Solving the heat-flow problem with transient relativistic fluid dynamics
  Israel-Stewart theory is a causal, stable formulation of relativistic dissipative fluid dynamics. This theory has been shown to give a decent description of the dynamical behavior of a relativistic fluid in cases where shear stress becomes important. In principle, it should also be applicable to situations where heat flow becomes important. However, it has been shown that there are cases where Israel-Stewart theory cannot reproduce phenomena associated with heat flow. In this paper, we derive a relativistic dissipative fluid-dynamical theory from kinetic theory which provides a good description of all dissipative phenomena, including heat flow. We explicitly demonstrate this by comparing this theory with numerical solutions of the relativistic Boltzmann equation. 
G. S. Denicol, H. Niemi, I. Bouras, E. Molnar, Z. Xu, D. H. Rischke,   and C. Greiner
nucl-th hep-ph hep-th