TL;DR
This paper introduces a thermodynamical framework for multi-gradient fluids using Hamilton's principle, extending classical fluid dynamics to include higher-order gradients and dissipative effects while respecting thermodynamic laws.
Contribution
It develops a generalized equation of motion for multi-gradient fluids derived from an internal energy function, incorporating dissipation and thermodynamics.
Findings
Derived a thermodynamically consistent equation of motion for multi-gradient fluids.
Extended first integrals of flow to more complex fluid models.
Formulated energy equations compatible with the second law of thermodynamics.
Abstract
An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation of motion which generalizes the case of perfect compressible fluids. First integrals of flows are extended cases of perfect compressible fluids. The equation of motion and the equation of energy are written for dissipative cases, and are compatible with the second law of thermodynamics.
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