Research in Engineering and Aviation

Variational Multi-fluid Dynamics and Causal Heat Conductivity

December 2009

Author(s): N. Andersson, and G. L. Comer

Proceedings Royal Society A, v. 466 n. 2117, pp. 1373-1387. DOI: 10.1098/rspa.2009.0423


We discuss heat conductivity from the point of view of a variational multi-fluid model, treating entropy as a dynamical entity. We demonstrate that a two-fluid model with a massive fluid component and a massless entropy can reproduce a number of key results from extended irreversible thermodynamics. In particular, we show that the entropy entrainment is intimately linked to the thermal-relaxation time that is required to make heat propagation in solids causal. We also discuss non-local terms that arise naturally in a dissipative multi-fluid model, and relate these terms to those of phonon hydrodynamics. Finally, we formulate a complete heat-conducting two-component model and discuss briefly the new dissipative terms that arise. 

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