Multi-gradient fluids

Henri Gouin (1)

1 IUSTI - Institut universitaire des systèmes thermiques industriels

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.

Mots clés: Mathematics Subject Classification (2000) 76A02 · 76E30 · 76M30; First integrals · Laws of thermodynamics; Multi-gradient fluids · Equation of motion · Equation of energy ·

Domaines: Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]

Henri Gouin. Multi-gradient fluids. Ricerche di matematica, In press, ⟨10.1007/s11587-018-0397-8⟩. ⟨hal-01731201⟩