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Thermal vorticity and thermal chirality in relativistic thermally conducting fluid. (English) Zbl 1475.85011

Summary: The present work focuses on the study of dissipation caused by heat flow in a Carter’s theory of a heat conducting fluid which is expected to be applicable to a particular astrophysical context like early phases of evolution of stellar objects that are far from thermal equilibrium. The dynamical response of entropy fluid in the interaction of heat flow with the motion of matter part of fluid is investigated on the basis of a pair of Maxwell’s like equations that govern the evolution of a heat conducting fluid pioneered by Carter. It is found that the variation of thermal vorticity flux along thermal vorticity tube is coupled to the twist of fluid’s vortex tube and to the spacelike twist of heat flow lines. The proper time rate of change of the thermal vorticity flux in a stream tube associated with the motion of the entropy fluid is related to the combined effect of fluid’s vorticity and spaclike twist of heat flow lines together with the existence of string like structure formed by the entropy flow lines and \(\widetilde{E}^a\)-lines associated with a particular evolution equation. A covariant solution of a pair of Maxwell’s like equations governing the motion of a heat conducting fluid is obtained under the assumption that the background spacetime representing the gravitational field of a heat conducting fluid is non-circular axisymmetric and stationary. In this case it is shown that the existence of meridional circulation of matter part of fluid is essential for the survival of toroidal components of heat flow vector. A conserved physical quantity called thermal chirality associated with the non-conserved thermal helicity is shown to exist under the assumption that the entropy fluid is in uniform rotation. The relation between the effective thermal angular momentum per entropon of the entropy fluid and twist of heat flow lines is obtained. It is shown that the heat flow causes the twist of the entropy fluid’s vortex lines if the entropy fluid flows are axisymmetric stationary and without meridional circulations but with uniform rotation.

MSC:

85A15 Galactic and stellar structure
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
80A19 Diffusive and convective heat and mass transfer, heat flow
76M23 Vortex methods applied to problems in fluid mechanics
35Q61 Maxwell equations
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