, and gives an explanation of some nontrivial thermal effects on the rotation of liquid crystal, vaporization of a one component fluid, and dissolution of a two component fluid." @default.
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• W1521228863 date "2014-11-25" @default.
• W1521228863 modified "2023-09-27" @default.
• W1521228863 title "A variational formulation for dissipative fluids in inhomogeneous temperature" @default.
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