A differential geometric description of thermodynamics in continuum mechanics with application to Fourier-Navier-Stokes fluids

A description of thermodynamics for continuum mechanical systems is presented in the coordinate-free language of exterior calculus. First, a careful description of the mathematical tools that are needed to formulate the relevant conservation laws is given. Second, following an axiomatic approach, the two thermodynamic principles will be described, leading to a consistent description of entropy creation mechanisms on manifolds. Third, a specialization to Fourier-Navier-Stokes fluids will be carried through. Published under an exclusive license by AIP Publishing.

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This article presents a description of thermodynamics for continuum mechanical systems using the coordinate-free language of exterior calculus. It provides a detailed description of the mathematical tools needed to formulate the relevant conservation laws and describes the two thermodynamic principles using an axiomatic approach, resulting in a consistent description of entropy creation mechanisms on manifolds. It also specializes in Fourier-Navier-Stokes fluids.